Things that Count - - The Late Modern Period (from 1800)

25 April 2015 by 203.217.71.141 -

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||1910-20s||Comptator (9 col)||Schubert & Salzer||~~Chain~~||%height=125px%[[Site.Comptator1910|http://meta-studies.net/pmwiki/uploads/Comptator125.jpg]]||

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||1910-20s||Comptator (9 col)||Schubert & Salzer||Rod||%height=125px%[[Site.Comptator1910|http://meta-studies.net/pmwiki/uploads/Comptator125.jpg]]||

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14 October 2014 by 203.206.47.149 -

14 September 2014 by 203.206.47.149 -

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serial 1230A 79429~~, 1972~~||%center% December 1973\\

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serial 1230A 79429||%center% December 1973\\

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serial 1350A 36719~~, 1973~~||%center% August 1973\\

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serial 1350A 36719||%center% August 1973\\

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serial 1333A 06752~~, 1973~~||

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serial 1333A 06752||

14 September 2014 by 203.206.47.149 -

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||%center% %height=250px%[[Site.HP-35-1972|http://meta-studies.net/pmwiki/uploads/HP35H250.jpg]]||%center% %height=250px%[[Site.HP-45-1973|http://meta-studies.net/pmwiki/uploads/HP-45H250.jpg]]||

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||%center% %height=250px%[[Site.HP-35-1972|http://meta-studies.net/pmwiki/uploads/HP35H250.jpg]]||%center% %height=250px%[[Site.HP-45-1973|http://meta-studies.net/pmwiki/uploads/HP-45H250.jpg]]||%center% %height=250px%[[Site.HP-45-1973|http://meta-studies.net/pmwiki/uploads/HP-65-15pc.jpg]]

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serial 1350A 36719, 1973||

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serial 1350A 36719, 1973||%center% August 1973\\
Hewlett Packard\\
HP 65 Calculator\\
serial 1333A 06752, 1973||

14 September 2014 by 203.206.47.149 -

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||%center% %height=250px% http://meta-studies.net/pmwiki/uploads/HP35H250.jpg||%center% %height=250px%http://meta-studies.net/pmwiki/uploads/HP-45H250.jpg||%center% %height=250px%http://meta-studies.net/pmwiki/uploads/HP-65-15pc.jpg||

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||(collection Calculant)|| ||

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||(collection Calculant)|| || ||

14 September 2014 by 203.206.47.149 -

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serial 1350A 36719, 1973||

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serial 1350A 36719, 1973||%center% August 1973\\
Hewlett Packard\\
HP 65 Calculator\\
serial 1333A 06752, 1973||

12 July 2014 by Jim Falk -

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||~1909 ||Kuli Calculator||Addix Co.||Key input, lever & gears||%height=175px%[[Site.~~Adder1908~~| http://meta-studies.net/pmwiki/uploads/Kuli50pcWeb.jpg]]||

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||~1909 ||Kuli Calculator||Addix Co.||Key input, lever & gears||%height=175px%[[Site.Kuli1909| http://meta-studies.net/pmwiki/uploads/Kuli50pcWeb.jpg]]||

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||~1909 ||Kuli Calculator||Addix Co.||Key input, lever & gears||%height=175px% http://meta-studies.net/pmwiki/uploads/Kuli50pcWeb.jpg||

12 July 2014 by Jim Falk -

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Early experiments with keyboards also were evident in the late C19, some of which are shown (:if equal {Site.PrintBook$:PSW} "True":)in TAB(EarlyKeyboards)(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:) Each of them is very different in appearance yet all four - the Spalding Adding machine of 1884 (of which only a very few were produced, and fewer still survive), the Centigraph of 1891 (also extremely rare), the more conventional looking layout of the Addix Adding Machine of 1905, ~~and~~ the similarly conceived Adder of 1908 ~~- all had a similar principle of operation. In each case the depression of the different number keys actuates a lever to move~~ a ~~gear wheel~~ a ~~corresponding number of notches, thus adding the number. Each of them~~ of ~~course achieves this in their own~~ way. And they have very different appearances with quite different forms of visual output of the accumulated number - dials (for the Spalding), a two digit display and arrow pointing out the 100s (up to 500) for the Centigraph, and a more conventional set of windows for the Addix and Adder indicating that there are many ways that a simple basic principle can be expressed. Each has the rather severe limitation of only being able to add a single digit (from 1 to 9 in the case of the first three). The Adder whilst quite similarly limited has the innovation of a "10" key enabling addition in the middle column. More importantly it is equipped with a clearing key enabling the three windows of the result register to be reset simultaneously to zero. None of these devices, however, was particularly useful given their clumsiness of operation (for example, in clearing a result, with the exception of the Adder), and limitations in function (essentially to addition of a single integer between 1 and 10).

The Kuli, first marketed in 1909 as a further development by the Addix Company, represented a transition from these machines to something potentially much more useful. It had a similar keyboard to the Adder including a "10" key which enabled numbers from 1 to 99 to be entered directly and a highly functional clearing crank handle. In addition, it also had a moveable carriage so that much larger numbers could be added by moving the carriage to the right to successively enter additional numbers~~. In principle this enabled multiplication and even division to be done on it, albeit with all the tedium of doing that by hand. The paper strips provided were intended to aid~~ this process. However, large and comparatively expensive as the machine was, its utility was not great enough to earn it any significant commercial success.

to:

Early experiments with keyboards also were evident in the late C19, some of which are shown (:if equal {Site.PrintBook$:PSW} "True":)in TAB(EarlyKeyboards)(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:) Each of them is very different in appearance yet all four - the Spalding Adding machine of 1884 (of which only a very few were produced, and fewer still survive), the Centigraph of 1891 (also extremely rare), the more conventional looking layout of the Addix Adding Machine of 1905, the similarly conceived Adder of 1908, and the Kuli of 1909 - all had a similar principle of operation. In each case the depression of the different number keys actuates a lever to move a gear wheel a corresponding number of notches, thus adding the number. Each of them of course achieves this in their own way. And they have very different appearances with quite different forms of visual output of the accumulated number - dials (for the Spalding), a two digit display and arrow pointing out the 100s (up to 500) for the Centigraph, and a more conventional set of windows for the Addix and Adder indicating that there are many ways that a simple basic principle can be expressed. Each has the rather severe limitation of only being able to add a single digit (from 1 to 9 in the case of the first three). The Adder whilst quite similarly limited has the innovation of a "10" key enabling addition in the middle column. More importantly it is equipped with a clearing key enabling the three windows of the result register to be reset simultaneously to zero. None of these devices, however, was particularly useful given their clumsiness of operation (for example, in clearing a result, with the exception of the Adder), and limitations in function (essentially to addition of a single integer between 1 and 10).

The Kuli, first marketed in 1909 as a further development by the Addix Company, represented a transition from these machines to something potentially much more useful. It had a similar keyboard to the Adder including a "10" key which enabled numbers from 1 to 99 to be entered directly and a highly functional clearing crank handle. In addition, it also had a moveable carriage so that much larger numbers could be added by moving the carriage to the right to successively enter additional numbers of hundreds, thousands, etc. In principle this enabled multiplication and even division to be done on it, albeit with all the tedium of doing that by hand. The paper strips provided were intended to allow the user to write down intermediate results in support of this process. However, large and comparatively expensive as the machine was, its utility was not great enough to earn it any significant commercial success.

11 July 2014 by Jim Falk -

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The most obvious other development beyond the subtleties of carry mechanism was the developments in the use of materials. Here we see the heavy two wheel mechanism of the Webb Adder, in brass and wood, counterposed against the SEE Adding Machine which is entirely composed of plastic, has a Pascaline-like weighted carry mechanism, but is built so lightly utilising a materials evolution over three centuries, that a much simplified approach was by now implementable.

A particularly elegant, if made of brass and thus heavy, device was the Swiss Conto (see above) which had not only knobs to enable numbers to be input with a quick turn (rather than requiring stylus input), but also an efficient carry and clearing mechanism.

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The most obvious other development beyond the subtleties of carry mechanism was the developments in the use of materials. Here we see the heavy two wheel mechanism of the Webb Adder, in brass and wood, counterposed against the Adix Adding Machine which for the first time incorporates aluminium amongst its 122 parts, whilst the SEE Adding Machine which is entirely composed of ~~plastic~~, ~~has a Pascaline~~-like weighted carry mechanism, but is built so lightly utilising a materials evolution over three centuries, that a much simplified approach was by now implementable.

A particularly elegant, if made of brass and thus heavy, device was the Swiss Conto (see above) which had not only knobs to enable numbers to be input with a quick turn (rather than requiring stylus input), but also an efficient carry and clearing mechanism.

As they became cheaper and more accessible not only to shopkeepers but ordinary citizens who might value the ~~assistance they offered, for example in their role as taxpayers,[^See for example, A.P. Kidwell, "'Yours for Improvement'—The Adding Machines~~ of Chicago, 1884–1930", '/IEEE Annals of the History of Computing/', July-September, 2001, pp. 3-6.^] these devices became increasingly popular. However, they suffered from the same problems of clumsy input and slow operation that afflicted the simple linear machines. Some such as the Adall could only add, others had no provision for zeroing, and all were slow to use. Further, such adders, whilst simple in concept and cheap to manufacture, were so slow to use for repetitive calculation that they were virtually useless for the key arithmetic operations of multiplication and division. A quick method for repeated addition and subtraction was required at minimum to achieve these other two functions. That required a more expensive approach and a much more elaborate machine, the first commercial variant of which was designed and sold as the "Arithmometer" by Thomas de Colmar.

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All of the above machines, whether based on rotating gears or lever mechanism had their limitations. As they became cheaper and more accessible not only to shopkeepers but ordinary citizens who might value the assistance they offered, for example in their role as taxpayers,[^See for example, A.P. Kidwell, "'Yours for Improvement'—The Adding Machines of Chicago, 1884–1930", '/IEEE Annals of the History of Computing/', July-September, 2001, pp. 3-6.^] these devices became increasingly popular. However, they suffered from the same problems of clumsy input and slow operation that afflicted the simple linear machines. Some such as the Adall could only add, others had no provision for zeroing, and all were slow to use. Further, such adders, whilst simple in concept and cheap to manufacture, were so slow to use for repetitive calculation that, with the partial exception of the Kuli, they were virtually useless for the key arithmetic operations of multiplication and division. But given multiplication could only occur on the Kuli through repeated entry of a number even there it did not really provide a practical method. A quick method for repeated addition and subtraction was required at minimum to achieve these other two functions. That required a more expensive approach and a much more elaborate machine, the first commercial variant of which was designed and sold as the "Arithmometer" by Thomas de Colmar.

11 July 2014 by Jim Falk -

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The Kuli, first marketed in 1909 as a further development by the Addix Company, represented a transition from these machines to something potentially much more useful. It had a similar keyboard to the Adder including a "10" key which enabled numbers from 1 to 99 to be entered directly and a highly functional clearing crank handle. In addition, it also had a moveable carriage so that much larger numbers could be added by moving the carriage to the right to successively enter additional numbers. In principle this enabled multiplication and even division to be done on it, albeit with all the tedium of doing that by hand. The paper strips provided were intended to aid this process. However, large and comparatively expensive as the machine was, its utility was not great enough to earn it any significant commercial success.

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|tablend

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||tablend

11 July 2014 by Jim Falk -

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||1903 ||Adix Adding Machine||~~Manheim~~||Key input, lever & gears||%height=175px%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/AdixH175.jpg]]||

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||1903 ||Adix Adding Machine||Adix Co.||Key input, lever & gears||%height=175px%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/AdixH175.jpg]]||

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||tablend

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||~1909 ||Kuli Calculator||Addix Co.||Key input, lever & gears||%height=175px%[[Site.Adder1908| http://meta-studies.net/pmwiki/uploads/Kuli50pcWeb.jpg]]||

|tablend

16 June 2014 by Jim Falk -

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||~~1908~~ ||Standard Desk Calcumeter||James Walsh ||7 Wheels||%height=50px% [[Site.1908Calcumeter|http://meta-studies.net/pmwiki/uploads/CalcumeterH50.jpg]]||

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||~1912 ||Standard Desk Calcumeter||James Walsh ||7 Wheels||%height=50px% [[Site.1908Calcumeter|http://meta-studies.net/pmwiki/uploads/CalcumeterH50.jpg]]||

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||~~1908~~ ||Standard Desk Calcumeter||James Walsh ||7 Wheels||%height=50px% http://meta-studies.net/pmwiki/uploads/CalcumeterH50.jpg||

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||~1912 ||Standard Desk Calcumeter||James Walsh ||7 Wheels||%height=50px% http://meta-studies.net/pmwiki/uploads/CalcumeterH50.jpg||

15 June 2014 by Jim Falk -

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The main advantage of these devices was that they were cheap to manufacture and could be easily mass-produced. A lot of innovation is evident in the detail of these machines. A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which used rotations of a wheel to wind on successive numbers whilst a ball bearing, moving in a spiral groove, tracked the successive rotations.

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The main advantage of these devices was that they were cheap to manufacture and could be easily mass-produced. A lot of innovation is evident in the detail of these machines. A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which used rotations of a wheel to wind on successive numbers whilst a ball bearing, moving in a spiral groove, tracked the successive rotations. The Calcumeter from the same period uses a spring (instead of gravity as with Pascal's sautoir) to capture the potential energy from rotating an input wheel, releasing it when a carry is required as the wheel passes from 9 to 0.

13 June 2014 by Jim Falk -

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||1908 ||Standard Desk Calcumeter||James Walsh ||7 Wheels||%height=50px% [[Site.1908Calcumeter|http://meta-studies.net/pmwiki/uploads/~~Calcumeter~~.jpg]]||

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||1908 ||Standard Desk Calcumeter||James Walsh ||7 Wheels||%height=50px% [[Site.1908Calcumeter|http://meta-studies.net/pmwiki/uploads/CalcumeterH50.jpg]]||

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13 June 2014 by Jim Falk -

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||1908 ||Standard Desk Calcumeter||James Walsh ||7 Wheels||%height=~~60px~~% [[Site.1908Calcumeter|http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg]]||

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||1908 ||Standard Desk Calcumeter||James Walsh ||7 Wheels||%height=50px% [[Site.1908Calcumeter|http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg]]||

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||1908 ||Standard Desk Calcumeter||James Walsh ||7 Wheels||%height=50px% http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg||

13 June 2014 by Jim Falk -

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||1908 ||Standard Desk Calcumeter||James Walsh ||7 Wheels||%height=~~75px~~% [[Site.1908Calcumeter|http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg]]||

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||1908 ||Standard Desk Calcumeter||James Walsh ||7 Wheels||%height=60px% [[Site.1908Calcumeter|http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg]]||

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||1908 ||Standard Desk Calcumeter||James Walsh ||7 Wheels||%height=60px% http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg||

13 June 2014 by Jim Falk -

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||1908 ||Standard Desk Calcumeter||James Walsh ||7 Wheels||%height=~~150px~~% [[Site.1908Calcumeter|http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg]]||

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||1908 ||Standard Desk Calcumeter||James Walsh ||7 Wheels||%height=75px% [[Site.1908Calcumeter|http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg]]||

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||1908 ||Standard Desk Calcumeter||James Walsh ||7 Wheels||%height=75px% http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg||

13 June 2014 by Jim Falk -

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||1908 ||Standard Desk Calcumeter||James Walsh ||7 Wheels||%height=150px% [[Site.1908Calcumeter|http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg]]||

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||1908 ||Standard Desk Calcumeter||James Walsh ||7 Wheels||%height=150px% http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg||

27 May 2014 by Jim Falk -

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The arithmometer in this collection demonstrates the high level of usability that the firm of Thomas had now achieved. It allows the multiplication of two numbers each as large as 9 million and the result can be read out to 16 places. Ivory markers are provided for the decimal point (and to delineate hundreds, thousands and millions for ease of use). The clearing and carry mechanisms are entirely reliable. Indeed, still bearing its original varnish, this particular machine operates reliably some 125 years after it was made. Indicating that its owner was serious about its use in practice the machine appears to have been re-mounted by the famous instrument maker, Stanley, (sometime after 1900) in a better quality and stronger box fixed to a cast iron frame. This allows the machine to be tilted at a suitable angle for easy use. As the only surviving Thomas known to have this improvement, this machine seems to stand as a precursor to later innovations under Payen when he added a (rather less robust) hinged tilt base to his machines.

to:

The arithmometer in this collection demonstrates the high level of usability that the firm of Thomas had now achieved. It allows the multiplication of two numbers each as large as 9 million and the result can be read out to 16 places. Ivory markers are provided for the decimal point (and to delineate hundreds, thousands and millions for ease of use). The clearing and carry mechanisms are entirely reliable. Indeed, still bearing its original varnish, this particular machine operates reliably some 125 years after it was made. Indicating that its owner was serious about its use in practice the machine appears to have been re-mounted by the famous instrument maker, Stanley, (sometime after 1900) in a better quality and stronger box fixed to a cast iron frame. This allows the machine to be tilted at a suitable angle for easy use. As the only surviving Thomas known to have this improvement, this machine seems to stand as a precursor to later innovations under Payen when he added a (rather less robust) hinged tilt base to his machines. Indicatively, the zero numbers were all painted red, presumably as a precaution against the evident danger that, in actual use, arithmometers would not be properly zeroed prior to a new calculation being commenced.

27 May 2014 by Jim Falk -

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Early experiments with keyboards also were evident in the late C19, some of which are shown (:if equal {Site.PrintBook$:PSW} "True":)in TAB(EarlyKeyboards)(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:) Each of them is very different in appearance yet all four - the Spalding Adding machine of 1884 (of which only a very few were produced, and fewer still survive), the Centigraph of 1891 (also extremely rare), the more conventional looking layout of the Addix Adding Machine of 1905, and the similarly conceived Adder of 1908 - all had a similar principle of operation. In each case the depression of the different number keys actuates a lever to move a gear wheel a corresponding number of notches, thus adding the number. Each of them of course achieves this in their own way. And they have very different appearances with quite different forms of visual output of the accumulated number - dials (for the Spalding), a two digit display and arrow pointing out the 100s (up to 500) for the Centigraph, and a more conventional set of windows for the Addix and Adder indicating that there are many ways that a simple basic principle can be expressed. Each has the rather severe limitation of only being able to add a single digit (from 1 to 9 in the case of the first three). The Adder whilst quite similarly limited has the innovation of a "10" key enabling addition in the middle column. More importantly it is equipped with a clearing key enabling the three windows of the result register to be reset simultaneously to zero. None of these devices, however, was particularly useful given their clumsiness of operation (for example, in clearing a result, with the exception of the Adder), and limitations in function (essentially to addition of a single ~~digit~~).

to:

Early experiments with keyboards also were evident in the late C19, some of which are shown (:if equal {Site.PrintBook$:PSW} "True":)in TAB(EarlyKeyboards)(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:) Each of them is very different in appearance yet all four - the Spalding Adding machine of 1884 (of which only a very few were produced, and fewer still survive), the Centigraph of 1891 (also extremely rare), the more conventional looking layout of the Addix Adding Machine of 1905, and the similarly conceived Adder of 1908 - all had a similar principle of operation. In each case the depression of the different number keys actuates a lever to move a gear wheel a corresponding number of notches, thus adding the number. Each of them of course achieves this in their own way. And they have very different appearances with quite different forms of visual output of the accumulated number - dials (for the Spalding), a two digit display and arrow pointing out the 100s (up to 500) for the Centigraph, and a more conventional set of windows for the Addix and Adder indicating that there are many ways that a simple basic principle can be expressed. Each has the rather severe limitation of only being able to add a single digit (from 1 to 9 in the case of the first three). The Adder whilst quite similarly limited has the innovation of a "10" key enabling addition in the middle column. More importantly it is equipped with a clearing key enabling the three windows of the result register to be reset simultaneously to zero. None of these devices, however, was particularly useful given their clumsiness of operation (for example, in clearing a result, with the exception of the Adder), and limitations in function (essentially to addition of a single integer between 1 and 10).

27 May 2014 by Jim Falk -

Changed line 180 from:

Early experiments with keyboards ~~can be seen below~~ (:if equal {Site.PrintBook$:PSW} "True":)in TAB(EarlyKeyboards)(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:) Each of them is very different in appearance yet all four - the Spalding Adding machine of 1884 (of which only a very few were produced, and fewer still survive), the Centigraph of 1891 (also extremely rare), the more conventional looking layout of the Addix Adding Machine of 1905, and the similarly conceived Adder of 1908 - all had a similar principle of operation. In each case the depression of the different number keys actuates a lever to move a gear wheel a corresponding number of notches, thus adding the number. Each of them of course achieves this in their own way. And they have very different appearances with quite different forms of visual output of the accumulated number - dials (for the Spalding), a two digit display and arrow pointing out the 100s (up to 500) for the Centigraph, and a more conventional set of windows for the Addix and Adder indicating that there are many ways that a simple basic principle can be expressed. Each has the rather severe limitation of only being able to add a single digit (from 1 to 9 in the case of the first three). The Adder whilst quite similarly limited has the innovation of a "10" key enabling addition in the middle column. More importantly it is equipped with a clearing key enabling the three windows of the result register to be reset simultaneously to zero. None of these devices, however, was particularly useful given their clumsiness of operation (for example, in clearing a result, with the exception of the Adder), and limitations in function (essentially to addition of a single digit).

to:

Early experiments with keyboards also were evident in the late C19, some of which are shown (:if equal {Site.PrintBook$:PSW} "True":)in TAB(EarlyKeyboards)(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:) Each of them is very different in appearance yet all four - the Spalding Adding machine of 1884 (of which only a very few were produced, and fewer still survive), the Centigraph of 1891 (also extremely rare), the more conventional looking layout of the Addix Adding Machine of 1905, and the similarly conceived Adder of 1908 - all had a similar principle of operation. In each case the depression of the different number keys actuates a lever to move a gear wheel a corresponding number of notches, thus adding the number. Each of them of course achieves this in their own way. And they have very different appearances with quite different forms of visual output of the accumulated number - dials (for the Spalding), a two digit display and arrow pointing out the 100s (up to 500) for the Centigraph, and a more conventional set of windows for the Addix and Adder indicating that there are many ways that a simple basic principle can be expressed. Each has the rather severe limitation of only being able to add a single digit (from 1 to 9 in the case of the first three). The Adder whilst quite similarly limited has the innovation of a "10" key enabling addition in the middle column. More importantly it is equipped with a clearing key enabling the three windows of the result register to be reset simultaneously to zero. None of these devices, however, was particularly useful given their clumsiness of operation (for example, in clearing a result, with the exception of the Adder), and limitations in function (essentially to addition of a single digit).

27 May 2014 by Jim Falk -

Changed line 180 from:

Early experiments with keyboards can be seen below (:if equal {Site.PrintBook$:PSW} "True":)in TAB(EarlyKeyboards)(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:) Each of them is very different in appearance yet all ~~three~~ - the Spalding Adding machine of 1884 (of which only a very few were produced, and fewer still survive), the Centigraph of 1891 (also extremely rare), ~~and~~ the more conventional looking layout of the Addix Adding Machine of 1905, and the similarly conceived Adder of 1908 - all had a similar principle of operation. In each case the depression of the different number keys actuates a lever to move a gear wheel a corresponding number of notches, thus adding the number. Each of them of course achieves this in their own way. And they have very different appearances with quite different forms of visual output of the accumulated number - dials (for the Spalding), a two digit display and arrow pointing out the 100s (up to 500) for the Centigraph, and a more conventional set of windows for the Addix ~~indicating that there are many ways that a simple basic principle can be~~ expressed. Each has the rather severe limitation of only being able to add a single digit (from 1 to 9). The Adder whilst quite similarly limited has the innovation of a 10 key enabling addition in the middle column, as well as clearing key, which enabled the register to be reset to zero in each column. None of them, however, was particularly useful given their clumsiness of operation (for example, in clearing a result, with the exception of the Adder), and limitations in function (essentially to addition of a single digit).

to:

Early experiments with keyboards can be seen below (:if equal {Site.PrintBook$:PSW} "True":)in TAB(EarlyKeyboards)(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:) Each of them is very different in appearance yet all four - the Spalding Adding machine of 1884 (of which only a very few were produced, and fewer still survive), the Centigraph of 1891 (also extremely rare), the more conventional looking layout of the Addix Adding Machine of 1905, and the similarly conceived Adder of 1908 - all had a similar principle of operation. In each case the depression of the different number keys actuates a lever to move a gear wheel a corresponding number of notches, thus adding the number. Each of them of course achieves this in their own way. And they have very different appearances with quite different forms of visual output of the accumulated number - dials (for the Spalding), a two digit display and arrow pointing out the 100s (up to 500) for the Centigraph, and a more conventional set of windows for the Addix and Adder indicating that there are many ways that a simple basic principle can be expressed. Each has the rather severe limitation of only being able to add a single digit (from 1 to 9 in the case of the first three). The Adder whilst quite similarly limited has the innovation of a "10" key enabling addition in the middle column. More importantly it is equipped with a clearing key enabling the three windows of the result register to be reset simultaneously to zero. None of these devices, however, was particularly useful given their clumsiness of operation (for example, in clearing a result, with the exception of the Adder), and limitations in function (essentially to addition of a single digit).

27 May 2014 by Jim Falk -

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!!!!Early keyboard adding machines

27 May 2014 by Jim Falk -

Changed lines 179-181 from:

Early experiments with keyboards can be seen below (:if equal {Site.PrintBook$:PSW} "True":)in TAB(EarlyKeyboards)(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:) Each of them is very different in appearance yet all three - the Spalding Adding machine of 1884 (of which only a very few were produced, and fewer still survive), the Centigraph of 1891 (also extremely rare), and the more conventional looking layout of the Addix Adding Machine of 1905 ~~- all had a similar principle~~ of ~~operation.~~ ~~In each case the depression~~ of ~~the different number keys actuates a lever to move a gear wheel~~ a ~~corresponding number of notches, thus adding the~~ number~~. Each~~ of ~~them of course achieves this in their own way. And they have very different appearances with quite different forms of visual output of the accumulated number - dials (for~~ the ~~Spalding), a two digit display and arrow pointing out the 100s (up to 500) for~~ the ~~Centigraph, and a more conventional set of windows for the Addix indicating that there are many ways~~ that ~~a simple basic principle can be expressed. None of them, however, was particularly useful given their clumsiness~~ of ~~operation (for example, in clearing~~ a ~~result), and limitations in function (essentially to~~ addition).

to:

Early experiments with keyboards can be seen below (:if equal {Site.PrintBook$:PSW} "True":)in TAB(EarlyKeyboards)(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:) Each of them is very different in appearance yet all three - the Spalding Adding machine of 1884 (of which only a very few were produced, and fewer still survive), the Centigraph of 1891 (also extremely rare), and the more conventional looking layout of the Addix Adding Machine of 1905, and the similarly conceived Adder of 1908 - all had a similar principle of operation. In each case the depression of the different number keys actuates a lever to move a gear wheel a corresponding number of notches, thus adding the number. Each of them of course achieves this in their own way. And they have very different appearances with quite different forms of visual output of the accumulated number - dials (for the Spalding), a two digit display and arrow pointing out the 100s (up to 500) for the Centigraph, and a more conventional set of windows for the Addix indicating that there are many ways that a simple basic principle can be expressed. Each has the rather severe limitation of only being able to add a single digit (from 1 to 9). The Adder whilst quite similarly limited has the innovation of a 10 key enabling addition in the middle column, as well as clearing key, which enabled the register to be reset to zero in each column. None of them, however, was particularly useful given their clumsiness of operation (for example, in clearing a result, with the exception of the Adder), and limitations in function (essentially to addition of a single digit).

Added line 200:

||1908 ||Adder Adding Machine||A. J. Postans||Key input, lever & gears||%height=175px%[[Site.Adder1908| http://meta-studies.net/pmwiki/uploads/AdderW.jpg]]||

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||1908 ||Adder Adding Machine||A. J. Postans||Key input, lever & gears||%height=175px% http://meta-studies.net/pmwiki/uploads/AdderW.jpg||

28 April 2014 by Jim Falk -

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||align=center cellpadding=3 border=0 ~~tableclass~~=long id=Locke"The Locke Adder"

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||align=center cellpadding=3 border=0 class=long id=Locke"The Locke Adder"

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||align=center cellpadding=6 border=0 ~~tableclass~~=long id=SimpleLinearCalcs"Simple Linear Calculators"

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||align=center cellpadding=6 border=0 class=long id=SimpleLinearCalcs"Simple Linear Calculators"

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||align=center cellpadding=6 border=0 ~~tableclass~~=long id=SimpleLinearCalcs"Simple Linear Calculators"

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||align=center cellpadding=6 border=0 class=long id=SimpleLinearCalcs"Simple Linear Calculators"

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||align=center cellpadding=6 border=0 ~~tableclass~~=long id=SimpleRotationalCalcs"Simple Rotational Calculators"

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||align=center cellpadding=6 border=0 class=long id=SimpleRotationalCalcs"Simple Rotational Calculators"

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||align=center cellpadding=6 border=0 ~~tableclass~~=long id=SimpleRotationalCalcs"Simple Rotational Calculators"

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||align=center cellpadding=6 border=0 class=long id=SimpleRotationalCalcs"Simple Rotational Calculators"

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||align=center cellpadding=6 border=0 ~~tableclass~~=long id=Arithmometers"Arithmometers"

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||align=center cellpadding=6 border=0 class=long id=Arithmometers"Arithmometers"

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||align=center cellpadding=6 border=0 ~~tableclass~~=long id=DemoPinwheels"Demonstration Pinwheel Calculator"

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||align=center cellpadding=6 border=0 class=long id=DemoPinwheels"Demonstration Pinwheel Calculator"

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||align=center cellpadding=6 border=0 ~~tableclass~~=long id=DemoPinwheels"Demonstration Pinwheel Calculator"

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||align=center cellpadding=6 border=0 class=long id=DemoPinwheels"Demonstration Pinwheel Calculator"

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||align=center cellpadding=6 border=0 ~~tableclass~~=long id=PinwheelCalcs"Pinwheel Calculators"

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||align=center cellpadding=6 border=0 class=long id=PinwheelCalcs"Pinwheel Calculators"

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||align=center cellpadding=6 border=0 ~~tableclass~~=long id=PinwheelCalcs"Pinwheel Calculators"

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||align=center cellpadding=6 border=0 class=long id=PinwheelCalcs"Pinwheel Calculators"

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||align=center cellpadding=6 border=0 ~~tableclass~~=long id=RackCalcs"Proportional Rack Calculators"

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||align=center cellpadding=6 border=0 class=long id=RackCalcs"Proportional Rack Calculators"

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||align=center cellpadding=6 border=0 ~~tableclass~~=long id=CurtaCalcs"Curta Calculators"

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||align=center cellpadding=6 border=0 class=long id=CurtaCalcs"Curta Calculators"

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||align=center cellpadding=6 border=0 ~~tableclass~~=long id=HPCacl"Hewlett Packard Pocket Scientific Calculators"

to:

||align=center cellpadding=6 border=0 class=long id=HPCacl"Hewlett Packard Pocket Scientific Calculators"

03 April 2014 by 1800 -

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||Wilhelm Schickard's machine|| Calculating Machine||

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||Wilhelm Schickard's machine||Calculating Machine||

01 April 2014 by 1800 -

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||~~%center%~~Locke Adder 1905-10||
||%center%(collection Calculant)||

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||Locke Adder 1905-10 (collection Calculant)||

01 April 2014 by 1800 -

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||%center% ~~Locke Adder~~ 1905-10||
||%center% (collection Calculant)||

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||%center%Locke Adder 1905-10||
||%center%(collection Calculant)||

01 April 2014 by 1800 -

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|| Locke Adder 1905-10||
|| (collection Calculant)||

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||%center% Locke Adder 1905-10||
||%center% (collection Calculant)||

01 April 2014 by 1800 -

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||Locke Adder| 1905-10||

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|| Locke Adder 1905-10||

01 April 2014 by 1800 -

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||Locke Adder| 1905-10||

01 April 2014 by 1800 -

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(:cellnr:)%newwin%Mini:CentigraphW.~~jpg~~

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(:cellnr:)%newwin%Mini:CentigraphW.gif

01 April 2014 by 1800 -

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||1891 ||Centigraph Adding Machine||Am. Add. Co.||Key input, lever & gear||%height=175px%[[Site.Centigraph1891| http://meta-studies.net/pmwiki/uploads/CentigraphW175.~~jpg~~]]||

to:

||1891 ||Centigraph Adding Machine||Am. Add. Co.||Key input, lever & gear||%height=175px%[[Site.Centigraph1891| http://meta-studies.net/pmwiki/uploads/CentigraphW175.gif]]||

30 March 2014 by 1800 -

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(:cell:)%newwin%Mini:ThomasDeColmar.jpg

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~~(:cell:)%newwin%Mini:Bunzel.jpg~~

30 March 2014 by 1800 -

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(:cell:)%newwin%Mini:~~HP-45~~.~~jpg~~

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(:cell:)%newwin%Mini:MADAS_Smaller.png

30 March 2014 by 1800 -

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(:cell:)%newwin%Mini:ComptometerWoodie.png

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~~(:cell:)%newwin%Mini:ComptometerWoodie.png~~

30 March 2014 by 1800 -

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~~(:title The Late Modern Period (from 1800) :)~~

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to:

(:if equal {Site.PrintBook$:PSW} "False":)
(:table class=pictures width=100% align=left class=border cwidth=7:)

(:cellnr:)%newwin%Mini:CentigraphW.jpg

(:cell:)%newwin%Mini:Bunzel.jpg

(:cell:)%newwin%Mini:Millionair.png

(:cell:)%newwin%Mini:ComptometerWoodie.png

(:cell:)%newwin%Mini:Curta1-1948.png

(:cell:)%newwin%Mini:HP-45.jpg

(:tableend:)
(:ifend:)
(:ifend:)

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(:title The Late Modern Period (from 1800) :)

27 March 2014 by 1800 -

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%center%%height=200px%%id=Spalding% http://meta-studies.net/pmwiki/uploads/SpaldingW200.jpg|1884: Spalding Adding Machine\

to:

%center%%height=200px%%id=Spalding% http://meta-studies.net/pmwiki/uploads/SpaldingW200.jpg|1884: Spalding Adding Machine\\

27 March 2014 by 1800 -

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Early experiments with keyboards can be seen below (:if equal {Site.PrintBook$:PSW} "True":)in TAB(EarlyKeyboards)(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:) Each of them is very different in appearance yet all three - the Spalding Adding machine of 1884 (of which only a very few were produced, and fewer still survive), the Centigraph of 1891 (also extremely rare), and the more conventional looking layout of the Addix Adding Machine of 1905. ~~In each case the depression~~ of ~~the different number keys actuates a lever to move a gear wheel~~ a ~~corresponding number of notches, thus adding the~~ number~~. Different forms of visual output~~ of ~~the accumulated number - dials (for the Spalding), a two digit display and arrow pointing out the 100s (up to 500) for~~ the ~~Centigraph, and a more conventional set of windows for the~~ Addix.

to:

Early experiments with keyboards can be seen below (:if equal {Site.PrintBook$:PSW} "True":)in TAB(EarlyKeyboards)(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:) Each of them is very different in appearance yet all three - the Spalding Adding machine of 1884 (of which only a very few were produced, and fewer still survive), the Centigraph of 1891 (also extremely rare), and the more conventional looking layout of the Addix Adding Machine of 1905 - all had a similar principle of operation. In each case the depression of the different number keys actuates a lever to move a gear wheel a corresponding number of notches, thus adding the number. Each of them of course achieves this in their own way. And they have very different appearances with quite different forms of visual output of the accumulated number - dials (for the Spalding), a two digit display and arrow pointing out the 100s (up to 500) for the Centigraph, and a more conventional set of windows for the Addix indicating that there are many ways that a simple basic principle can be expressed. None of them, however, was particularly useful given their clumsiness of operation (for example, in clearing a result), and limitations in function (essentially to addition).

27 March 2014 by 1800 -

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%center%Spalding Adding ~~Machine1884~~\\

to:

%center%Spalding Adding Machine 1884\\

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%center%%height=200px%%id=~~Webb~~% http://meta-studies.net/pmwiki/uploads/SpaldingW200.jpg|1884: Spalding Adding Machine\

to:

%center%%height=200px%%id=Spalding% http://meta-studies.net/pmwiki/uploads/SpaldingW200.jpg|1884: Spalding Adding Machine\

27 March 2014 by 1800 -

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||1891 ||Centigraph Adding Machine||Am. Add. Co.||Key input, lever & gear||%height=~~75px~~%[[Site.Centigraph1891| http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg]]||

to:

||1891 ||Centigraph Adding Machine||Am. Add. Co.||Key input, lever & gear||%height=175px%[[Site.Centigraph1891| http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg]]||

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||1891 ||Centigraph Adding Machine||Am. Add. Co.||Key input, lever & gear||%height=~~75px~~% http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg||

to:

||1891 ||Centigraph Adding Machine||Am. Add. Co.||Key input, lever & gear||%height=175px% http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg||

27 March 2014 by 1800 -

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align=center cellpadding=6 border=0 id=EarlyKeyboards"Early keyboards"

to:

||align=center cellpadding=6 border=0 id=EarlyKeyboards"Early keyboards"

27 March 2014 by 1800 -

Changed lines 182-183 from:

~~||1891 ||Centigraph Adding Machine||Am. Add. Co.~~||~~Key input~~||~~lever & gear~~||~~%height=75px%[[Site~~.~~Centigraph1891| http://meta-studies~~.~~net/pmwiki/uploads/CentigraphW175~~.~~jpg]]~~||
~~||1903 ||Adix Adding Machine~~||~~Manheim~~|~~|Key input~~||lever & gears||%height=175px%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/AdixH175.jpg]]||

to:

align=center cellpadding=6 border=0 id=EarlyKeyboards"Early keyboards"
||1891 ||Centigraph Adding Machine||Am. Add. Co.||Key input, lever & gear||%height=75px%[[Site.Centigraph1891| http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg]]||
||1903 ||Adix Adding Machine||Manheim||Key input, lever & gears||%height=175px%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/AdixH175.jpg]]||

Changed lines 192-193 from:

||1891 ||Centigraph Adding Machine||Am. Add. Co.||Key input~~||lever &~~ gear||%height=75px% http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg||
||1903 ||Adix Adding Machine||Manheim||Key input||lever & gears||%height=175px% http://meta-studies.net/pmwiki/uploads/AdixH175.jpg||

to:

||1891 ||Centigraph Adding Machine||Am. Add. Co.||Key input, lever & gear||%height=75px% http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg||
||1903 ||Adix Adding Machine||Manheim||Key input, lever & gears||%height=175px% http://meta-studies.net/pmwiki/uploads/AdixH175.jpg||

27 March 2014 by 1800 -

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||1903 ||Adix Adding Machine||Manheim||Key input lever & gears||%height=175px%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/AdixH175.jpg]]||

to:

||1903 ||Adix Adding Machine||Manheim||Key input||lever & gears||%height=175px%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/AdixH175.jpg]]||

27 March 2014 by 1800 -

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||1891 ||Centigraph Adding Machine||Am. Add. Co.||Key input, lever & gear||%height=75px%[[Site.Centigraph1891| http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg]]||

to:

||1891 ||Centigraph Adding Machine||Am. Add. Co.||Key input||lever & gear||%height=75px%[[Site.Centigraph1891| http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg]]||

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||1891 ||Centigraph Adding Machine||Am. Add. Co.||Key input~~, lever~~ & gear||%height=75px% http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg||
||1903 ||Adix Adding Machine||Manheim||Key input lever & gears||%height=175px% http://meta-studies.net/pmwiki/uploads/AdixH175.jpg||

to:

||1891 ||Centigraph Adding Machine||Am. Add. Co.||Key input||lever & gear||%height=75px% http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg||
||1903 ||Adix Adding Machine||Manheim||Key input||lever & gears||%height=175px% http://meta-studies.net/pmwiki/uploads/AdixH175.jpg||

27 March 2014 by 1800 -

Deleted line 141:

~~||1903 ||Adix Adding Machine\\Original model||Manheim||Key input\\lever &\\gears||%height=175px%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/AdixH175.jpg]]||~~

Deleted line 153:

~~||1903 ||Adix Adding Machine Original model||Manheim||Key input lever & gears||%height=175px% http://meta-studies.net/pmwiki/uploads/AdixH175.jpg||~~

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||1891 ||Centigraph ~~Adder~~||Am. Add. Co.||Key input, lever & gear||%height=75px%[[Site.Centigraph1891| http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg]]||
||1903 ||Adix Adding Machine ~~Original model~~||Manheim||Key input lever & gears||%height=175px%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/AdixH175.jpg]]||

to:

||1891 ||Centigraph Adding Machine||Am. Add. Co.||Key input, lever & gear||%height=75px%[[Site.Centigraph1891| http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg]]||
||1903 ||Adix Adding Machine||Manheim||Key input lever & gears||%height=175px%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/AdixH175.jpg]]||

Changed lines 191-192 from:

||1891 ||Centigraph ~~Adder~~||Am. Add. Co.||Key input, lever & gear||%height=75px% http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg||
||1903 ||Adix Adding Machine ~~Original model~~||Manheim||Key input lever & gears||%height=175px% http://meta-studies.net/pmwiki/uploads/AdixH175.jpg||

to:

||1891 ||Centigraph Adding Machine||Am. Add. Co.||Key input, lever & gear||%height=75px% http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg||
||1903 ||Adix Adding Machine||Manheim||Key input lever & gears||%height=175px% http://meta-studies.net/pmwiki/uploads/AdixH175.jpg||

27 March 2014 by 1800 -

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(:cellnr:) %height=200px% [[Site.Spalding1884|%center% http://meta-studies.net/pmwiki/uploads/SpaldingW200~~.jpg~~.jpg]]%%

to:

(:cellnr:) %height=200px% [[Site.Spalding1884|%center% http://meta-studies.net/pmwiki/uploads/SpaldingW200.jpg]]%%

Deleted line 183:

~~||1884 ||Spalding Adding Machine||C.G. Spalding ||Key input, lever & dialsl||%height=75px%[[Site.Spalding1884| http://meta-studies.net/pmwiki/uploads/SpaldingW100.jpg]]||~~

Deleted line 192:

~~||1884 ||Spalding Adding Machine||C.G. Spalding ||Key input, lever & dialsl||%height=75px% http://meta-studies.net/pmwiki/uploads/SpaldingW100.jpg||~~

27 March 2014 by 1800 -

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Early experiments with keyboards can be seen ~~in the Adix adding machine of 1903~~.

to:

Early experiments with keyboards can be seen below (:if equal {Site.PrintBook$:PSW} "True":)in TAB(EarlyKeyboards)(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:) Each of them is very different in appearance yet all three - the Spalding Adding machine of 1884 (of which only a very few were produced, and fewer still survive), the Centigraph of 1891 (also extremely rare), and the more conventional looking layout of the Addix Adding Machine of 1905. In each case the depression of the different number keys actuates a lever to move a gear wheel a corresponding number of notches, thus adding the number. Different forms of visual output of the accumulated number - dials (for the Spalding), a two digit display and arrow pointing out the 100s (up to 500) for the Centigraph, and a more conventional set of windows for the Addix.

Changed lines 171-172 from:

(:cellnr:) %height=200px% [[Site.~~Webb1869~~|%center% http://meta-studies.net/pmwiki/uploads/~~WebbH200~~.jpg]]%%
%center%~~Webb Patent Adder and Talley Board 1869~~\\

to:

(:cellnr:) %height=200px% [[Site.Spalding1884|%center% http://meta-studies.net/pmwiki/uploads/SpaldingW200.jpg.jpg]]%%
%center%Spalding Adding Machine1884\\

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%center%%height=200px%%id=Webb% http://meta-studies.net/pmwiki/uploads/~~WebbH200~~.jpg|~~1869~~:~~Webb Patent Adder and Talley Board\~~\

to:

%center%%height=200px%%id=Webb% http://meta-studies.net/pmwiki/uploads/SpaldingW200.jpg|1884: Spalding Adding Machine\

Deleted line 181:

Other simple rotational adding devices in this collection are shown (:if equal {Site.PrintBook$:PSW} "True":)in TAB(SimpleRotationalCalcs)(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)

27 March 2014 by 1800 -

Changed lines 164-179 from:

The main advantage of these devices was that they were cheap to manufacture and could be easily mass-produced. A lot of innovation is evident in the detail of these machines. A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which used rotations of a wheel to wind on successive numbers whilst a ball bearing, moving in a spiral groove, tracked the successive rotations. ~~Early experiments with keyboards can be seen in the Adix adding machine of~~ 1903.

~~The most obvious other development beyond the subtleties of carry mechanism was the developments in the use of materials~~. ~~Here we see the heavy two wheel mechanism of the Webb~~ Adder, in brass and wood, counterposed against the Adix Adding Machine which for the first time incorporates aluminium amongst its 122 parts, whilst the SEE Adding Machine which is entirely composed of plastic, has a Pascaline-like weighted carry mechanism, but is built so lightly utilising a materials evolution over three centuries, that a much simplified approach was by now implementable.

A particularly elegant, if made of brass and thus heavy, device was the Swiss Conto (see above) which had not only knobs to enable numbers to be input with a quick turn (rather than requiring stylus input), but also an efficient carry and clearing mechanism.

As they became cheaper and more accessible not only to shopkeepers but ordinary citizens who might value the assistance they offered, for example in their role as taxpayers,[^See for example, A.P. Kidwell, "'Yours for Improvement'—The Adding Machines of Chicago, 1884–1930", '/IEEE Annals of the History of Computing/', July-September, 2001, pp. 3-6.^] these devices became increasingly popular. However, they suffered from the same problems of clumsy input and slow operation that afflicted the simple linear machines. Some such as the Adall could only add, others had no provision for zeroing, and all were slow to use. Further, such adders, whilst simple in concept and cheap to manufacture, were so slow to use for repetitive calculation that they were virtually useless for the key arithmetic operations of multiplication and division. A quick method for repeated addition and subtraction was required at minimum to achieve these other two functions. That required a more expensive approach and a much more elaborate machine, the first commercial variant of which was designed and sold as the "Arithmometer" by Thomas de Colmar.

!!!Commercial "four function" calculating machines

!!!!Arithmometers

Thomas de Colmar first made public his design for a calculating machine capable of doing all four functions (addition, subtraction, multiplication and division) when he was granted a patent for it in 1820.[^Patent no. 1420, 18 November 1820^] His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.[^For the most authoritative website on the Thomas de Colmar machines and history see Valéry Monier's magisterial site [[http://www.arithmometre.org]], viewed 20 July 2013.^] The first design consisted of four step drums (along the lines invented by Leibniz, but not necessarily based on having ever heard of, let alone seen the internal mechanism of Leibniz's invention).[^see Friedrich W. Kistermann, "When Could Anyone Have Seen Leibniz's Stepped Wheel?", '/IEEE Annals of the History of Computing/', Volume 21, Number 2, 1999, pp. 68-72. However, as Stephen Johnston (see reference below) points out, images of Leibniz's machine were available from the late C18, see for example 1744 engraving in Annegret Kehrbaum and Bernhard Korte, '/Calculi: Bilder des Rechnens einst und heute (Images of Computing in Olden and Modern Times)/', Opladen, 1995, p. 61.^]

Whether or not Thomas reinvented the step drum, even in this first design, the four integers to be added (or subtracted) were set by sliding four corresponding cogs to the appropriate position on such drums. The cogs were moved by sliding nobs along four (square section) axles which were in turn attached to output dial wheels which showed the correct number through small windows. A carry mechanism was incorporated. Rather than being turned by a crank handle the stepped drums were turned by a ribbon that was pulled out from the side. All later designs used a crank handle to turn the drums as is shown in the diagram by Franz Reuleaux in 1862 shown (:if equal {Site.PrintBook$:PSW} "True":)in FIG(Reuleaux)(:ifend:) below.

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The main advantage of these devices was that they were cheap to manufacture and could be easily mass-produced. A lot of innovation is evident in the detail of these machines. A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which used rotations of a wheel to wind on successive numbers whilst a ball bearing, moving in a spiral groove, tracked the successive rotations.

Early experiments with keyboards can be seen in the Adix adding machine of 1903.
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(:cellnr:) %height=200px% [[Site.Webb1869|%center% http://meta-studies.net/pmwiki/uploads/WebbH200.jpg]]%%
%center%Webb Patent Adder and Talley Board 1869\\
%center%(collection Calculant)
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(:if equal {Site.PrintBook$:PSW} "True":)
%center%%height=200px%%id=Webb% http://meta-studies.net/pmwiki/uploads/WebbH200.jpg|1869:Webb Patent Adder and Talley Board\\
(collection Calculant)
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Other simple rotational adding devices in this collection are shown (:if equal {Site.PrintBook$:PSW} "True":)in TAB(SimpleRotationalCalcs)(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)

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||1884 ||Spalding Adding Machine||C.G. Spalding ||Key input, lever & dialsl||%height=75px%[[Site.Spalding1884| http://meta-studies.net/pmwiki/uploads/SpaldingW100.jpg]]||
||1891 ||Centigraph Adder||Am. Add. Co.||Key input, lever & gear||%height=75px%[[Site.Centigraph1891| http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg]]||
||1903 ||Adix Adding Machine Original model||Manheim||Key input lever & gears||%height=175px%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/AdixH175.jpg]]||
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(collection Calculant - all above)
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(:if equal {Site.PrintBook$:PSW} "True":)
||align=center cellpadding=6 border=0 id=EarlyKeyboards"Early keyboards"
||Date||Description||Maker||Type||Device||
||1884 ||Spalding Adding Machine||C.G. Spalding ||Key input, lever & dialsl||%height=75px% http://meta-studies.net/pmwiki/uploads/SpaldingW100.jpg||
||1891 ||Centigraph Adder||Am. Add. Co.||Key input, lever & gear||%height=75px% http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg||
||1903 ||Adix Adding Machine Original model||Manheim||Key input lever & gears||%height=175px% http://meta-studies.net/pmwiki/uploads/AdixH175.jpg||
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%center%%height=250px%%id=Woodie% http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491\\
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%center%%height=250px%%id=Woodie% http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491 (collection Calculant)

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%center%%height=250px%%id=Woodie% http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491

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%center%%height=250px%%id=Woodie% http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491\\

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%center%%height=250px%%id=Brunsviga% http://meta-studies.net/pmwiki/uploads/Brunsviga1896H250.jpg|
~1896: Brunsviga Schuster Pinwheel Calculator\\
Serial 3406 (collection Calculant)

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%center%%height=250px%%id=Brunsviga% http://meta-studies.net/pmwiki/uploads/Brunsviga1896H250.jpg|~1896: Brunsviga Schuster Pinwheel Calculator\\
Serial 3406\\
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%center%%height=250px%%id=Woodie% http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg]|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491

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%center%%height=250px%%id=Woodie% http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491

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%center%%id=Locke% http://meta-studies.net/pmwiki/uploads/Locke170.jpg|The Locke Adder\\(collection Calculant)

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||%center% July1972\\Hewlett Packard\\HP 35 Calculator\\serial 1230A 79429, 1972||%center% December 1973\\Hewlett Packard\\HP 45 Calculator\\serial 1350A 36719, 1973||

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||%center% July1972\\
Hewlett Packard\\
HP 35 Calculator\\
serial 1230A 79429, 1972||%center% December 1973\\
Hewlett Packard\\
HP 45 Calculator\\
serial 1350A 36719, 1973||

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||%center% July1972\\
Hewlett Packard\\
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serial 1230A 79429, 1972||%center% December 1973\\
Hewlett Packard\\
HP 45 Calculator\\
serial 1350A 36719, 1973||

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%center%%height=200px%%id=Ropp% http://meta-studies.net/pmwiki/uploads/Ropp200.jpg~~"Ropp's Calculator"~~|1892: Ropp's Commercial Calculator\\

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%center%%height=200px%%id=Ropp% http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp's Commercial Calculator\\

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%center%%height=200px%%id=convertiseur% http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg~~"Conversion device"~~|~1790: Conversion device\\

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%center%%height=200px%%id=convertiseur% http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg|~1790: Conversion device\\

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%center%%id=Locke% http://meta-studies.net/pmwiki/uploads/Locke170.jpg~~"The Locke Adder"~~|The Locke Adder\\(collection Calculant)

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%center%%height=200px%%id=Webb% http://meta-studies.net/pmwiki/uploads/WebbH200.jpg~~"Webb Adder"~~|1869:Webb Patent Adder and Talley Board\\

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%center%%height=200px%%id=Reuleaux% http://meta-studies.net/pmwiki/uploads/Misc/ThomasMechRelH200.jpg~~"Thomas mechanism"~~|1862: Thomas de Colmar arithmometer mechanism\\

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%center%%height=200px%%id=Reuleaux% http://meta-studies.net/pmwiki/uploads/Misc/ThomasMechRelH200.jpg|1862: Thomas de Colmar arithmometer mechanism\\

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%center%%height=200px%%id=CalculantStepDrum% http://meta-studies.net/pmwiki/uploads/TIMDrumH200.jpg~~"Step drum"~~|Step drum (in a later 'TIM' arithmometer)\\

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%center%%height=200px%%id=CalculantStepDrum% http://meta-studies.net/pmwiki/uploads/TIMDrumH200.jpg|Step drum (in a later 'TIM' arithmometer)\\

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%center%%height=300px%%id=ThomasDe% http://meta-studies.net/pmwiki/uploads/ThomasDeColmarH300.jpg~~"Thomas Arithmometer"~~|1884: Thomas de Colmar Arithmometer\\

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%center%%height=300px%%id=ThomasDe% http://meta-studies.net/pmwiki/uploads/ThomasDeColmarH300.jpg|1884: Thomas de Colmar Arithmometer\\

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%center%%height=250px%%id=Brunsviga% http://meta-studies.net/pmwiki/uploads/Brunsviga1896H250.jpg~~"Brunsviga Calculator"~~|

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%center%%height=200px%%id=Rack% http://meta-studies.net/pmwiki/uploads/Misc/RackMechH200.jpg~~"Rack mechanism"~~|Rack mechanism\\

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||align=center cellpadding=6 border=0 ~~tableclass=long~~ id=RackCalcs"Proportional Rack Calculators"

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||align=center cellpadding=6 border=0 id=RackCalcs"Proportional Rack Calculators"

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~~(:table align=~~center id=Woodie~~"Woodie"~~ :)
%center%%height=250px%%Woodie% http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg~~"1896 comptometer"~~|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491

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%center%%height=250px%%id=Woodie% http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg]|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491

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||align=center cellpadding=6 border=0 ~~tableclass=long~~ id=CurtaCalcs"Curta Calculators"

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%center% %height=250px%%id=Schickardreminder% http://meta-studies.net/pmwiki/uploads/Schickard1W300_1.jpg~~"Schickard's Calculator"~~|1623: Recreation of Wilhelm Schickard's calculating machine\\

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%center% %height=250px%%id=Schickardreminder% http://meta-studies.net/pmwiki/uploads/Schickard1W300_1.jpg|1623: Recreation of Wilhelm Schickard's calculating machine\\

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%center% %height=250px%%id=Bamberger% http://meta-studies.net/pmwiki/uploads/BambergerOmegaH250.jpg~~"Bamberger Omega"~~|1904-1905: Bamberger's Omega calculating machine\\

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%center% %height=250px%%id=Bamberger% http://meta-studies.net/pmwiki/uploads/BambergerOmegaH250.jpg|1904-1905: Bamberger's Omega calculating machine\\

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%center%%height=250px%%id=Bollee% http://meta-studies.net/pmwiki/uploads/BolleeMAB1890H250.jpg~~"Bollée calculator"~~|Leon Bollée Calculating Machine\\

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%center%%height=250px%%id=Bollee% http://meta-studies.net/pmwiki/uploads/BolleeMAB1890H250.jpg|Leon Bollée Calculating Machine\\

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%center%%height=300px%%id=Millionaire% http://meta-studies.net/pmwiki/uploads/MillionairH300.jpg~~"Millionaire calculator"~~|1912: Millionaire Calculating Machine, serial 2015 (10x10x20)\\

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%center%%height=300px%%id=Millionaire% http://meta-studies.net/pmwiki/uploads/MillionairH300.jpg|1912: Millionaire Calculating Machine, serial 2015 (10x10x20)\\

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%center%%height=250px%%id=Herzstark% http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometerH250.jpg~~"Herzstark arithmometer"~~|~1929: "Herzstark" electric Calculating Machine serial 6549\\

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%center%%height=250px%%id=Herzstark% http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometerH250.jpg|~1929: "Herzstark" electric Calculating Machine serial 6549\\

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%center%%height=250px%%id=HerzstarkMech% http://meta-studies.net/pmwiki/uploads/HerzstarkMechH250.jpg~~"Herzstark mechanism"~~|1950s-1960s: Underneath view of the Herzstark mechanism (note the stepped drums)\\

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%center%%height=250px%%id=HerzstarkMech% http://meta-studies.net/pmwiki/uploads/HerzstarkMechH250.jpg|1950s-1960s: Underneath view of the Herzstark mechanism (note the stepped drums)\\

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%center%%height=250px%%id=MADAS20BTG% http://meta-studies.net/pmwiki/uploads/MADAS_SmallerH250.jpg~~"MADAS 20BTG"~~|1950s-1960s: MADAS\\

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||align=center cellpadding=6 border=0 ~~tableclass=long~~ id=HPCacl"Hewlett Packard Pocket Scientific Calculators"

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||align=center cellpadding=6 border=0 id=HPCacl"Hewlett Packard Pocket Scientific Calculators"

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The ~~above~~ arithmometer ~~demonstrates the high level of usability that the firm of Thomas had now achieved. It allows the multiplication of two numbers each as large~~ as ~~9 million and the result can be read out to 16~~ places. Ivory markers are provided for the decimal point (and to delineate hundreds, thousands and millions for ease of use). The clearing and carry mechanisms are entirely reliable. Indeed, still bearing its original varnish, this particular machine operates reliably some 125 years after it was made. Indicating that its owner was serious about its use in practice the machine appears to have been re-mounted by the famous instrument maker, Stanley, (sometime after 1900) in a better quality and stronger box fixed to a cast iron frame. This allows the machine to be tilted at a suitable angle for easy use. As the only surviving Thomas known to have this improvement, this machine seems to stand as a precursor to later innovations under Payen when he added a (rather less robust) hinged tilt base to his machines.~~[[<<]]~~

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The arithmometer in this collection demonstrates the high level of usability that the firm of Thomas had now achieved. It allows the multiplication of two numbers each as large as 9 million and the result can be read out to 16 places. Ivory markers are provided for the decimal point (and to delineate hundreds, thousands and millions for ease of use). The clearing and carry mechanisms are entirely reliable. Indeed, still bearing its original varnish, this particular machine operates reliably some 125 years after it was made. Indicating that its owner was serious about its use in practice the machine appears to have been re-mounted by the famous instrument maker, Stanley, (sometime after 1900) in a better quality and stronger box fixed to a cast iron frame. This allows the machine to be tilted at a suitable angle for easy use. As the only surviving Thomas known to have this improvement, this machine seems to stand as a precursor to later innovations under Payen when he added a (rather less robust) hinged tilt base to his machines.

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The ~~above~~ three arithmometers ~~demonstrate the sorts of improvements to~~ the basic arithmometer design which now emerged. The first, a TIM ("Time is Money" ) arithmometer manufactured by Ludwig Spitz and Co. of Berlin-Tempelhof in 1909 was greatly strengthened from the Thomas design to create a much more robust and reliable machine. First produced in a wooden box it was later made much stronger by installing it in a cast iron frame which held all parts rigidly.[^See Ernst Martin, '/The Calculating Machines (Die Rechenmaschinen): Their History and Development/', ed. and trs. by Peggy Aldridge Kidwell and ~~Michael R~~. ~~Williams, MIT Press, Mass., 1992, p. 191–4^] Beginning a change in style that would be emulated~~ in many other machines the brass panels were now enamelled black consistent with the management, industrial and commercial settings where it was intended to find its market. The other two machines in this set would also originally have had a similar black finish. (Unfortunately, there was a ~~tendency in the late C20 to "take the machines back to brass" in~~ the ~~same way that~~ in the ~~1960s there was a trend to remove the original finish from wood on vintage furniture, and plaster from brick walls in old~~ houses.)~~[[<<]]~~

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The three arithmometers (FIG(Arithmometers) in this collection demonstrate the sorts of improvements to the basic arithmometer design which now emerged. The first, a TIM ("Time is Money" ) arithmometer manufactured by Ludwig Spitz and Co. of Berlin-Tempelhof in 1909 was greatly strengthened from the Thomas design to create a much more robust and reliable machine. First produced in a wooden box it was later made much stronger by installing it in a cast iron frame which held all parts rigidly.[^See Ernst Martin, '/The Calculating Machines (Die Rechenmaschinen): Their History and Development/', ed. and trs. by Peggy Aldridge Kidwell and Michael R. Williams, MIT Press, Mass., 1992, p. 191–4^] Beginning a change in style that would be emulated in many other machines the brass panels were now enamelled black consistent with the management, industrial and commercial settings where it was intended to find its market. The other two machines in this set would also originally have had a similar black finish. (Unfortunately, there was a tendency in the late C20 to "take the machines back to brass" in the same way that in the 1960s there was a trend to remove the original finish from wood on vintage furniture, and plaster from brick walls in old houses.)

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The above principle was incorporated into a MADAS arithmometer, developed by Erwin Janz and manufactured by Egli in Zurich, starting in 1913. The acronym MADAS was short for "Multiplication, Addition, Division - Automatically, Substraction"). The achievement of an entirely automatic division process - the first ever for an arithmometer style calculator. In this collection there is a MADAS IX Maxima calculator (produced in 1917), an ambitious machine also in that it could accept 9 digits, up to one thousand million, as input and could display 16 digits (representing numbers up to ten thousand trillion) in its results register. Two MADAS models were produced and by 1920 about 1,000 were being produced with some 7,000 having been sold from countries as wide apart as Europe and Australia.[^Martin Reese, Hamburg, '/55 erfolgreiche Jahre: MADAS-Rechenautomaten aus der Schweiz 1913 - 1968/', http://www.rechnerlexikon.de/files/MADAS—8-2010.pdf, viewed 18 February 2012.^]

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The above principle was incorporated into a MADAS arithmometer, developed by Erwin Janz and manufactured by Egli in Zurich, starting in 1913. The acronym MADAS was short for "Multiplication, Addition, Division - Automatically, Substraction"). The achievement of an entirely automatic division process - the first ever for an arithmometer style calculator - was a considerable triumph. In this collection there is a MADAS IX Maxima calculator (produced in 1917), an ambitious machine also in that it could accept 9 digits, up to one thousand million, as input and could display 16 digits (representing numbers up to ten thousand trillion) in its results register. Two MADAS models were produced and by 1920 about 1,000 were being produced with some 7,000 having been sold from countries as wide apart as Europe and Australia.[^Martin Reese, Hamburg, '/55 erfolgreiche Jahre: MADAS-Rechenautomaten aus der Schweiz 1913 - 1968/', http://www.rechnerlexikon.de/files/MADAS—8-2010.pdf, viewed 18 February 2012.^]

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The pinwheel calculator was developed as an improvement on the arithmometer more or less simultaneously in Russia in 1878 by Swedish engineer Willgodt Theophil Odhner (1845-1905) and in the US in 1874, by Frank Stephen Baldwin (1838-1925). Although they worked independently of each ~~there~~ machines were so similar that the 'Ohdner' or 'Baldwin' machine became more or less interchangeable terms.[^Diana H. Hook and Jeremy M. Norman, '/Origins of Cyberspace/', Novato, California, 2002, p. 255.^]. The designs utilised a clever 'counting gear' in which the number of teeth protruding could be adjusted by sliders (and later a push-down keyboard). A pinwheel and the internal mechanism (with some pinwheels removed) from a Walther pinwheel calculator in this collection is shown (:if equal {Site.PrintBook$:PSW} "True":)in TAB(DemoPinwheels)(:ifend:) below.

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The pinwheel calculator was developed as an improvement on the arithmometer more or less simultaneously in Russia in 1878 by Swedish engineer Willgodt Theophil Odhner (1845-1905) and in the US in 1874, by Frank Stephen Baldwin (1838-1925). Although they worked independently of each other their machines were so similar that the 'Ohdner' or 'Baldwin' machine became more or less interchangeable terms.[^Diana H. Hook and Jeremy M. Norman, '/Origins of Cyberspace/', Novato, California, 2002, p. 255.^]. The designs utilised a clever 'counting gear' in which the number of teeth protruding could be adjusted by sliders (and later a push-down keyboard). A pinwheel and the internal mechanism (with some pinwheels removed) from a Walther pinwheel calculator in this collection is shown (:if equal {Site.PrintBook$:PSW} "True":)in TAB(DemoPinwheels)(:ifend:) below.

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As the range of dates for the set of pinwheel calculators in this collection suggests, the pinwheel design was highly successful and capable of being improved on for the better part of three quarters of a century. The second Ohdner in the collection is from 1938, and although possessing some improvements (such as the capacity to move the carriage back and forth with tab keys), was little different in concept. The same can be said for the Facit calculator from around 1945, and even from the 1950s, near the end of the production of such machines, despite its more modern finish and use of plastic fittings (and some improvements such as clearing levers), the Walther 160 remains quite similar in operation to the Brunsviga of 1896, which, significantly, still works as smoothly as the Walther.~~[[<<]]~~

The main progress that had been made was thus not so much in functionality as in production methodology. This is epitomised by the Walther 160 and later Walther calculators. Karl Walther's ancestors made rifles and in 1858 he established his own hunting and shooting rifle company.[^"Walther Company History", [[http://www.carl-walther.de/cw.php?lang=en&content=history]], viewed 23 July 2013.^]. He developed then into pistols including the famous Walther PP series military pistols production of which began in 1928 ~~and were a worldwide~~ success. However, the second world war in 1945 left his son Fritz with 80 patents and little else. He was able to rebuild the business both in relation to weapons, but also by diversifying into making office machinery, and in particular calculators. By the 1950s he had four large factories equipped with advanced machinery and technique.[^Ray Mackay, "The Walther Company: Historic Recollections", December 1997. [[http://www.xnumber.com/xnumber/walther.htm]], viewed 22 July 2013.^] The Walther 160 was by now a classic product of modern manufacturing technology, mass produced, comparatively lightly made, and accessibly cheap. As a result many thousands of them were sold. By 1970 the Walther Office Machines company (Walther ~~Büromaschinen~~ GmbH) employed 2000 staff and was producing almost 120,000 machines per year, with about 50% for export.[^John Wolff, "John Wolff's Web Museum: Walther Calculators Overview" [[http://home.vicnet.net.au/~wolff/calculators/Walther/Walther.htm]], viewed 23 July 2013.^]

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As the range of dates for the set of pinwheel calculators in this collection suggests, the pinwheel design was highly successful and capable of being improved on for the better part of three quarters of a century. The second Ohdner in the collection is from 1938, and although possessing some improvements (such as the capacity to move the carriage back and forth with tab keys), was little different in concept. The same can be said for the Facit calculator from around 1945, and even from the 1950s, near the end of the production of such machines, despite its more modern finish and use of plastic fittings (and some improvements such as clearing levers), the Walther 160 remains quite similar in operation to the Brunsviga of 1896, which, significantly, still works as smoothly as the Walther.

The main progress that had been made was thus not so much in functionality as in production methodology. This is epitomised by the Walther 160 and later Walther calculators. Karl Walther's ancestors made rifles and in 1858 he established his own hunting and shooting rifle company.[^"Walther Company History", [[http://www.carl-walther.de/cw.php?lang=en&content=history]], viewed 23 July 2013.^]. He developed then into pistols including the famous Walther PP series military pistols, production of which began in 1928. They proved to be a worldwide success. However, the second world war in 1945 left his son Fritz with 80 patents and little else. He was able to rebuild the business both in relation to weapons, but also by diversifying into making office machinery, and in particular calculators. By the 1950s he had four large factories equipped with advanced machinery and technique.[^Ray Mackay, "The Walther Company: Historic Recollections", December 1997. [[http://www.xnumber.com/xnumber/walther.htm]], viewed 22 July 2013.^] The Walther 160 was by now a classic product of modern manufacturing technology, mass produced, comparatively lightly made, and accessibly cheap. As a result many thousands of them were sold. By 1970 the Walther Office Machines company (Walther Büromaschinen GmbH) employed 2000 staff and was producing almost 120,000 machines per year, with about 50% for export.[^John Wolff, "John Wolff's Web Museum: Walther Calculators Overview" [[http://home.vicnet.net.au/~wolff/calculators/Walther/Walther.htm]], viewed 23 July 2013.^]

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A further approach to the problem of the four functions is found in the American invention by Felt, of a device that he called the comptometer ~~and~~ patented in 1887. It performs the task of addition by a system of keys and levers. The keys press down rods which from key 1 to key 9 increase incrementally in length for each successive key. This difference in displacement, magnified by a lever turns an accumulating gear through 1 to 9 teeth as appropriate.~~[[<<]]~~

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A further approach to the problem of the four functions is found in the American invention by Felt, of a device that he called the comptometer. He patented it in 1887. It performs the task of addition by a system of keys and levers. The keys press down rods which, from key 1 to key 9, increase incrementally in length for each successive key. This difference in displacement, magnified by a lever turns an accumulating gear through 1 to 9 teeth as appropriate.

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The comptometer was a highly successful innovation and was sufficiently cheap and useful to reach a broad market. Characterised by extremely effective marketing and capable of being mass produced the device continued to be marketed for some 80 years ~~unusually~~ for such innovations ~~leaving~~ its inventor extremely wealthy. By then its essential mechanism was being utilised by more than one company. Shown below (:if equal {Site.PrintBook$:PSW} "True":)in TAB(Comptometers)(:ifend:) is the remaining comptometer in this collection, this time made of plastic in the 1950s by the British Bell Punch company. Also shown is a demonstration model showing the keys and lever system used in the Bell Punch machine.

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The comptometer was a highly successful innovation and was sufficiently cheap and useful to reach a broad market. Characterised by extremely effective marketing and capable of being mass produced the device continued to be marketed for some 80 years. Unusually for such innovations it left its inventor extremely wealthy. By then its essential mechanism was being utilised by more than one company. Shown below (:if equal {Site.PrintBook$:PSW} "True":)in TAB(Comptometers)(:ifend:) is the remaining comptometer in this collection, this time made of plastic in the 1950s by the British Bell Punch company. Also shown is a demonstration model showing the keys and lever system used in the Bell Punch machine.

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Finally there is the last and most beautifully miniaturised of the four function manual mechanical calculators ~~designed by Curt~~ Herzstark. Curt was born in 1902 as the son of Samuel Herzstark who had established a calculator manufacturing company in Vienna in 1905-6. Curt's father died in 1937 but by then Curt was both Director of the company and a highly competent designer in his own right. He recognised the need for a miniaturised four function calculator which could be carried in an engineer's pocket. He began to design this as a cylindrical calculator which could be held in one hand and operated with the other. It could utilise the modern new light weight alloys of aluminium, magnesium, etc. By the end of 1937 he had the form of what he wished to accomplish firmly in his mind. It would be compact, lightweight, and in order to allow a carry mechanism which would allow the crank to be turned only one way, it would use ~~and~~ internal process of complementary arithmetic for subtraction. Then came Hitler. ~~Herzstark found himself in 1943~~ arrested and imprisoned in Buchenwald concentration camp ~~where~~ he was placed in a small technical camp to manufacture components to assist the Nazi war effort (in particular, parts of the V I and II missile bombs).

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Finally there is the last and most beautifully miniaturised of the four function manual mechanical calculators. They were designed by Curt Herzstark. Curt was born in 1902 as the son of Samuel Herzstark who had established a calculator manufacturing company in Vienna in 1905-6. Curt's father died in 1937 but by then Curt was both Director of the company and a highly competent designer in his own right. He recognised the need for a miniaturised four function calculator which could be carried in an engineer's pocket. He began to design this as a cylindrical calculator which could be held in one hand and operated with the other. It could utilise the modern new light weight alloys of aluminium, magnesium, etc. By the end of 1937 he had the form of what he wished to accomplish firmly in his mind. It would be compact, lightweight, and in order to allow a carry mechanism which would allow the crank to be turned only one way, it would use an internal process of complementary arithmetic for subtraction. Then came Hitler. In 1943 Herzstark found himself arrested and imprisoned in the Buchenwald concentration camp. There his engineering skill was noticed and he was placed in a small technical camp to manufacture components to assist the Nazi war effort (in particular, parts of the V I and II missile bombs).

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The first model (the Model 1) began production in 1947. Below left (:if equal {Site.PrintBook$:PSW} "True":)in TAB(CurtaCalcs)(:ifend:) is a (rare) example of the Model I Curta ( with pin sliders which were soon improved upon) in mint condition coming from the first 5500 made in ~July 1948, the year after production began and in the first 5,500 made. As can be seen the sliders are pins which were used by Curta before he introduced bakelite handles on them. Centre is a later Curta from 1967 complete with the original box in which it was sold and its instructions, all in mint condition. On the right is a Curta Model II from 1962. The Model II ~~was a larger machine capable of~~ a number input to 11 significant figures, compared with the more compact Model I which could accept a number accurate to 8 significant figures. Note the very 'modern' anodised aluminium sliders on the Model II which comes also with an optional leather carry case (not shown).

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The first model (the Model 1) began production in 1947. Below left (:if equal {Site.PrintBook$:PSW} "True":)in TAB(CurtaCalcs)(:ifend:) is a (rare) example of the Model I Curta. It still has the pin sliders which were soon to be improved upon and is in mint condition. It was made in ~July 1948, the year after production began, and is in the first 5,500 made. As can be seen the sliders are pins which were used by Curta before he introduced bakelite handles on them. Centre is a later Curta from 1967 complete with the original box in which it was sold and its instructions, all in mint condition. On the right is a Curta Model II from 1962. The Model II was a larger machine capable of a number input to 11 significant figures, compared with the more compact Model I which could accept a number accurate to 8 significant figures. Note the very 'modern' anodised aluminium sliders on the Model II which comes also with an optional leather carry case (not shown here).

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On the Curta above, left we see the clearing ring protruding. Bringing all numbers to zero is achieved by lifting the top section and turning the clearing ring. Adding is achieved by setting successive numbers and turning the crank through a full turn. Ingeniously, pulling the crank up sets it for subtraction. Multiplication is done in the usual manner of multiplying by each successive integer of the multiplier with the upper register being advanced for each one by lifting the top section and rotating it one notch. Division is by the usual method of long division by repeated subtractions. Once more, for each partial product the operator must either correctly judge the correct number of times to turn the crank, or if an overflow is forced, reverse the operation by pushing in the crank and turning it one full turn. In short it is an excellent machine for addition and subtraction, but involves the normal acquired skill, and tedium, required by multiplication and division in any of the mechanical calculators not equipped to do it automatically.~~[[<<]]~~

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On the Curta above, left we see the clearing ring protruding. Bringing all numbers to zero is achieved by lifting the top section and turning the clearing ring. Adding is achieved by setting successive numbers and turning the crank through a full turn. Ingeniously, pulling the crank up sets it for subtraction. Multiplication is done in the usual manner of multiplying by each successive integer of the multiplier with the upper register being advanced for each one by lifting the top section and rotating it one notch. Division is by the usual method of long division by repeated subtractions. Once more, for each partial product the operator must either correctly judge the correct number of times to turn the crank, or if an overflow is forced, reverse the operation by pushing in the crank and turning it one full turn. In short it is an excellent machine for addition and subtraction, but involves the normal acquired skill, and tedium, required by multiplication and division in any of the mechanical calculators not equipped to do it automatically.

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The earliest of these machines had been that of Schickard (below, left). In the upper part is a set of rotatable Napier's rods revealed by windows to give partial products. In the lower part is the world's first known stylus operated adding machine to add these partial products up. A late and unique expression of these in this collection (below, right) is Justin Bamberger's Omega Calculating Machine (1903-6). In the upper section is a set of Napier's bones revealed by moveable windows for discovering the partial products of two multiplied numbers. In the lower section is a Locke adding machine for adding them up.

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The earliest of these machines had been that of Schickard (below, left) which was invented in 1623. As described earlier, it used a set of rotatable Napier's rods in its upper part to yield partial products of the multiplication of two numbers, whilst in its lower part was the world's first known stylus operated adding machine which could be used to add the partial products up. A later and unique expression of the same principles can be found in this collection (below, right). It is Justin Bamberger's Omega Calculating Machine (1903-6). In the upper section is a set of Napier's bones revealed by moveable windows for discovering the partial products of two multiplied numbers. In the lower section is a Locke adding machine for adding them up.

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The earliest of these machines had been that of Schickard (~~immediately below in~~ FIG(Schickardreminder))~~. In the upper part of it is a set of rotatable Napier's rods revealed by windows to give partial products. In the lower part is~~ the ~~world's first known stylus operated adding machine to add these partial products~~ up.

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The earliest of these machines had been that of Schickard (FIG(Schickardreminder)) which was invented in 1623. As described earlier, it used a set of rotatable Napier's rods in its upper part to yield partial products of the multiplication of two numbers, whilst in its lower part was the world's first known stylus operated adding machine which could be used to add the partial products up.in

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A ~~late~~ and unique expression of the same ~~principle in this collection is Justin Bamberger's Omega Calculating Machine~~ (~~1903-6~~), ~~shown in FIG(~~Bamberger~~) below.~~ In the upper section is a set of Napier's bones revealed by moveable windows for discovering the partial products of two multiplied numbers. In the lower section is a Locke adding machine for adding them up.

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A later and unique expression of the same principles can be found in this collection (shown in FIG(Bamberger) ). It is Justin Bamberger's Omega Calculating Machine (1903-6). In the upper section is a set of Napier's bones revealed by moveable windows for discovering the partial products of two multiplied numbers. In the lower section is a Locke adding machine for adding them up.

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Bamberger's Omega ~~uses~~ linear strips rather than the rotatable mechanisms ~~of both halves of the Schickard. It also has some additional provision for storing intermediate results to assist long division, including the register on~~ the ~~top right, and~~ the ~~notebook. Otherwise~~ the ~~two machines are very similar in operation and both, with some considerable effort~~, ~~can be used to perform all four functions of arithmetic. The fact that neither took off in the market place may be in part a factor of their difficulty~~ of ~~use and part a lack of adequately determined~~ marketing.~~[[<<]]~~

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Bamberger's Omega used linear strips rather than the rotatable mechanisms in the upper and lower sections of the Schickard calculator. It also has some additional provision for storing intermediate results to assist long division, including the register on the top right, and the notebook. Otherwise the two machines are very similar in operation and both, with some considerable effort, can be used to perform all four functions of arithmetic. The fact that neither took off in the market place may be in part a factor of their difficulty of use and part a lack of adequately determined marketing.

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The Millionaire calculating machine combines the idea of the physical embodiment of multiplication tables with that of the proportional rack. It is able to interrogate a multiplication table represented by metal rods, and in a single crank of the handle multiplies the multiplicand by a number set between 1 and 9 then advancing its internal carriage one place ready for the next multiplier to be set and applied. Thus, for example, to multiply 4689 x 2568 an arithmometer or pinwheel would take 21 cranks of the handle (8+6+5+2) whereas the Millionaire could achieve the same outcome with only four cranks of the handle. In the lid was a set of tables of factors to assist division, a brush to keep the machine clean, and a special bolt so when being transported the carriage was held clamped in place, since if the machine were dropped the carriage was heavy enough to punch through the end of the case.~~[[<<]]~~

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The Millionaire calculating machine combines the idea of the physical embodiment of multiplication tables with that of the proportional rack. It is able to interrogate a multiplication table represented by metal rods, and in a single crank of the handle multiplies the multiplicand by a number set between 1 and 9 then advancing its internal carriage one place ready for the next multiplier to be set and applied. Thus, for example, to multiply 4689 x 2568 an arithmometer or pinwheel would take 21 cranks of the handle (8+6+5+2) whereas the Millionaire could achieve the same outcome with only four cranks of the handle. In the lid was a set of tables of factors to assist division, a brush to keep the machine clean, and a special bolt so when being transported the carriage was held clamped in place, since if the machine were dropped the carriage was heavy enough to punch through the end of the case.

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Electricity could be utilised in appliances once it was available through an electricity grid. In the US, the first electrical supply was in 1882 for lighting, with 85 customers. Electrification spread over subsequent decades, primarily in the big cities through private power companies in the first two decades of the C20. In 1926 in the UK separate electricity grids began to be connected into a national grid. It was not surprising therefore that this period of the early C20 was conducive to the introduction of electric motors to many purposes, including adding machines.

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Electricity could be utilised in appliances once it was available through an electricity grid. In the US, the first electrical supply was constructed in 1882 for lighting, with 85 customers. Electrification spread over subsequent decades, primarily in the big cities through private power companies in the first two decades of the C20. In 1926 in the UK separate electricity grids began to be connected into a national grid. It was not surprising therefore that this period of the early C20 was conducive to the introduction of electric motors to many purposes, including adding machines.

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Using switches it was therefore possible to build a very efficient calculating machine. Valves were too bulky, energy consuming, and unreliable for a consumer device but prior sales of mechanical calculators had by now established a massive potential market. The invention of the transistor in 1947 at Bell Telephone labs, based on the quantum properties of crystals, laid the way for "solid state" electric switches at tiny scale, able to be turned on and off by one another. Light emitting diodes (LEDs) - another solid state device which emitted light when electrons forced into a higher energy ("excited") state fell back to their stable energy - began to appear as practical output devices in 1962.

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Using switches it was therefore possible to build a very efficient calculating machine. Valves were too bulky, energy consuming, and unreliable for a consumer device but prior sales of mechanical calculators had by now established a massive potential market. The invention of the transistor in 1947 at Bell Telephone labs, based on the quantum properties of crystals, laid the way for "solid state" electric switches at tiny scale, able to be turned on and off by one another. Light emitting diodes (LEDs) - another solid state device which emitted light when electrons having been forced into a higher energy ("excited") state fell back to their stable energy - began to appear as practical output devices in 1962.

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It was in July 1972, that the old ways for scientists and citizen alike were definitively undermined. In that month, to some astonishment, the Hewlett Packard company produced the HP-35 electronic 'pocket' calculator (see (:if equal {Site.PrintBook$:PSW} "True":)in TAB(HPCacl)(:ifend:) below). It was an extraordinary leap forward, equipped not only with a red ~~lit showing smooth performance of the arithmetic functions but also reciprocals, powers, square roots, logarithms and anti-logarithms (base e and 10), the trigonometric functions, pi,~~ and ~~a system of registers which enabled chain operations without having to write down intermediate results.~~ For those of a technical orientation who could afford it, all else was now as obsolete as gaslight. Hewlett Packard followed quickly with the HP-45 appearing in the following year with a configurable display, more functions and registers, a variety of constants, and a more compact shape, more suited for the male shirt top pocket. A year later in 1974 the HP-65 was launched with all that could be done by the HP-45 but with the added feature of being user-programmable through a small built in magnetic strip reader. With that the diminutive HP calculator had taken a huge step towards the first mass-marketed personal computers (the TRS-80 - the author wrote his second book on one of these in 1981 - launched by Tandy, and the Apple-II by Apple, both launched in 1977).

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It was in July 1972, that the old ways for scientists and citizen alike were definitively undermined. In that month, to some astonishment, the Hewlett Packard company produced the HP-35 electronic 'pocket' calculator (see (:if equal {Site.PrintBook$:PSW} "True":)in TAB(HPCacl)(:ifend:) below). It was an extraordinary leap forward, equipped not only with a a red LED display, and showing smooth performance of the arithmetic functions but also with provision to calculate reciprocals, powers, square roots, logarithms and anti-logarithms (base e and 10), the trigonometric functions, pi, and a system of registers which enabled chain operations without having to write down intermediate results.

For those of a technical orientation who could afford it, all else was now as obsolete as gaslight. Hewlett Packard followed quickly with the HP-45 appearing in the following year with a configurable display, more functions and registers, a variety of constants, and a more compact shape, more suited for the male shirt top pocket. A year later in 1974 the HP-65 was launched with all that could be done by the HP-45 but with the added feature of being user-programmable through a small built in magnetic strip reader. With that the diminutive HP calculator had taken a huge step towards the first mass-marketed personal computers (the TRS-80 - the author wrote his second book on one of these in 1981 - launched by Tandy, and the Apple-II by Apple, both launched in 1977).

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The launch of the HP-35 marks what might be called the "First Vanishing Point" - the point at which all the arithmetic operations and common scientific functions required for calculation became available in a single small electronic calculator, capable of being carried on a belt or in a shirt pocket (albeit in serious peril of it falling out when one bent over to pick something up). Electronic calculators now proliferated throughout the developed and developing world displacing the rigours of mental arithmetic and caught in an 'arms race' to make them smaller, more powerful, easier to use, and find a niche in a highly competitive and very cluttered market.~~[[<<]]~~

Forty years later, in 2012, electronic solid state calculators could be found in their billions across the world. By then what might be labelled the "Second Vanishing Point" - the point at which these electronic calculators began to disappear, displaced now by "virtual calculators" encoded in the software of desk and lap-top computers, tablets, smart phones, and much else was ~~perhaps~~ in sight ~~but not yet~~ arrived. But from that vantage point, even the stand-alone electronic calculators, might begin to follow their mechanical predecessors of two decades before ~~as they faded~~ into the misty light of receding memory.

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The launch of the HP-35 marks what might be called the "First Vanishing Point" - the point at which all the arithmetic operations and common scientific functions required for calculation became available in a single small electronic calculator, capable of being carried on a belt or in a shirt pocket (albeit in serious peril of it falling out when one bent over to pick something up). Electronic calculators now proliferated throughout the developed and developing world displacing the rigours of mental arithmetic and caught in an 'arms race' to make them smaller, more powerful, easier to use, and find a niche in a highly competitive and very cluttered market.

Forty years later, in 2012, electronic solid state calculators could be found in their billions across the world. By then what might be labelled the "Second Vanishing Point" - the point at which these electronic calculators began to disappear, displaced now by "virtual calculators" encoded in the software of desk and lap-top computers, tablets, smart phones, and much else was coming into in sight (although probably had not yet arrived). But from that vantage point, even the stand-alone electronic calculators, might soon begin to follow their mechanical predecessors of two decades before fading into the misty light of receding memory.

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This leads to the following observation: to learn how to use a calculating technology is not just a matter of understanding its concept. It also requires the acquisition of a type of knowledge which Jean-François Gauvin[^Jean-François Gauvin , Habits of Knowledge: Artisans, Savants and Mechanical Devices in Seventeenth-Century French Natural Philosophy, The Department of the History of Science, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of History of Science, Harvard University, Cambridge, Mass., USA, November 2008, pp. 113. ^] refers to as "gestural". Gestural knowledge is the embodied knowledge that artisans rely on when they execute work of high craft skill. The first time someone ~~looks at~~ a Thomas de Colmar arithmometer learning how to add and subtract takes some time. Doing division and multiplication is much more challenging, especially if attempted without a good knowledge of how it can be done on paper. The first time is slow and subject to mistakes. It is only after repeated practice that the gestures required become so practiced that they are quick, instinctive and reliable. It is only then that the potential for calculation with such a device can be can be judged. And it would only have been after this sort of practice that one could credit the Gentleman's Magazine of 1857 claim that:

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This leads to the following observation: to learn how to use a calculating technology is not just a matter of understanding its concept. It also requires the acquisition of a type of knowledge which Jean-François Gauvin[^Jean-François Gauvin , Habits of Knowledge: Artisans, Savants and Mechanical Devices in Seventeenth-Century French Natural Philosophy, The Department of the History of Science, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of History of Science, Harvard University, Cambridge, Mass., USA, November 2008, pp. 113. ^] refers to as "gestural". Gestural knowledge is the embodied knowledge that artisans rely on when they execute work of high craft skill. The first time someone tries to use a Thomas de Colmar arithmometer learning how to add and subtract on it efficiently takes some time. Doing division and multiplication is much more challenging, especially if attempted without a good knowledge of how it can be done on paper. The first time is slow and subject to mistakes. It is only after repeated practice that the gestures required become so practiced that they are quick, instinctive and reliable. It is only then that the potential for calculation with such a device can be can be judged. And it would only have been after this sort of practice that one could credit the Gentleman's Magazine of 1857 claim that:

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The achievement of the late mechanical calculators (such as the MADAS and the Euklid-Mercedes) was that they ~~did~~ greatly ~~simplify~~ what ~~what~~ needed to be learned by their operators ~~to achieve efficiently all four arithmetic operations. But they did so still~~ at considerable economic cost. The Comptometer was really best for addition and (with practice) subtraction. With its key input it was fast, and its simple design was amenable to cheaper construction and mass-production. So it found a different and expanded market in the rapidly expanding commercial and government organisations of the C20. It has been said and is probably true that its inventors and promoters, Felt and Tarrant, were probably the first people in the world to become truly wealthy from the invention, production and sale of calculators.

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The achievement of the late mechanical calculators (such as the MADAS and the Euklid-Mercedes) was that they greatly simplified what needed to be learned by their operators in order to achieve an efficient performance of all four arithmetic operations. But these calculators achieved this only at considerable economic cost. The Comptometer was really best for addition and (with practice) subtraction. With its key input it was fast, and its simple design was amenable to cheaper construction and mass-production. So it found a different and expanded market in the rapidly expanding commercial and government organisations of the C20. It has been said and is probably true that its inventors and promoters, Felt and Tarrant, were probably the first people in the world to become truly wealthy from the invention, production and sale of calculators.

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The final conquest of the electronic calculator occurred when literacy, design, familiarity, cost and perceived need coincided to sweep all else before it. Never had the market been more prevalent in the negotiation of daily life. Science and technology now dominated every corner of the developed world and was making rapid inroads elsewhere. Literacy was at its highest in the developed world with arithmetic education now a requirement for every child in the extended period of compulsory schooling. Money promised ~~to free time and technology~~ was now widely accepted as being the answer to drudgery. Further ~~still~~, there was a social acceptance of life-long change, and an emerging concept of the desirability of 'life-long learning'. The new consumer calculators were increasingly cheap, required little knowledge to use, displaced the mental effort of recall of multiplication tables and mental and written arithmetic. Printers attached to them produced now comparatively permanent records. And the whole increasingly seamlessly fitted a world which would soon be interconnected through computers and telecommunications into an ever more pervasive communications web. Calculators had not only reached a desired end. They also had found their moment when that end was widely required.

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The final conquest of the electronic calculator occurred when literacy, design, familiarity, cost and perceived need coincided to sweep all else before it. Never had the market been more prevalent in the negotiation of daily life. Science and technology now dominated every corner of the developed world and was making rapid inroads elsewhere. Literacy was at its highest in the developed world with arithmetic education now a requirement for every child in the extended period of compulsory schooling. Money promised was supposed to free time. Technology was now widely accepted as being the answer to drudgery. Further, there was a growing social acceptance of life-long change, and an emerging concept of the desirability of 'life-long learning'. The new consumer calculators were increasingly cheap, required little knowledge to use, displaced the mental effort of recall of multiplication tables and mental and written arithmetic. Printers attached to them produced now comparatively permanent records. And the whole increasingly seamlessly fitted a world which would soon be interconnected through computers and telecommunications into an ever more pervasive communications web. Calculators had not only reached a desired end. They also had found their moment when that end was widely required.

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Thomas de Colmar himself was the director of an insurance company. In the 1820s the insurance industry was rapidly expanding as a consequence of free trade and the transport revolution, and France had become international ~~centres~~ of the industry.[^Peter Borscheid, "Europe: Overview", in Peter Borscheid and Niels Vigo Haueter (eds), '/World Insurance: The Evolution of a Global Risk Network/', Oxford University Press, Oxford, 2012, p. 39.^] The likely consequent intensification of work no doubt galvanised Thomas's interest in finding an efficient way of handling multiple calculations. But given his responsibilities in an intense commercial environment is unlikely that he would have been able to spend all or even a great deal of his time on designing and building more arithmometers over the next several decades. Indeed it was not until several decades later that, in 1844, the arithmometer, very much re-designed, appeared at a French national exhibition. There it could be found amongst precision instruments in a category of 'diverse measures, counters and calculating machines'.[^ibid.^] Johnston thus argues that far from being a lone pioneer, the machines of Thomas were in competition (and regarded initially as a poor second) to others. However, over a half century, the machines of Thomas, as they evolved, prevailed.[^As cited by Johnston, Jean Marguin, '/Histoire des instruments et machines à calculer/', Paris, 1994, p. 111: 'Pendant un demi-siècle, la machine y régna seule.'^] Johnston notes that to achieve this "Thomas campaigned both through the press and in commissioned publications. He also engaged in the rituals of patronage, rituals that we might more readily associate with the decoratively elaborate calculating machines of the 18th century."[^Johnston, "Making the arithmometer count".^] However, the design of the Thomas machine was sufficiently beautifully executed to make it an appropriate gift to persons of high standing, a property essential to its successful promotion.

Indeed the Thomas arithmometer did take off as a consumer product in France, the UK and Europe and variants continued to sell right up to the first world war. They were not cheap. For example, in 1872 British engineer Henry Brunel wrote that "I have just got what my mother irreverently calls 'a new toy' – to wit a calculating machine price ~~£12~~ which does all the common operations of arithmetic viz addition, multiplication, subtraction & division in the twinkling of an eye. It is really a very useful article worth its weight in brass."[^ Brunel to Adams, 18 March 1866, Bristol University Library, Brunel Collection, Letter Book VII, f. 106, cited in Johnston, ibid.^] In terms of today's purchasing power, ~~£12~~ from 1872 was the equivalent of £5,840 (~US$8,900) in 2013 (based on average earnings).[^Calculated using the [[http://www.measuringworth.com]] calculator on 21 July 2013^]

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Thomas de Colmar himself was the director of an insurance company. In the 1820s the insurance industry was rapidly expanding as a consequence of free trade and the transport revolution, and France had become an international centre of the industry.[^Peter Borscheid, "Europe: Overview", in Peter Borscheid and Niels Vigo Haueter (eds), '/World Insurance: The Evolution of a Global Risk Network/', Oxford University Press, Oxford, 2012, p. 39.^] The likely consequent intensification of work no doubt galvanised Thomas's interest in finding an efficient way of handling multiple calculations. But given his responsibilities in an intense commercial environment is unlikely that he would have been able to spend all or even a great deal of his time on designing and building more arithmometers over the next several decades. Indeed it was not until several decades later that, in 1844, the arithmometer, very much re-designed, appeared at a French national exhibition. There it could be found amongst precision instruments in a category of 'diverse measures, counters and calculating machines'.[^ibid.^] Johnston thus argues that far from being a lone pioneer, the machines of Thomas were in competition (and regarded initially as a poor second) to others. However, over a half century, the machines of Thomas, as they evolved, prevailed.[^As cited by Johnston, Jean Marguin, '/Histoire des instruments et machines à calculer/', Paris, 1994, p. 111: 'Pendant un demi-siècle, la machine y régna seule.'^] Johnston notes that to achieve this "Thomas campaigned both through the press and in commissioned publications. He also engaged in the rituals of patronage, rituals that we might more readily associate with the decoratively elaborate calculating machines of the 18th century."[^Johnston, "Making the arithmometer count".^] However, the design of the Thomas machine was sufficiently beautifully executed to make it an appropriate gift to persons of high standing, a property essential to its successful promotion.

Indeed the Thomas arithmometer did take off as a consumer product in France, the UK and Europe and variants continued to sell right up to the first world war. They were not cheap. For example, in 1872 British engineer Henry Brunel wrote that "I have just got what my mother irreverently calls 'a new toy' – to wit a calculating machine price £12 which does all the common operations of arithmetic viz addition, multiplication, subtraction & division in the twinkling of an eye. It is really a very useful article worth its weight in brass."[^ Brunel to Adams, 18 March 1866, Bristol University Library, Brunel Collection, Letter Book VII, f. 106, cited in Johnston, ibid.^] In terms of today's purchasing power, £12 from 1872 was the equivalent of £5,840 (~US$8,900) in 2013 (based on average earnings).[^Calculated using the [[http://www.measuringworth.com]] calculator on 21 July 2013^]

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The repairs carried out on this machine were not uncharacteristic of what was required to keep the arithmometer in reliable working order. The machines however were subject to breakage and expensive to repair. The market for such an expensive machine was quite limited, and despite its uprecedented success, as Johnston concludes, ~~that~~ Thomas's work on the machine still fell "more into the category of vanity publishing than mass production".[^ibid^] Nevertheless, it formed the standard against which improvements were sought and new designs contemplated.

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The repairs carried out on this machine were not uncharacteristic of what was required to keep the arithmometer in reliable working order. The machines however were subject to breakage and expensive to repair. The market for such an expensive machine was quite limited, and despite its uprecedented success, as Johnston concludes, Thomas's work on the machine still fell "more into the category of vanity publishing than mass production".[^ibid^] Nevertheless, it formed the standard against which improvements were sought and new designs contemplated.

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||~1917 ||Madas IX Maxima||Madas||Auto Division||%width=250px%[[Site.Madas-IX-Maxima| http://meta-studies.net/pmwiki/uploads/MADAS-1917W250.jpg]]||

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||~1917 ||Madas\\IX\\Maxima||Madas||Auto\\Division||%width=250px%[[Site.Madas-IX-Maxima| http://meta-studies.net/pmwiki/uploads/MADAS-1917W250.jpg]]||

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As with previous calculating machines, commercial success for the arithmometer machine was far from assured. The aesthetics of the design still reflected the high status market where it could have become just another prestigious mathematical machine in the cabinets of curiosities of those of elevated status. The somewhat circuitous route to that later success is described by Stephen Johnston.[^Stephen Johnston, "Making the arithmometer count", '/Bulletin of the Scientific Instrument Society/', Volume 52, 1997, pp. 12-21.^~~] As~~ Johnston ~~notes~~, ~~Thomas did not of course~~ make these early machines. The first of his machines to survive was made by in Paris by Devrine, as usual a local clock (and instrument) maker.

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As with previous calculating machines, commercial success for the arithmometer machine was far from assured. The high finish in lacquered brass and ivory, heavy brass mechanism in the arithmometer's design still reflected the high status market it was initially seen as appealing to. Thus, it could have become just another prestigious mathematical machine in the cabinets of curiosities of those of elevated status. The somewhat circuitous route to its later success is described by Stephen Johnston.[^Stephen Johnston, "Making the arithmometer count", '/Bulletin of the Scientific Instrument Society/', Volume 52, 1997, pp. 12-21.^] As Johnston notes, Thomas did not himself make these early machines. The first of his machines to survive was made by in Paris by Devrine, as usual a local clock (and instrument) maker.

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The late modern period, spanning the nineteenth century through the two world wars of the twentieth century and ending roughly in the middle of that century, was a time of enormous economic, technological, cultural and political change. The role of calculators, from one point of view, was a comparatively minor part of this ~~panoramic and turbulent time,~~ and ~~yet, it also was profoundly shaped by it, and helped facilitate its~~ development.

As already suggested, none of these devices that were created during this period sprung from their inventors minds completely unprecedented. The roots spread back into the early Modern period from the earliest forms of embodied calculation (for example, the use of calculi). The period following the inventions already mentioned of Schickard, Pascal, Moreland and Leibniz were followed by a multitude of devices built on similar basic principles, but all with the limitation that they were not widely taken up because as yet need had not developed to resonate with the limited capabilities and often high cost of the inventions. Nevertheless, as time passed a web of developments would continue to emerge that would eventually create that moment when such a resonance might take place. Central to this was the use to which these devices might be put.

Usefulness arises in a context, and the social, political, economic and technological context was in a process of unprecedented transformation across Europe. The late C18 was characterised most dramatically with the execution of Louis XVI in 1793 by a transition between the power of the ancienne regime to ~~new political~~ forces. Into the following century across Europe the emerging power of merchant and market increasingly swept aside the old aristocracy in the shaping of the politics, economics and infrastructure of what, in a process evolving from the Treaty of Westphalia (1648) had emerged as 'sovereign' nation states. Improving systems of transportation facilitated a process of ever intensifying trade across and between states was involving monarchs, peasants, artisans, merchants and financiers alike.[^For more on this see Camilleri and Falk, '/Worlds in Transition/', pp. 134-44.^] Ever more efficient processes of printing and dissemination facilitated production and dissemination of ideas. A period of comparative peace between nations in the late C18 was marked by a revolution in agricultural production. But this was just one way in which a synergy between scientific and technological innovation was finding purchase within transforming systems of production, commerce, governance and more broadly lived experience. In addition, science was beginning to be harnessed to actual production. Steam replaced horse, and then from the mid ~~C-19~~ to the mid-C20, electrical networks spread across Europe and then much of the rest of the modern world allowing the introduction of many new technologies.

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The late modern period, spanning the nineteenth century through the two world wars of the twentieth century and ending roughly in the middle of that century, was a time of enormous economic, technological, cultural and political change. The role of calculators, from one point of view, was a comparatively minor part of this time of panoramic and turbulent change, and yet, it also was profoundly shaped by it, and helped facilitate its development.

As already suggested, none of these devices that were created during this period sprung from their inventors' minds completely unprecedented. The roots spread back into the early Modern period from the earliest forms of embodied calculation (for example, the use of calculi). The period following the inventions already mentioned of Schickard, Pascal, Moreland and Leibniz were followed by a multitude of devices built on similar basic principles, but all with the limitation that they were not widely taken up because as yet need had not developed to resonate with the limited capabilities and often high cost of the inventions. Nevertheless, as time passed a web of developments would continue to emerge that would eventually create that moment when such a resonance might take place. Central to this was the use to which these devices might be put.

Usefulness arises in a context, and the social, political, economic and technological context was in a process of unprecedented transformation across Europe. The late C18 was characterised most dramatically with the execution of Louis XVI, in 1793, by a transition between the power of the ancienne regime to that of new political forces. Into the following century across Europe the emerging power of merchant and market increasingly swept aside the old aristocracy in the shaping of the politics, economics and infrastructure of what, in a process evolving from the Treaty of Westphalia (1648) had emerged as 'sovereign' nation states. Improving systems of transportation facilitated a process of ever intensifying trade across and between states was involving monarchs, peasants, artisans, merchants and financiers alike.[^For more on this see Camilleri and Falk, '/Worlds in Transition/', pp. 134-44.^] Ever more efficient processes of printing and dissemination facilitated production and dissemination of ideas. A period of comparative peace between nations in the late C18 was marked by a revolution in agricultural production. But this was just one way in which a synergy between scientific and technological innovation was finding purchase within transforming systems of production, commerce, governance and more broadly lived experience. In addition, science was beginning to be harnessed to actual production. Steam replaced horse, and then from the mid C19 to the mid-C20, electrical networks spread across Europe and then much of the rest of the modern world allowing the introduction of many new technologies.

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Not only was the conception of nature being transformed through a more technical, and indeed mathematical account, but new literacies and cognitive skills ~~required to deal with an economy that was ever more shaped by the market, production~~ that was ever more shaped by ~~science, and products whose use required continual processes of cultural learning. Mass education in reading and basic mathematical skills were now an increasing necessity~~ and ~~steadily the period of "childhood" was extended including~~ the ~~invention~~ of ~~the~~ "~~teenager~~", to allow an extended period of socially conceded time in which this personal development could take place.

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Not only was the conception of nature being transformed through a more technical, and indeed mathematical account, but new literacies and cognitive skills were now required. Skills were now more broadly required to deal with an economy that was ever more shaped by the market, production that was ever more shaped by science, and products whose use required continual processes of cultural learning. Mass education in reading and basic mathematical skills were now an increasing necessity. Steadily the period of "childhood" was being extended (including, eventually, the invention of the "teenager") to allow an extended period of socially conceded time in which this personal development could take place.

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As the above suggests, historical periods do not easily fit together as simply defined blocks of time with nice clear boundaries. Rather they are useful labels for different times of change, which whilst usefully distinguished, overlap each other to allow for the transitions which take place across them. The process of technological change in particular, in any particular period, ~~has roots back before~~ and ~~layers on~~ innovations which precede it. Indeed, not only did prior inventions provide a base on which new more commercially successful devices might be built, but also old methods could be persistently found in use sometimes right through the late Modern period. One of the most common of these, which may still be found in use in some places, was ready reckoners.

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As the above suggests, historical periods do not easily fit together as simply defined blocks of time with nice clear boundaries. Rather they are useful labels for different times of change, which whilst usefully distinguished, overlap each other to allow for the transitions which take place across them. The process of technological change in particular, in any particular period, is layered over, and has roots reaching back to the innovations which precede it. Indeed, not only did prior inventions provide a base on which new more commercially successful devices might be built, but also old methods could be persistently found in use sometimes right through the late Modern period. One of the most common of these, which may still be found in use in some places, was ready reckoners.

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Ready reckoners were in widespread use by shopkeepers and many others from the C17 on. They presented tables of precalculated results of many kinds of multiplication~~. These included the much needed calculations of the price for multiples of an item for sale, or per unit~~ of ~~weight. They could also be used to look up the calculations needed for wages~~ and ~~interest.[^see~~ Bruce O.B. Williams and Roger G. Johnson, "Ready Reckoners", '/IEEE Annals of the History of Computing/', October-December, 2005, pp. 64-80.^] One such, from 1892 is "Ropp's Commercial Calculator: a practical arithmetic for practical purposes, containing a complete system of useful, accurate, and convenient tables, together with simple, short, and practical methods for rapid calculation", published in the US and used widely into the early C20. This one, shown below(:if equal {Site.PrintBook$:PSW} "True":) in FIG(Ropp)(:ifend:), is the 1892 World's Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.

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Ready reckoners were in widespread use by shopkeepers and many others from the C17 on. They presented tables of precalculated results of many kinds of multiplication and division, addition of fractions, important constants, unit conversions, logarithms, and much else. Frequently they included the much needed calculations of the price for multiples of an item for sale, or per unit of weight and could also be used to look up the calculations needed for wages and interest and .[^see Bruce O.B. Williams and Roger G. Johnson, "Ready Reckoners", '/IEEE Annals of the History of Computing/', October-December, 2005, pp. 64-80.^] One such, from 1892 is "Ropp's Commercial Calculator: a practical arithmetic for practical purposes, containing a complete system of useful, accurate, and convenient tables, together with simple, short, and practical methods for rapid calculation", published in the US and used widely into the early C20. This one, shown below(:if equal {Site.PrintBook$:PSW} "True":) in FIG(Ropp)(:ifend:), is the 1892 World's Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.

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The dominant role of ready reckoners at this period is indicated by M. Norton Wise's comment in relation to Victorian England that:

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The dominant role of ready reckoners in this period is indicated by M. Norton Wise's comment in relation to Victorian England that:

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Subtraction could be achieved by units of motion in the opposite direction, or where that was not possible, the addition of [[Site.~~OperatingInstructionsForAPascaline|complementary~~ numbers]].

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Subtraction could be achieved by units of motion in the opposite direction, or where that was not possible, the addition of (:if equal {Site.PrintBook$:PSW} "False":)[[Site.OperatingInstructionsForAPascaline|complementary numbers]](:ifend:)(:if equal {Site.PrintBook$:PSW} "True":)complementary numbers(:ifend:).

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One such line of development was based on the possibility of adding linear displacements of strips of metal. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe, later to be known as the Addiator (of which there is one in this collection)~~, of which a bewildering number of different designs~~ appeared in the late C19 and early C20. Some used strips or rods, and some used chains which were more versatile. A rather beautiful Locke Adder which uses strips moved by knobs, from 1905-10, sold by Clarence Locke, is shown (:if equal {Site.PrintBook$:PSW} "True":)in FIG(Locke)(:ifend:) below.

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One such line of development was based on the possibility of adding linear displacements of strips of metal. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe, later to be known as the Addiator (of which there is one in this collection). A bewildering number of different designs around this idea appeared in the late C19 and early C20. Some used strips or rods, and some used chains which were more versatile. A rather beautiful Locke Adder which uses strips moved by knobs, from 1905-10, sold by Clarence Locke, is shown (:if equal {Site.PrintBook$:PSW} "True":)in FIG(Locke)(:ifend:) below.

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The above relied either on the movement by a stylus or knobs of strips, rods or chains to ~~create~~ addition. Some (such as the Locke adder) used a simplified form of complementary arithmetic for subtraction,~~t others allowed a such as the Golden Gem allowed reverse motion~~, ~~and others again such as the Addiator could be turned over to perform~~ the ~~subtraction.~~ Most (but not the Locke Adder) had a simple provision for carries ~~and~~ some (such as the Scribola - which also had a very early printout) had clearing levers to bring the display back to zero for the next calculation. All however, whilst affordable, were cumbersome and slow to use since each digit had to be individually entered by performing a sliding motion. It was much quicker to add the numbers on paper using mental arithmetic, but of course, here that capability was lacking, or where ~~the effort of doing it was considered tedious, then these devices began to find a market in the first half of the C20, and thousands~~ were produced and sold across the more industrialised countries of Europe, the British Empire and the USA.

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The above relied either on the movement by a stylus, or knobs, of strips, rods or chains to achieve an addition. Some (such as the Locke adder) used a simplified form of complementary arithmetic for subtraction. Others, such as the Golden Gem, allowed reverse motion for direct subtraction. Others, such as the Addiator, could be turned over to perform the subtraction on the reverse side. Most (but not the Locke Adder) had a simple provision for carries. And some (such as the Scribola (which also had a very early approach to printing its result on a paper strip) had clearing levers to bring its display back to zero for the next calculation. All however, whilst affordable, were cumbersome and slow to use since each digit had to be individually entered by performing a sliding motion. It was much quicker to add the numbers on paper using mental arithmetic. But, of course, where that capability was lacking, or where it was insufficiently well practised and the effort of doing it was consequently considered tedious, then these devices began to find a market in the first half of the C20. Thousands were produced and sold across the more industrialised countries of Europe, the British Empire and the USA.

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The main advantage of these devices was that they were cheap to manufacture and could be easily mass-produced. ~~We can~~ of course see a lot of innovation in the detail of these machines. A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which simply used successive rotations of a wheel to wind on successive numbers whilst a ball bearing, moving in a spiral groove, tracked the successive rotations. Early experiments with keyboards can be seen in the Adix adding machine of 1903.

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The main advantage of these devices was that they were cheap to manufacture and could be easily mass-produced. A lot of innovation is evident in the detail of these machines. A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which used rotations of a wheel to wind on successive numbers whilst a ball bearing, moving in a spiral groove, tracked the successive rotations. Early experiments with keyboards can be seen in the Adix adding machine of 1903.

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Popular though some of these were as they became cheaper and more accessible not only to shopkeepers but ordinary citizens who might value the assistance they offered, for example in their role as taxpayers,[^See for example, A.P. Kidwell, ~~"'Yours for Improvement'—The Adding Machines of Chicago, 1884–1930", '/IEEE Annals of the History of Computing/', July-September, 2001, pp. 3-6.^] they suffered from~~ the ~~same problems of clumsy input and slow operation that afflicted the simple linear machines~~. ~~Some such as the Adall could only add~~, ~~others had no provision for zeroing, and all were slow to use~~. ~~Further, such adders, whilst simple in concept and cheap to manufacture, were so slow to use for repetitive calculation~~ that ~~they were virtually useless for the key arithmetic operations of multiplication and division. A quick method~~ repeated addition and subtraction was required at minimum to achieve these other two functions. That required a more expensive approach and a much more elaborate machine, the first commercial variant of which was designed and sold as the "Arithmometer" by Thomas de Colmar.

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A particularly elegant, if made of brass and thus heavy, device was the Swiss Conto (see above) which had not only knobs to enable numbers to be input with a quick turn (rather than requiring stylus input), but also an efficient carry and clearing mechanism.

As they became cheaper and more accessible not only to shopkeepers but ordinary citizens who might value the assistance they offered, for example in their role as taxpayers,[^See for example, A.P. Kidwell, "'Yours for Improvement'—The Adding Machines of Chicago, 1884–1930", '/IEEE Annals of the History of Computing/', July-September, 2001, pp. 3-6.^] these devices became increasingly popular. However, they suffered from the same problems of clumsy input and slow operation that afflicted the simple linear machines. Some such as the Adall could only add, others had no provision for zeroing, and all were slow to use. Further, such adders, whilst simple in concept and cheap to manufacture, were so slow to use for repetitive calculation that they were virtually useless for the key arithmetic operations of multiplication and division. A quick method for repeated addition and subtraction was required at minimum to achieve these other two functions. That required a more expensive approach and a much more elaborate machine, the first commercial variant of which was designed and sold as the "Arithmometer" by Thomas de Colmar.

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Thomas de Colmar first made public his design for a calculating machine capable of doing all four functions (addition, subtraction, multiplication and division) when he was granted a patent for it in 1820.[^Patent no. 1420, 18 November 1820^]. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.[^For the most authoritative website on the Thomas de Colmar machines and history see Valéry Monier's magisterial site [[http://www.arithmometre.org]], viewed 20 July 2013.^] The first design consisted of four step drums (along the lines invented by Leibniz, but not necessarily based on having ever heard of, let alone seen the internal mechanism of Leibniz's invention[^see Friedrich W. Kistermann, "When Could Anyone Have Seen Leibniz's Stepped Wheel?", '/IEEE Annals of the History of Computing/', Volume 21, Number 2, 1999, pp. 68-72. However, as Stephen Johnston (see reference below) points out, images of Leibniz's machine were available from the late C18, see for example 1744 engraving in Annegret Kehrbaum and Bernhard Korte, '/Calculi: Bilder des Rechnens einst und heute (Images of Computing in Olden and Modern Times)/', Opladen, 1995, p. 61.^]).

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Thomas de Colmar first made public his design for a calculating machine capable of doing all four functions (addition, subtraction, multiplication and division) when he was granted a patent for it in 1820.[^Patent no. 1420, 18 November 1820^] His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.[^For the most authoritative website on the Thomas de Colmar machines and history see Valéry Monier's magisterial site [[http://www.arithmometre.org]], viewed 20 July 2013.^] The first design consisted of four step drums (along the lines invented by Leibniz, but not necessarily based on having ever heard of, let alone seen the internal mechanism of Leibniz's invention).[^see Friedrich W. Kistermann, "When Could Anyone Have Seen Leibniz's Stepped Wheel?", '/IEEE Annals of the History of Computing/', Volume 21, Number 2, 1999, pp. 68-72. However, as Stephen Johnston (see reference below) points out, images of Leibniz's machine were available from the late C18, see for example 1744 engraving in Annegret Kehrbaum and Bernhard Korte, '/Calculi: Bilder des Rechnens einst und heute (Images of Computing in Olden and Modern Times)/', Opladen, 1995, p. 61.^]

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The ~~above~~ diagram shows ~~the~~ crank handle on the right top which drives the rotation of the step drum (shown centre right). In front of the crank handle can be seen a "slider nob" which moves the cog along the axle to engage ~~with~~ correct number of teeth of the step drum. To the ~~left is a reversing mechanism connected to an output dial. The~~ reversing mechanism ~~allows the~~ output dial ~~to be rotated in~~ the opposite direction, if the nob that activates it (situated above) is shifted from the "addition" to the "subtraction" position.

Immediately below (:if equal {Site.PrintBook$:PSW} "~~True~~"~~:)in FIG~~(~~CalculantStepDrum)(:ifend:) is a picture of a step drum from a later arithmometer, but based on the Thomas mechanism, showing the slider,~~ drum ~~with its 'counting gear' positioned for~~ the ~~input of '5'. In this arithmometer the input number selected shows in~~ the ~~immediately adjacent window~~. ~~Note the square section axle on which the counting gear moves~~.

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The diagram shows a crank handle on the right top which drives the rotation of the step drum (shown centre right). In front of the crank handle can be seen a "slider nob" which moves the cog along the axle to engage the correct number of teeth of the step drum (corresponding to the number to be added). To the left is a reversing mechanism connected to an output dial. The reversing mechanism allows the output dial to be rotated in the opposite direction, if the nob that activates it (situated above) is shifted from the "addition" to the "subtraction" position (where an internal gear reverses the internal rotational motion).

Immediately below (:if equal {Site.PrintBook$:PSW} "True":)in FIG(CalculantStepDrum)(:ifend:) is a picture of a step drum from a later arithmometer, but based on the Thomas mechanism, showing the slider, drum with its 'counting gear' positioned for the input of '5'. In this arithmometer the input number selected shows in the immediately adjacent window. Note the square section axle on which the counting gear moves. This allows the counting gear to engage the axle whatever its position along it.

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The Thomas was arranged so that the input mechanism could be shifted in relation to the output dials. In this way it was possible to carry out "long multiplications" (by repeated additions) or "long division" (by repeated subtraction). However, in the early decades the machine was not particularly reliable. In particular, the Thomas arithmometer did not really have a reliable carry mechanism until a patented mechanism was introduced in 1865, and this remained the fundamental system for carry arithmometers for the next 50 years.

As with previous calculating machines that commercial success of this machine was far from assured. The aesthetics of the design still reflects the high status market where it could have become just another prestigious mathematical machine in the cabinets of curiosities of those of elevated status. The somewhat circuitous route to that later success is described by Stephen Johnston.[^Stephen Johnston, "Making the arithmometer count", '/Bulletin of the Scientific Instrument Society/', Volume 52, 1997, pp. 12-21.^] As Johnston notes, Thomas did not of course make these early machines. The first of his machines to survive was made by in Paris by Devrine, as usual a local clock (and instrument) maker.

to:

The Thomas arithmometer was arranged so that the input mechanism could be shifted in relation to the output dials. In this way it was possible to carry out "long multiplications" (by repeated additions) or "long division" (by repeated subtraction). However, in the early decades the machine was not particularly reliable. In particular, the Thomas arithmometer did not really have a reliable carry mechanism until a patented mechanism was introduced in 1865, and this remained the fundamental system for carry in successive generations of arithmometers for the next 50 years.

As with previous calculating machines, commercial success for the arithmometer machine was far from assured. The aesthetics of the design still reflected the high status market where it could have become just another prestigious mathematical machine in the cabinets of curiosities of those of elevated status. The somewhat circuitous route to that later success is described by Stephen Johnston.[^Stephen Johnston, "Making the arithmometer count", '/Bulletin of the Scientific Instrument Society/', Volume 52, 1997, pp. 12-21.^] As Johnston notes, Thomas did not of course make these early machines. The first of his machines to survive was made by in Paris by Devrine, as usual a local clock (and instrument) maker.

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Felt first demonstrated this famously with a model constructed in a wooden macaroni box in 1885. He patented his design in 1887 and began selling it from his manufacturing company in Chicago. In 1890 he gave it the name "the Comptometer" and energetically promoted it.[^/'Origins of Cyberspace, p. 244.^] Below (:if equal {Site.PrintBook$:PSW} "True":)in FIG(Woodie)(:ifend:) is the Comptometer in this collection - an example from 1896 of the first model, cased in wood, and one of the 40 oldest known to still be in existence. Remarkably with a drop of oil on the springs it still works perfectly.

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Felt first demonstrated this famously with a model constructed in a wooden macaroni box in 1885. He patented his design in 1887 and began selling it from his manufacturing company in Chicago. In 1890 he gave it the name "the Comptometer" and energetically promoted it.[^'/Origins of Cyberspace, p. 244.^] Below (:if equal {Site.PrintBook$:PSW} "True":)in FIG(Woodie)(:ifend:) is the Comptometer in this collection - an example from 1896 of the first model, cased in wood, and one of the 40 oldest known to still be in existence. Remarkably with a drop of oil on the springs it still works perfectly.

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->Mr. Munich said: "See, Herzstark, I understand you've been working on a new thing, a small calculating machine. Do you know, I can give you a tip. We will allow you to make and draw everything. If it is really worth something, then we will give it to the Fuhrer as a present after we win the war. Then, surely, you will be made an Aryan." For me, that was the first time I thought to myself, my God, if you do this, you can extend your life. And then and there I started to draw the CURTA, the way I had imagined it.[^/'An Interview with Curt Herzstark/', OH 140, conducted by Erwin Tomash on 10-11 September 1987, Nendeln, Liechtenstein, (English Translation).^]

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->Mr. Munich said: "See, Herzstark, I understand you've been working on a new thing, a small calculating machine. Do you know, I can give you a tip. We will allow you to make and draw everything. If it is really worth something, then we will give it to the Fuhrer as a present after we win the war. Then, surely, you will be made an Aryan." For me, that was the first time I thought to myself, my God, if you do this, you can extend your life. And then and there I started to draw the CURTA, the way I had imagined it.[^'/An Interview with Curt Herzstark/', OH 140, conducted by Erwin Tomash on 10-11 September 1987, Nendeln, Liechtenstein, (English Translation).^]

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These machines thus constitute the pinacle reached in the development of the personal hand-operated mechanical digital calculator - able to carry out all four functions by means of a crank operated machine of exquisite miniaturised workmanship and design. Production ceased in November 1970 although sales continued through 1973. At least 150,000 of the various calculator models were made.[^/'An Interview with Curt Herzstark/'^] For more on the Curta see the marvellous collection of documents and simulations at '/The Curta Caclulator Page/'.[^/'The CURTA Calculator Page/', [[http://www.vcalc.net/cu.htm]], viewed 25 July 2013.^]

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These machines thus constitute the pinacle reached in the development of the personal hand-operated mechanical digital calculator - able to carry out all four functions by means of a crank operated machine of exquisite miniaturised workmanship and design. Production ceased in November 1970 although sales continued through 1973. At least 150,000 of the various calculator models were made.[^'/An Interview with Curt Herzstark/'^] For more on the Curta see the marvellous collection of documents and simulations at '/The Curta Caclulator Page/'.[^'/The CURTA Calculator Page/', [[http://www.vcalc.net/cu.htm]], viewed 25 July 2013.^]

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%center% Leon Bollée Calculating Machine "A New Calculating Machine of very General Applicability"\\/'The Manufacturer and Builder 1890/'[^1890: Leon Bollée Calculating Machine, "A New Calculating Machine of very General Applicability", '/The Manufacturer and Builder/', July 1890, p. 156. Original print article.^]\\

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%center% Leon Bollée Calculating Machine "A New Calculating Machine of very General Applicability"\\'/The Manufacturer and Builder 1890/'[^1890: Leon Bollée Calculating Machine, "A New Calculating Machine of very General Applicability", '/The Manufacturer and Builder/', July 1890, p. 156. Original print article.^]\\

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/'The Manufacturer and Builder 1890/'[^1890: Leon Bollée Calculating Machine, "A New Calculating Machine of very General Applicability", '/The Manufacturer and Builder/', July 1890, p. 156. Original print article.^]\\

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'/The Manufacturer and Builder 1890/'[^1890: Leon Bollée Calculating Machine, "A New Calculating Machine of very General Applicability", '/The Manufacturer and Builder/', July 1890, p. 156. Original print article.^]\\

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Manufactured by H.W. Egli, some 4,655 Millionaires were sold between 1895 and 1935[^/'Origins of Cyberspace/' p. 242.^] at a 1912 price of about US$480[^Price list in Edmonds Collins, '/The Millionaire Calculating Machine/', pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. See also price of US$500 at 1914 prices given by Luc de Brabandere cited in B.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, published in '/Slide Rule and Calculation monographs/', Slide Rule Circle, UK, 2002, pp. 59-98.^] (about $11,700 in 2013 US dollars[^Calculated using the [[http://www.measuringworth.com]] calculator on 24 July 2013^]). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,[^Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant).^] and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones. The machine still operates reliably after more than 100 years.

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Manufactured by H.W. Egli, some 4,655 Millionaires were sold between 1895 and 1935[^'/Origins of Cyberspace/' p. 242.^] at a 1912 price of about US$480[^Price list in Edmonds Collins, '/The Millionaire Calculating Machine/', pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. See also price of US$500 at 1914 prices given by Luc de Brabandere cited in B.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, published in '/Slide Rule and Calculation monographs/', Slide Rule Circle, UK, 2002, pp. 59-98.^] (about $11,700 in 2013 US dollars[^Calculated using the [[http://www.measuringworth.com]] calculator on 24 July 2013^]). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,[^Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant).^] and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones. The machine still operates reliably after more than 100 years.

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Samuel Herzstark (1867-1937), the father of Curt Herzstark who built the Curta, also was a pioneer in calculator construction and together with Gustav Perger established the Austria Calculator Machines Manufacturing Company in Vienna in 1905-6. In an interview in 1987 Curt Herzstark reports that in 1907 Samuel became the first to attach an electric motor to an arithmometer, which he equipped also with a keyboard. Curt also notes that this machine was equipped with automatic division.[^/'An Interview with Curt Herzstark/', OH 140, conducted by Erwin Tomash on 10-11 September 1987, Nendeln, Liechtenstein, (English Translation).^] However after the 1914-18 War Herzstark returned to a demolished business. He restarted with a combination of importing and selling calculators from other manufacturers, assembling old stock of his own design, and then as the business built up designing new machines. Below (:if equal {Site.PrintBook$:PSW} "True":)in FIG(Herzstark)(:ifend:) is an arithmometer in this collection branded by Samuel Herzstark from 1929. It is actually a Badenia (manufactured by the German Company Math. Bauerle in the Black Forest) which Herzstark was at that time re-badging and selling.

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Samuel Herzstark (1867-1937), the father of Curt Herzstark who built the Curta, also was a pioneer in calculator construction and together with Gustav Perger established the Austria Calculator Machines Manufacturing Company in Vienna in 1905-6. In an interview in 1987 Curt Herzstark reports that in 1907 Samuel became the first to attach an electric motor to an arithmometer, which he equipped also with a keyboard. Curt also notes that this machine was equipped with automatic division.[^'/An Interview with Curt Herzstark/', OH 140, conducted by Erwin Tomash on 10-11 September 1987, Nendeln, Liechtenstein, (English Translation).^] However after the 1914-18 War Herzstark returned to a demolished business. He restarted with a combination of importing and selling calculators from other manufacturers, assembling old stock of his own design, and then as the business built up designing new machines. Below (:if equal {Site.PrintBook$:PSW} "True":)in FIG(Herzstark)(:ifend:) is an arithmometer in this collection branded by Samuel Herzstark from 1929. It is actually a Badenia (manufactured by the German Company Math. Bauerle in the Black Forest) which Herzstark was at that time re-badging and selling.

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->M. Thomas's arithmometer may be used without the least trouble or possibility of error, not only for addition, subtraction, multiplication, and division, but also for much more complex operations, such as the extraction of the square root, involution, the resolution of triangles, etc...A multiplication of eight figures by eight others is made in eighteen seconds; a division of sixteen figures by eight figures, in twenty four seconds; and in one minute and a quarter one can extract the square root of sixteen figures, and also prove the accuracy of the calculation...[^/'The Gentleman's Magazine/', Volume 202, "The monthly intelligencer", January 1857, p. 100, [[http://books.google.fr/books?id=Rf0IAAAAIAAJ&pg=PA100&dq=arithmometer&as_brr=1#v=onepage&q=arithmometer&f=false]], viewed 23 July 2013.^]

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->M. Thomas's arithmometer may be used without the least trouble or possibility of error, not only for addition, subtraction, multiplication, and division, but also for much more complex operations, such as the extraction of the square root, involution, the resolution of triangles, etc...A multiplication of eight figures by eight others is made in eighteen seconds; a division of sixteen figures by eight figures, in twenty four seconds; and in one minute and a quarter one can extract the square root of sixteen figures, and also prove the accuracy of the calculation...[^'/The Gentleman's Magazine/', Volume 202, "The monthly intelligencer", January 1857, p. 100, [[http://books.google.fr/books?id=Rf0IAAAAIAAJ&pg=PA100&dq=arithmometer&as_brr=1#v=onepage&q=arithmometer&f=false]], viewed 23 July 2013.^]

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The above three arithmometers demonstrate the sorts of improvements to the basic arithmometer design which now emerged. The first, a TIM ("Time is Money" ) arithmometer manufactured by Ludwig Spitz and Co. of Berlin-Tempelhof in 1909 was greatly strengthened from the Thomas design to create a much more robust and reliable machine. First produced in a wooden box it was later made much stronger by installing it in a cast iron frame which held all parts rigidly.[^See Ernst Martin, '/The Calculating Machines (Die Rechenmaschinen): Their History and Development/', ~~ed~~. and trs. by Peggy Aldridge Kidwell and Michael R. Williams, MIT Press, Mass., 1992, p. 191–4^] Beginning a change in style that would be emulated in many other machines the brass panels were now enamelled black consistent with the management, industrial and commercial settings where it was intended to find its market. The other two machines in this set would also originally have had a similar black finish. (Unfortunately, there was a tendency in the late C20 to "take the machines back to brass" in the same way that in the 1960s there was a trend to remove the original finish from wood on vintage furniture, and plaster from brick walls in old houses.)[[<<]]

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The above three arithmometers demonstrate the sorts of improvements to the basic arithmometer design which now emerged. The first, a TIM ("Time is Money" ) arithmometer manufactured by Ludwig Spitz and Co. of Berlin-Tempelhof in 1909 was greatly strengthened from the Thomas design to create a much more robust and reliable machine. First produced in a wooden box it was later made much stronger by installing it in a cast iron frame which held all parts rigidly.[^See Ernst Martin, '/The Calculating Machines (Die Rechenmaschinen): Their History and Development/', ed. and trs. by Peggy Aldridge Kidwell and Michael R. Williams, MIT Press, Mass., 1992, p. 191–4^] Beginning a change in style that would be emulated in many other machines the brass panels were now enamelled black consistent with the management, industrial and commercial settings where it was intended to find its market. The other two machines in this set would also originally have had a similar black finish. (Unfortunately, there was a tendency in the late C20 to "take the machines back to brass" in the same way that in the 1960s there was a trend to remove the original finish from wood on vintage furniture, and plaster from brick walls in old houses.)[[<<]]

23 March 2014 by 1800 -

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Usefulness arises in a context, and the social, political, economic and technological context was in a process of unprecedented transformation across Europe. The late C18 was characterised most dramatically with the execution of Louis XVI in 1793 by a transition between the power of the ancienne regime to new political forces. Into the following century across Europe the emerging power of merchant and market increasingly swept aside the old aristocracy in the shaping of the politics, economics and infrastructure of what, in a process evolving from the Treaty of Westphalia (1648) had emerged as 'sovereign' nation states. Improving systems of transportation facilitated a process of ever intensifying trade across and between states was involving monarchs, peasants, artisans, merchants and financiers alike.[^For more on this see Camilleri and Falk, //Worlds in Transition//, pp. 134-44.^] Ever more efficient processes of printing and dissemination facilitated production and dissemination of ideas. A period of comparative peace between nations in the late C18 was marked by a revolution in agricultural production. But this was just one way in which a synergy between scientific and technological innovation was finding purchase within transforming systems of production, commerce, governance and more broadly lived experience. In addition, science was beginning to be harnessed to actual production. Steam replaced horse, and then from the mid C-19 to the mid-C20, electrical networks spread across Europe and then much of the rest of the modern world allowing the introduction of many new technologies.

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Usefulness arises in a context, and the social, political, economic and technological context was in a process of unprecedented transformation across Europe. The late C18 was characterised most dramatically with the execution of Louis XVI in 1793 by a transition between the power of the ancienne regime to new political forces. Into the following century across Europe the emerging power of merchant and market increasingly swept aside the old aristocracy in the shaping of the politics, economics and infrastructure of what, in a process evolving from the Treaty of Westphalia (1648) had emerged as 'sovereign' nation states. Improving systems of transportation facilitated a process of ever intensifying trade across and between states was involving monarchs, peasants, artisans, merchants and financiers alike.[^For more on this see Camilleri and Falk, '/Worlds in Transition/', pp. 134-44.^] Ever more efficient processes of printing and dissemination facilitated production and dissemination of ideas. A period of comparative peace between nations in the late C18 was marked by a revolution in agricultural production. But this was just one way in which a synergy between scientific and technological innovation was finding purchase within transforming systems of production, commerce, governance and more broadly lived experience. In addition, science was beginning to be harnessed to actual production. Steam replaced horse, and then from the mid C-19 to the mid-C20, electrical networks spread across Europe and then much of the rest of the modern world allowing the introduction of many new technologies.

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->In the period that followed, science began its victorious march on a broad front even into those distant realms of nature which could be entered only by technology.... Even the phrase 'description of nature' lost more and more of its original significance of a living and meaningful account of nature. Increasingly it came to mean the mathematical description of nature.[^Werner Heisenberg, //The Physicist's Conception of Nature//, Hutchinson Scientific and Technical, London, 1958, p. 11.^]

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->In the period that followed, science began its victorious march on a broad front even into those distant realms of nature which could be entered only by technology.... Even the phrase 'description of nature' lost more and more of its original significance of a living and meaningful account of nature. Increasingly it came to mean the mathematical description of nature.[^Werner Heisenberg, '/The Physicist's Conception of Nature/', Hutchinson Scientific and Technical, London, 1958, p. 11.^]

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Ready reckoners were in widespread use by shopkeepers and many others from the C17 on. They presented tables of precalculated results of many kinds of multiplication. These included the much needed calculations of the price for multiples of an item for sale, or per unit of weight. They could also be used to look up the calculations needed for wages and interest.[^see Bruce O.B. Williams and Roger G. Johnson, "Ready Reckoners", //IEEE Annals of the History of Computing//, October-December, 2005, pp. 64-80.^] One such, from 1892 is "Ropp's Commercial Calculator: a practical arithmetic for practical purposes, containing a complete system of useful, accurate, and convenient tables, together with simple, short, and practical methods for rapid calculation", published in the US and used widely into the early C20. This one, shown below(:if equal {Site.PrintBook$:PSW} "True":) in FIG(Ropp)(:ifend:), is the 1892 World's Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.

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Ready reckoners were in widespread use by shopkeepers and many others from the C17 on. They presented tables of precalculated results of many kinds of multiplication. These included the much needed calculations of the price for multiples of an item for sale, or per unit of weight. They could also be used to look up the calculations needed for wages and interest.[^see Bruce O.B. Williams and Roger G. Johnson, "Ready Reckoners", '/IEEE Annals of the History of Computing/', October-December, 2005, pp. 64-80.^] One such, from 1892 is "Ropp's Commercial Calculator: a practical arithmetic for practical purposes, containing a complete system of useful, accurate, and convenient tables, together with simple, short, and practical methods for rapid calculation", published in the US and used widely into the early C20. This one, shown below(:if equal {Site.PrintBook$:PSW} "True":) in FIG(Ropp)(:ifend:), is the 1892 World's Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.

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->By the 1860's, the favorite device for lessening the work of the computer (human), the mathematical table, had become an object whose dizzying rows of printed figures would fascinate the Victorian public. These tables displayed the limitless fecundity of numbers, and transformed them into a commodity that would bring the power of calculation within the reach of the ordinary citizen. The centrality of tables of numbers and calculation to mid-Victorian life was famously portrayed by Charles Dickens' character Thomas Gradgrind, who always had a rule and a pair of scales and the multiplication table in his pocket.[^M.N. Wise, //The Values of Precision//, Princeton University Press, USA, 1995, p. 318.^]

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->By the 1860's, the favorite device for lessening the work of the computer (human), the mathematical table, had become an object whose dizzying rows of printed figures would fascinate the Victorian public. These tables displayed the limitless fecundity of numbers, and transformed them into a commodity that would bring the power of calculation within the reach of the ordinary citizen. The centrality of tables of numbers and calculation to mid-Victorian life was famously portrayed by Charles Dickens' character Thomas Gradgrind, who always had a rule and a pair of scales and the multiplication table in his pocket.[^M.N. Wise, '/The Values of Precision/', Princeton University Press, USA, 1995, p. 318.^]

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*something else that can be moved (for example, although it was barely used,[^An exception is the ingenious MONIAC hydraulic computer used to demonstrate macroeconomic theory. See for example, Anna Corkhill 'A superb explanatory device' //University of Melbourne Collections//, issue 10, June 2012^] the height of columns of water).

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*something else that can be moved (for example, although it was barely used,[^An exception is the ingenious MONIAC hydraulic computer used to demonstrate macroeconomic theory. See for example, Anna Corkhill 'A superb explanatory device' '/University of Melbourne Collections/', issue 10, June 2012^] the height of columns of water).

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Popular though some of these were as they became cheaper and more accessible not only to shopkeepers but ordinary citizens who might value the assistance they offered, for example in their role as taxpayers,[^See for example, A.P. Kidwell, "'Yours for Improvement'—The Adding Machines of Chicago, 1884–1930", //IEEE Annals of the History of Computing//, July-September, 2001, pp. 3-6.^] they suffered from the same problems of clumsy input and slow operation that afflicted the simple linear machines. Some such as the Adall could only add, others had no provision for zeroing, and all were slow to use. Further, such adders, whilst simple in concept and cheap to manufacture, were so slow to use for repetitive calculation that they were virtually useless for the key arithmetic operations of multiplication and division. A quick method repeated addition and subtraction was required at minimum to achieve these other two functions. That required a more expensive approach and a much more elaborate machine, the first commercial variant of which was designed and sold as the "Arithmometer" by Thomas de Colmar.

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Popular though some of these were as they became cheaper and more accessible not only to shopkeepers but ordinary citizens who might value the assistance they offered, for example in their role as taxpayers,[^See for example, A.P. Kidwell, "'Yours for Improvement'—The Adding Machines of Chicago, 1884–1930", '/IEEE Annals of the History of Computing/', July-September, 2001, pp. 3-6.^] they suffered from the same problems of clumsy input and slow operation that afflicted the simple linear machines. Some such as the Adall could only add, others had no provision for zeroing, and all were slow to use. Further, such adders, whilst simple in concept and cheap to manufacture, were so slow to use for repetitive calculation that they were virtually useless for the key arithmetic operations of multiplication and division. A quick method repeated addition and subtraction was required at minimum to achieve these other two functions. That required a more expensive approach and a much more elaborate machine, the first commercial variant of which was designed and sold as the "Arithmometer" by Thomas de Colmar.

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Thomas de Colmar first made public his design for a calculating machine capable of doing all four functions (addition, subtraction, multiplication and division) when he was granted a patent for it in 1820.[^Patent no. 1420, 18 November 1820^]. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.[^For the most authoritative website on the Thomas de Colmar machines and history see Valéry Monier's magisterial site [[http://www.arithmometre.org]], viewed 20 July 2013.^] The first design consisted of four step drums (along the lines invented by Leibniz, but not necessarily based on having ever heard of, let alone seen the internal mechanism of Leibniz's invention[^see Friedrich W. Kistermann, "When Could Anyone Have Seen Leibniz's Stepped Wheel?", //IEEE Annals of the History of Computing//, Volume 21, Number 2, 1999, pp. 68-72. However, as Stephen Johnston (see reference below) points out, images of Leibniz's machine were available from the late C18, see for example 1744 engraving in Annegret Kehrbaum and Bernhard Korte, //Calculi: Bilder des Rechnens einst und heute (Images of Computing in Olden and Modern Times)//, Opladen, 1995, p. 61.^]).

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Thomas de Colmar first made public his design for a calculating machine capable of doing all four functions (addition, subtraction, multiplication and division) when he was granted a patent for it in 1820.[^Patent no. 1420, 18 November 1820^]. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.[^For the most authoritative website on the Thomas de Colmar machines and history see Valéry Monier's magisterial site [[http://www.arithmometre.org]], viewed 20 July 2013.^] The first design consisted of four step drums (along the lines invented by Leibniz, but not necessarily based on having ever heard of, let alone seen the internal mechanism of Leibniz's invention[^see Friedrich W. Kistermann, "When Could Anyone Have Seen Leibniz's Stepped Wheel?", '/IEEE Annals of the History of Computing/', Volume 21, Number 2, 1999, pp. 68-72. However, as Stephen Johnston (see reference below) points out, images of Leibniz's machine were available from the late C18, see for example 1744 engraving in Annegret Kehrbaum and Bernhard Korte, '/Calculi: Bilder des Rechnens einst und heute (Images of Computing in Olden and Modern Times)/', Opladen, 1995, p. 61.^]).

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%center%1862: Diagram of the Thomas de Colmar arithmometer mechanism.[^ Franz Reuleaux, //Die Thomas'sche Rechenmaschine//, Freiberg, 1862 reproduced in Reuleaux's article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^]\\ (Click on the image for an enlargement.)\\(Source: Museum of the History of Science, University of Oxford.)

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%center%1862: Diagram of the Thomas de Colmar arithmometer mechanism.[^ Franz Reuleaux, '/Die Thomas'sche Rechenmaschine/', Freiberg, 1862 reproduced in Reuleaux's article in '/Der Civilingenieur/', 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^]\\ (Click on the image for an enlargement.)\\(Source: Museum of the History of Science, University of Oxford.)

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diagram.[^ Franz Reuleaux, //Die Thomas'sche Rechenmaschine//, Freiberg, 1862 reproduced in Reuleaux's article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^] \\(Source: Museum of the History of Science, University of Oxford.)

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diagram.[^ Franz Reuleaux, '/Die Thomas'sche Rechenmaschine/', Freiberg, 1862 reproduced in Reuleaux's article in '/Der Civilingenieur/', 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^] \\(Source: Museum of the History of Science, University of Oxford.)

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As with previous calculating machines that commercial success of this machine was far from assured. The aesthetics of the design still reflects the high status market where it could have become just another prestigious mathematical machine in the cabinets of curiosities of those of elevated status. The somewhat circuitous route to that later success is described by Stephen Johnston.[^Stephen Johnston, "Making the arithmometer count", //Bulletin of the Scientific Instrument Society//, Volume 52, 1997, pp. 12-21.^] As Johnston notes, Thomas did not of course make these early machines. The first of his machines to survive was made by in Paris by Devrine, as usual a local clock (and instrument) maker.

Thomas de Colmar himself was the director of an insurance company. In the 1820s the insurance industry was rapidly expanding as a consequence of free trade and the transport revolution, and France had become international centres of the industry.[^Peter Borscheid, "Europe: Overview", in Peter Borscheid and Niels Vigo Haueter (eds), //World Insurance: The Evolution of a Global Risk Network//, Oxford University Press, Oxford, 2012, p. 39.^] The likely consequent intensification of work no doubt galvanised Thomas's interest in finding an efficient way of handling multiple calculations. But given his responsibilities in an intense commercial environment is unlikely that he would have been able to spend all or even a great deal of his time on designing and building more arithmometers over the next several decades. Indeed it was not until several decades later that, in 1844, the arithmometer, very much re-designed, appeared at a French national exhibition. There it could be found amongst precision instruments in a category of 'diverse measures, counters and calculating machines'.[^ibid.^] Johnston thus argues that far from being a lone pioneer, the machines of Thomas were in competition (and regarded initially as a poor second) to others. However, over a half century, the machines of Thomas, as they evolved, prevailed.[^As cited by Johnston, Jean Marguin, //Histoire des instruments et machines à calculer//, Paris, 1994, p. 111: 'Pendant un demi-siècle, la machine y régna seule.'^] Johnston notes that to achieve this "Thomas campaigned both through the press and in commissioned publications. He also engaged in the rituals of patronage, rituals that we might more readily associate with the decoratively elaborate calculating machines of the 18th century."[^Johnston, "Making the arithmometer count".^] However, the design of the Thomas machine was sufficiently beautifully executed to make it an appropriate gift to persons of high standing, a property essential to its successful promotion.

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As with previous calculating machines that commercial success of this machine was far from assured. The aesthetics of the design still reflects the high status market where it could have become just another prestigious mathematical machine in the cabinets of curiosities of those of elevated status. The somewhat circuitous route to that later success is described by Stephen Johnston.[^Stephen Johnston, "Making the arithmometer count", '/Bulletin of the Scientific Instrument Society/', Volume 52, 1997, pp. 12-21.^] As Johnston notes, Thomas did not of course make these early machines. The first of his machines to survive was made by in Paris by Devrine, as usual a local clock (and instrument) maker.

Thomas de Colmar himself was the director of an insurance company. In the 1820s the insurance industry was rapidly expanding as a consequence of free trade and the transport revolution, and France had become international centres of the industry.[^Peter Borscheid, "Europe: Overview", in Peter Borscheid and Niels Vigo Haueter (eds), '/World Insurance: The Evolution of a Global Risk Network/', Oxford University Press, Oxford, 2012, p. 39.^] The likely consequent intensification of work no doubt galvanised Thomas's interest in finding an efficient way of handling multiple calculations. But given his responsibilities in an intense commercial environment is unlikely that he would have been able to spend all or even a great deal of his time on designing and building more arithmometers over the next several decades. Indeed it was not until several decades later that, in 1844, the arithmometer, very much re-designed, appeared at a French national exhibition. There it could be found amongst precision instruments in a category of 'diverse measures, counters and calculating machines'.[^ibid.^] Johnston thus argues that far from being a lone pioneer, the machines of Thomas were in competition (and regarded initially as a poor second) to others. However, over a half century, the machines of Thomas, as they evolved, prevailed.[^As cited by Johnston, Jean Marguin, '/Histoire des instruments et machines à calculer/', Paris, 1994, p. 111: 'Pendant un demi-siècle, la machine y régna seule.'^] Johnston notes that to achieve this "Thomas campaigned both through the press and in commissioned publications. He also engaged in the rituals of patronage, rituals that we might more readily associate with the decoratively elaborate calculating machines of the 18th century."[^Johnston, "Making the arithmometer count".^] However, the design of the Thomas machine was sufficiently beautifully executed to make it an appropriate gift to persons of high standing, a property essential to its successful promotion.

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The above three arithmometers demonstrate the sorts of improvements to the basic arithmometer design which now emerged. The first, a TIM ("Time is Money" ) arithmometer manufactured by Ludwig Spitz and Co. of Berlin-Tempelhof in 1909 was greatly strengthened from the Thomas design to create a much more robust and reliable machine. First produced in a wooden box it was later made much stronger by installing it in a cast iron frame which held all parts rigidly.[^See Ernst Martin, //The Calculating Machines (Die Rechenmaschinen): Their History and Development//, ed. and trs. by Peggy Aldridge Kidwell and Michael R. Williams, MIT Press, Mass., 1992, p. 191–4^] Beginning a change in style that would be emulated in many other machines the brass panels were now enamelled black consistent with the management, industrial and commercial settings where it was intended to find its market. The other two machines in this set would also originally have had a similar black finish. (Unfortunately, there was a tendency in the late C20 to "take the machines back to brass" in the same way that in the 1960s there was a trend to remove the original finish from wood on vintage furniture, and plaster from brick walls in old houses.)[[<<]]

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The above three arithmometers demonstrate the sorts of improvements to the basic arithmometer design which now emerged. The first, a TIM ("Time is Money" ) arithmometer manufactured by Ludwig Spitz and Co. of Berlin-Tempelhof in 1909 was greatly strengthened from the Thomas design to create a much more robust and reliable machine. First produced in a wooden box it was later made much stronger by installing it in a cast iron frame which held all parts rigidly.[^See Ernst Martin, '/The Calculating Machines (Die Rechenmaschinen): Their History and Development/', ed. and trs. by Peggy Aldridge Kidwell and Michael R. Williams, MIT Press, Mass., 1992, p. 191–4^] Beginning a change in style that would be emulated in many other machines the brass panels were now enamelled black consistent with the management, industrial and commercial settings where it was intended to find its market. The other two machines in this set would also originally have had a similar black finish. (Unfortunately, there was a tendency in the late C20 to "take the machines back to brass" in the same way that in the 1960s there was a trend to remove the original finish from wood on vintage furniture, and plaster from brick walls in old houses.)[[<<]]

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The above principle was incorporated into a MADAS arithmometer, developed by Erwin Janz and manufactured by Egli in Zurich, starting in 1913. The acronym MADAS was short for "Multiplication, Addition, Division - Automatically, Substraction"). The achievement of an entirely automatic division process - the first ever for an arithmometer style calculator. In this collection there is a MADAS IX Maxima calculator (produced in 1917), an ambitious machine also in that it could accept 9 digits, up to one thousand million, as input and could display 16 digits (representing numbers up to ten thousand trillion) in its results register. Two MADAS models were produced and by 1920 about 1,000 were being produced with some 7,000 having been sold from countries as wide apart as Europe and Australia.[^Martin Reese, Hamburg, //55 erfolgreiche Jahre: MADAS-Rechenautomaten aus der Schweiz 1913 - 1968//, http://www.rechnerlexikon.de/files/MADAS—8-2010.pdf, viewed 18 February 2012.^]

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The above principle was incorporated into a MADAS arithmometer, developed by Erwin Janz and manufactured by Egli in Zurich, starting in 1913. The acronym MADAS was short for "Multiplication, Addition, Division - Automatically, Substraction"). The achievement of an entirely automatic division process - the first ever for an arithmometer style calculator. In this collection there is a MADAS IX Maxima calculator (produced in 1917), an ambitious machine also in that it could accept 9 digits, up to one thousand million, as input and could display 16 digits (representing numbers up to ten thousand trillion) in its results register. Two MADAS models were produced and by 1920 about 1,000 were being produced with some 7,000 having been sold from countries as wide apart as Europe and Australia.[^Martin Reese, Hamburg, '/55 erfolgreiche Jahre: MADAS-Rechenautomaten aus der Schweiz 1913 - 1968/', http://www.rechnerlexikon.de/files/MADAS—8-2010.pdf, viewed 18 February 2012.^]

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The pinwheel calculator was developed as an improvement on the arithmometer more or less simultaneously in Russia in 1878 by Swedish engineer Willgodt Theophil Odhner (1845-1905) and in the US in 1874, by Frank Stephen Baldwin (1838-1925). Although they worked independently of each there machines were so similar that the 'Ohdner' or 'Baldwin' machine became more or less interchangeable terms.[^Diana H. Hook and Jeremy M. Norman, //Origins of Cyberspace//, Novato, California, 2002, p. 255.^]. The designs utilised a clever 'counting gear' in which the number of teeth protruding could be adjusted by sliders (and later a push-down keyboard). A pinwheel and the internal mechanism (with some pinwheels removed) from a Walther pinwheel calculator in this collection is shown (:if equal {Site.PrintBook$:PSW} "True":)in TAB(DemoPinwheels)(:ifend:) below.

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The pinwheel calculator was developed as an improvement on the arithmometer more or less simultaneously in Russia in 1878 by Swedish engineer Willgodt Theophil Odhner (1845-1905) and in the US in 1874, by Frank Stephen Baldwin (1838-1925). Although they worked independently of each there machines were so similar that the 'Ohdner' or 'Baldwin' machine became more or less interchangeable terms.[^Diana H. Hook and Jeremy M. Norman, '/Origins of Cyberspace/', Novato, California, 2002, p. 255.^]. The designs utilised a clever 'counting gear' in which the number of teeth protruding could be adjusted by sliders (and later a push-down keyboard). A pinwheel and the internal mechanism (with some pinwheels removed) from a Walther pinwheel calculator in this collection is shown (:if equal {Site.PrintBook$:PSW} "True":)in TAB(DemoPinwheels)(:ifend:) below.

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Ohdner began manufacture of his machines in 1886 under the name "Original Ohdner" but sold his rights also to Grimme, Natalis and Co., Braunsweig, who began marketing the machines under the name Brunsviga.[^ibid^] In turn they also licenced agents such as Schuster to sell them. Reflecting a later start these machines were made from a wider range of materials than the arithmometers, including iron and nickel alloys as well as brass and steel. The Brunsviga was a quick success selling 20,000 units between 1892 and 1912.[[^Hook and Norman, //Origins of Cyberspace//, p. 255.^] Below (:if equal {Site.PrintBook$:PSW} "True":)in FIG(Brunsviga)(:ifend:) is the very early Brunsviga-Schuster pinwheel calculator from 1896, followed (:if equal {Site.PrintBook$:PSW} "True":)in TAB(PinwheelCalcs)(:ifend:) by the other pinwheel calculators in this collection.

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Ohdner began manufacture of his machines in 1886 under the name "Original Ohdner" but sold his rights also to Grimme, Natalis and Co., Braunsweig, who began marketing the machines under the name Brunsviga.[^ibid^] In turn they also licenced agents such as Schuster to sell them. Reflecting a later start these machines were made from a wider range of materials than the arithmometers, including iron and nickel alloys as well as brass and steel. The Brunsviga was a quick success selling 20,000 units between 1892 and 1912.[[^Hook and Norman, '/Origins of Cyberspace/', p. 255.^] Below (:if equal {Site.PrintBook$:PSW} "True":)in FIG(Brunsviga)(:ifend:) is the very early Brunsviga-Schuster pinwheel calculator from 1896, followed (:if equal {Site.PrintBook$:PSW} "True":)in TAB(PinwheelCalcs)(:ifend:) by the other pinwheel calculators in this collection.

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There were of course many variations on this theme. These included the "Frieden Wheel" which managed to achieve the same effect as the pinwheel but through simply a nicely timed use of a cam. More of that sort of mechanical detail for all the machines referred to here can be found in the classic book by Martin,[^Martin, //The Calculating Machines//^] and the marvellous websites of Rechnerlexikon[^[[http://www.rechnerlexikon.de/en/artikel/Spezial:Allpages]]^] and John Wolff[^[[http://home.vicnet.net.au/~wolff/calculators/]]^].

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There were of course many variations on this theme. These included the "Frieden Wheel" which managed to achieve the same effect as the pinwheel but through simply a nicely timed use of a cam. More of that sort of mechanical detail for all the machines referred to here can be found in the classic book by Martin,[^Martin, '/The Calculating Machines/'^] and the marvellous websites of Rechnerlexikon[^[[http://www.rechnerlexikon.de/en/artikel/Spezial:Allpages]]^] and John Wolff[^[[http://home.vicnet.net.au/~wolff/calculators/]]^].

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Felt first demonstrated this famously with a model constructed in a wooden macaroni box in 1885. He patented his design in 1887 and began selling it from his manufacturing company in Chicago. In 1890 he gave it the name "the Comptometer" and energetically promoted it.[^//Origins of Cyberspace, p. 244.^] Below (:if equal {Site.PrintBook$:PSW} "True":)in FIG(Woodie)(:ifend:) is the Comptometer in this collection - an example from 1896 of the first model, cased in wood, and one of the 40 oldest known to still be in existence. Remarkably with a drop of oil on the springs it still works perfectly.

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Felt first demonstrated this famously with a model constructed in a wooden macaroni box in 1885. He patented his design in 1887 and began selling it from his manufacturing company in Chicago. In 1890 he gave it the name "the Comptometer" and energetically promoted it.[^/'Origins of Cyberspace, p. 244.^] Below (:if equal {Site.PrintBook$:PSW} "True":)in FIG(Woodie)(:ifend:) is the Comptometer in this collection - an example from 1896 of the first model, cased in wood, and one of the 40 oldest known to still be in existence. Remarkably with a drop of oil on the springs it still works perfectly.

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->Mr. Munich said: "See, Herzstark, I understand you've been working on a new thing, a small calculating machine. Do you know, I can give you a tip. We will allow you to make and draw everything. If it is really worth something, then we will give it to the Fuhrer as a present after we win the war. Then, surely, you will be made an Aryan." For me, that was the first time I thought to myself, my God, if you do this, you can extend your life. And then and there I started to draw the CURTA, the way I had imagined it.[^//An Interview with Curt Herzstark//, OH 140, conducted by Erwin Tomash on 10-11 September 1987, Nendeln, Liechtenstein, (English Translation).^]

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->Mr. Munich said: "See, Herzstark, I understand you've been working on a new thing, a small calculating machine. Do you know, I can give you a tip. We will allow you to make and draw everything. If it is really worth something, then we will give it to the Fuhrer as a present after we win the war. Then, surely, you will be made an Aryan." For me, that was the first time I thought to myself, my God, if you do this, you can extend your life. And then and there I started to draw the CURTA, the way I had imagined it.[^/'An Interview with Curt Herzstark/', OH 140, conducted by Erwin Tomash on 10-11 September 1987, Nendeln, Liechtenstein, (English Translation).^]

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These machines thus constitute the pinacle reached in the development of the personal hand-operated mechanical digital calculator - able to carry out all four functions by means of a crank operated machine of exquisite miniaturised workmanship and design. Production ceased in November 1970 although sales continued through 1973. At least 150,000 of the various calculator models were made.[^//An Interview with Curt Herzstark//^] For more on the Curta see the marvellous collection of documents and simulations at //The Curta Caclulator Page//.[^//The CURTA Calculator Page//, [[http://www.vcalc.net/cu.htm]], viewed 25 July 2013.^]

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These machines thus constitute the pinacle reached in the development of the personal hand-operated mechanical digital calculator - able to carry out all four functions by means of a crank operated machine of exquisite miniaturised workmanship and design. Production ceased in November 1970 although sales continued through 1973. At least 150,000 of the various calculator models were made.[^/'An Interview with Curt Herzstark/'^] For more on the Curta see the marvellous collection of documents and simulations at '/The Curta Caclulator Page/'.[^/'The CURTA Calculator Page/', [[http://www.vcalc.net/cu.htm]], viewed 25 July 2013.^]

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%center% Leon Bollée Calculating Machine "A New Calculating Machine of very General Applicability"\\//The Manufacturer and Builder 1890//[^1890: Leon Bollée Calculating Machine, "A New Calculating Machine of very General Applicability", //The Manufacturer and Builder//, July 1890, p. 156. Original print article.^]\\

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%center% Leon Bollée Calculating Machine "A New Calculating Machine of very General Applicability"\\/'The Manufacturer and Builder 1890/'[^1890: Leon Bollée Calculating Machine, "A New Calculating Machine of very General Applicability", '/The Manufacturer and Builder/', July 1890, p. 156. Original print article.^]\\

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//The Manufacturer and Builder 1890//[^1890: Leon Bollée Calculating Machine, "A New Calculating Machine of very General Applicability", //The Manufacturer and Builder//, July 1890, p. 156. Original print article.^]\\

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/'The Manufacturer and Builder 1890/'[^1890: Leon Bollée Calculating Machine, "A New Calculating Machine of very General Applicability", '/The Manufacturer and Builder/', July 1890, p. 156. Original print article.^]\\

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Manufactured by H.W. Egli, some 4,655 Millionaires were sold between 1895 and 1935[^//Origins of Cyberspace// p. 242.^] at a 1912 price of about US$480[^Price list in Edmonds Collins, //The Millionaire Calculating Machine//, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. See also price of US$500 at 1914 prices given by Luc de Brabandere cited in B.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, published in //Slide Rule and Calculation monographs//, Slide Rule Circle, UK, 2002, pp. 59-98.^] (about $11,700 in 2013 US dollars[^Calculated using the [[http://www.measuringworth.com]] calculator on 24 July 2013^]). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,[^Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant).^] and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones. The machine still operates reliably after more than 100 years.

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Manufactured by H.W. Egli, some 4,655 Millionaires were sold between 1895 and 1935[^/'Origins of Cyberspace/' p. 242.^] at a 1912 price of about US$480[^Price list in Edmonds Collins, '/The Millionaire Calculating Machine/', pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. See also price of US$500 at 1914 prices given by Luc de Brabandere cited in B.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, published in '/Slide Rule and Calculation monographs/', Slide Rule Circle, UK, 2002, pp. 59-98.^] (about $11,700 in 2013 US dollars[^Calculated using the [[http://www.measuringworth.com]] calculator on 24 July 2013^]). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,[^Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant).^] and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones. The machine still operates reliably after more than 100 years.

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Samuel Herzstark (1867-1937), the father of Curt Herzstark who built the Curta, also was a pioneer in calculator construction and together with Gustav Perger established the Austria Calculator Machines Manufacturing Company in Vienna in 1905-6. In an interview in 1987 Curt Herzstark reports that in 1907 Samuel became the first to attach an electric motor to an arithmometer, which he equipped also with a keyboard. Curt also notes that this machine was equipped with automatic division.[^//An Interview with Curt Herzstark//, OH 140, conducted by Erwin Tomash on 10-11 September 1987, Nendeln, Liechtenstein, (English Translation).^] However after the 1914-18 War Herzstark returned to a demolished business. He restarted with a combination of importing and selling calculators from other manufacturers, assembling old stock of his own design, and then as the business built up designing new machines. Below (:if equal {Site.PrintBook$:PSW} "True":)in FIG(Herzstark)(:ifend:) is an arithmometer in this collection branded by Samuel Herzstark from 1929. It is actually a Badenia (manufactured by the German Company Math. Bauerle in the Black Forest) which Herzstark was at that time re-badging and selling.

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Samuel Herzstark (1867-1937), the father of Curt Herzstark who built the Curta, also was a pioneer in calculator construction and together with Gustav Perger established the Austria Calculator Machines Manufacturing Company in Vienna in 1905-6. In an interview in 1987 Curt Herzstark reports that in 1907 Samuel became the first to attach an electric motor to an arithmometer, which he equipped also with a keyboard. Curt also notes that this machine was equipped with automatic division.[^/'An Interview with Curt Herzstark/', OH 140, conducted by Erwin Tomash on 10-11 September 1987, Nendeln, Liechtenstein, (English Translation).^] However after the 1914-18 War Herzstark returned to a demolished business. He restarted with a combination of importing and selling calculators from other manufacturers, assembling old stock of his own design, and then as the business built up designing new machines. Below (:if equal {Site.PrintBook$:PSW} "True":)in FIG(Herzstark)(:ifend:) is an arithmometer in this collection branded by Samuel Herzstark from 1929. It is actually a Badenia (manufactured by the German Company Math. Bauerle in the Black Forest) which Herzstark was at that time re-badging and selling.

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->M. Thomas's arithmometer may be used without the least trouble or possibility of error, not only for addition, subtraction, multiplication, and division, but also for much more complex operations, such as the extraction of the square root, involution, the resolution of triangles, etc...A multiplication of eight figures by eight others is made in eighteen seconds; a division of sixteen figures by eight figures, in twenty four seconds; and in one minute and a quarter one can extract the square root of sixteen figures, and also prove the accuracy of the calculation...[^//The Gentleman's Magazine//, Volume 202, "The monthly intelligencer", January 1857, p. 100, [[http://books.google.fr/books?id=Rf0IAAAAIAAJ&pg=PA100&dq=arithmometer&as_brr=1#v=onepage&q=arithmometer&f=false]], viewed 23 July 2013.^]

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->M. Thomas's arithmometer may be used without the least trouble or possibility of error, not only for addition, subtraction, multiplication, and division, but also for much more complex operations, such as the extraction of the square root, involution, the resolution of triangles, etc...A multiplication of eight figures by eight others is made in eighteen seconds; a division of sixteen figures by eight figures, in twenty four seconds; and in one minute and a quarter one can extract the square root of sixteen figures, and also prove the accuracy of the calculation...[^/'The Gentleman's Magazine/', Volume 202, "The monthly intelligencer", January 1857, p. 100, [[http://books.google.fr/books?id=Rf0IAAAAIAAJ&pg=PA100&dq=arithmometer&as_brr=1#v=onepage&q=arithmometer&f=false]], viewed 23 July 2013.^]

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The history of the technology has been one of a competition between old habits, preparedness to learn new technique, and perceived need to do so. It is not easy to throw off old successful technique and replace it with the hard acquired new approaches. Part of the success of a technological innovation is thus likely to depend on the extent to which social forces may encourage through benefit, or require through necessity, the new learning required to use it. Most new inventions are of course promoted with claims that the benefits for user or employer will outstrip the costs of change. Not infrequently these benefits might be initially overstated. Thus for the arithmometer the //Gentleman's Magazine// claimed:

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The history of the technology has been one of a competition between old habits, preparedness to learn new technique, and perceived need to do so. It is not easy to throw off old successful technique and replace it with the hard acquired new approaches. Part of the success of a technological innovation is thus likely to depend on the extent to which social forces may encourage through benefit, or require through necessity, the new learning required to use it. Most new inventions are of course promoted with claims that the benefits for user or employer will outstrip the costs of change. Not infrequently these benefits might be initially overstated. Thus for the arithmometer the '/Gentleman's Magazine/' claimed:

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These overblown claims are reminiscent of similar claims for their inventions by Pascal (with this machine the user can do with ease, "without effort of memory" and "without even thinking of it", every possible arithmetic operation[^Pascal, ligé de retenir ou d'emprunter les nombres nécessaires, et combien d'erreurs se glissent dans ces rétentions et emprunts, à mois d'une très longue habitude et, en outre, d'une attention profonde et qui fatigue l'esprit en peu de temps. Cette machine délivre celui qui opère par elle de cette vexation; il suffit qu'il ait le jugement, elle le relève du défaut de la mémoire; et, sans rien retenir ni emprunter, elle fait d'elle-même ce qu'il désire, sans même qu'il y pense." p. 337^]) and Moreland (allowing addition and subtraction "without charging the memory or disturbing the mind[^S. Moreland, //A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence// 1672, title page.^]). They show the hope, that the mental activity could be replaced by the machine. But in reality, for all of these machines it was not just a question of the high cost of obtaining it, but the learning and practice required to use it.

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These overblown claims are reminiscent of similar claims for their inventions by Pascal (with this machine the user can do with ease, "without effort of memory" and "without even thinking of it", every possible arithmetic operation[^Pascal, ligé de retenir ou d'emprunter les nombres nécessaires, et combien d'erreurs se glissent dans ces rétentions et emprunts, à mois d'une très longue habitude et, en outre, d'une attention profonde et qui fatigue l'esprit en peu de temps. Cette machine délivre celui qui opère par elle de cette vexation; il suffit qu'il ait le jugement, elle le relève du défaut de la mémoire; et, sans rien retenir ni emprunter, elle fait d'elle-même ce qu'il désire, sans même qu'il y pense." p. 337^]) and Moreland (allowing addition and subtraction "without charging the memory or disturbing the mind[^S. Moreland, '/A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence/' 1672, title page.^]). They show the hope, that the mental activity could be replaced by the machine. But in reality, for all of these machines it was not just a question of the high cost of obtaining it, but the learning and practice required to use it.

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%center% %height=250px%%id=Schickardreminder% http://meta-studies.net/pmwiki/uploads/~~Schickard1H250~~.jpg"Schickard's Calculator"|1623: Recreation of Wilhelm Schickard's calculating machine\\

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%center% %height=250px%%id=Schickardreminder% http://meta-studies.net/pmwiki/uploads/Schickard1W300_1.jpg"Schickard's Calculator"|1623: Recreation of Wilhelm Schickard's calculating machine\\

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The Pascaline and Moreland's inventions may have served their inventors in range of ways, but it was not ~~in finding~~ a broad market~~. The learning required to use it was to~~ great, and the benefit to little in relation to existing technique. As noted earlier, even Thomas de Colmar's arithmometer and its early successors remained on the edge of this balance. Adding and subtracting could be quickly achieved, but then it was very expensive and not necessarily any faster than doing the job on paper. The appeal thus remained quite limited, not only because of the economic price to be paid (which was high), but also the cost of acquiring the necessary embodied skill to render them genuinely superior to existing customary practice.

What goes for the Thomas arithmometer, in this sense, goes also for every calculational technology, from counting on one's fingers, to the use of calculi on a counting board, or calculating with the abacus, the Pascaline, the Millionaire, logarithms, the MADAS most sophisticated mechanical calculator. Indeed even the HP-35 and HP-45 required a facility to do arithmetic backwards from the usual by its reliance on a method known as Reverse Polish. Thus for each technological development, whether Troncet or Omega, for it to find successful users each needed to be understood, and not only intellectually, but equally importantly, the potential users needed to be able to incorporate it into their embodied capacity, with each required gesture becoming so automatic as to require no or little thought.

The achievement of the late mechanical calculators (such as the MADAS and the Euklid-Mercedes) was that they did greatly simplify what what needed to be learned by their operators to achieve efficiently all four arithmetic operations but they did so still at considerable economic cost. ~~The Comptometer was really best for addition and (with practice) subtraction. With its key input it was fast, and its simple design was amenable to cheaper construction~~ and ~~mass-production. So it found a different~~ and ~~expanded market in the rapidly expanding commercial~~ and ~~government organisations of~~ the ~~C20. It has been said and is probably true that its inventors~~ and ~~promoters, Felt and Tarrant, were probably the first people in the world to become truly wealthy from~~ the invention, production and sale of calculators.

In the ~~above sense the history~~ of ~~calculation technology can be characterised not so much as the progress of mechanical invention, as it is sometimes presented, but as a more subtle evolving relationship between mind~~, body and material artefacts or put another way as interaction of of evolving technology, history, culture, mental skills, social capacities and aspirations. The search for a successful innovation was a strange mix of finding a place where these aspects converged to make the innovation seem useful, and at the same time not only economically but also culturally accessible. The requirement to change was not just set in the machine, but also in the humans who made up the society.

The final conquest of the electronic calculator occurred when literacy, design, familiarity, cost and perceived need coincided to sweep all else before it. Never had the market been more prevalent in the negotiation of daily life. Science and technology now dominated every corner of ~~the developed world~~ and was making rapid inroads elsewhere. Literacy was at its highest in the developed world with arithmetic education now a requirement for every child in the extended period of compulsory schooling. Money promised to free time and technology was now widely accepted as being the answer to drudgery. Further still, there was a social acceptance of life-long change, and an emerging concept of the desirability of 'life-long learning'. The new consumer calculators were increasingly cheap, required little knowledge to use, displaced the mental effort of recall of multiplication tables and mental and written arithmetic. Printers attached to them produced now permanent records. And the whole increasingly seamlessly fitted a world which would soon be interconnected through computers and telecommunications into an ever more pervasive communications web. Calculators had not only reached a desired end. They also had ~~found their moment when that~~ end was widely required.

One might ask if there is any lesson in this for the future. ~~Clearly the technology of calculation is now passing not only~~ the first but perhaps even towards the second vanishing point where it converges and merges with other electronic devices which themselves have become so much part of the habitude of daily life, especially in the developed world, that their presence is sinking into the invisibility of the routine environment. But in doing so much of habit had to be relearned, and in the consequence human thinking, as well as collective culture has transformed.

This is of course a history of one area of innovation. So it may have some relevance to other areas of ~~innovation in the world in which we now live. It is perhaps appropriate to remember that humans have reached the point where there~~ innovation is actually destabilising the physical world in which they live - a situation unimaginable for most of the time in which the developments discussed here have taken place. But it is the case that humans are now challenged with the requirement to achieve an unprecedented level of innovation if the planet is to remain stable. The story of innovation in calculators tells us that whilst the time may be ripe for us to accept a great deal of change, it will require re-learning to be comfortable with the many innovations that will be needed to achieve it. Getting there will require people to re-learn and reshape many attitudes, hidden assumptions and habitual ways of living. In seeking to make those changes, we might reflect on the many challenges overcome in the simpler long history of how humans have learned to calculate, and what that means for the learning and innovation that will now be required.

to:

The Pascaline and Moreland's inventions may have served their inventors in a range of ways, but it was not necessarily to find a broad market for them. The learning required to use it was too great, and the benefit too little in relation to existing technique. As noted earlier, even Thomas de Colmar's arithmometer and its early successors remained on the edge of this balance. Adding and subtracting could be quickly achieved, but then it was very expensive and not necessarily any faster than doing the job on paper. The appeal thus remained quite limited, not only because of the economic price to be paid (which was high), but also the cost of acquiring the necessary embodied skill to render them genuinely superior to existing customary practice.

What goes for the Thomas arithmometer, in this sense, goes also for every calculational technology, from counting on one's fingers, to the use of calculi on a counting board, or calculating with the abacus, the Pascaline, the Millionaire, logarithms, the MADAS, or any candidate for what was the most sophisticated mechanical calculator. Indeed even the HP-35 and HP-45 required a facility to do arithmetic backwards from the usual by its reliance on a method known as Reverse Polish. Thus for each technological development, whether Troncet or Omega, for it to find successful users each needed to be understood, and not only intellectually, but equally importantly, the potential users needed to be able to incorporate it into their embodied capacity, with each required gesture becoming so automatic as to require no or little thought.

The achievement of the late mechanical calculators (such as the MADAS and the Euklid-Mercedes) was that they did greatly simplify what what needed to be learned by their operators to achieve efficiently all four arithmetic operations. But they did so still at considerable economic cost. The Comptometer was really best for addition and (with practice) subtraction. With its key input it was fast, and its simple design was amenable to cheaper construction and mass-production. So it found a different and expanded market in the rapidly expanding commercial and government organisations of the C20. It has been said and is probably true that its inventors and promoters, Felt and Tarrant, were probably the first people in the world to become truly wealthy from the invention, production and sale of calculators.

In the above sense the history of calculation technology can be characterised not so much as the progress of mechanical invention, as it is sometimes presented, but as a more subtle evolving relationship between mind, body and material artefacts or put another way as an interaction between evolving technology, history, culture, mental skills, social capacities and aspirations. The search for a successful innovation was a strange mix of finding a place where these aspects converged to make the innovation seem useful, and at the same time not only economically but also culturally accessible. The requirement to change was not just set in the machine, but also in the humans who made up the society.

The final conquest of the electronic calculator occurred when literacy, design, familiarity, cost and perceived need coincided to sweep all else before it. Never had the market been more prevalent in the negotiation of daily life. Science and technology now dominated every corner of the developed world and was making rapid inroads elsewhere. Literacy was at its highest in the developed world with arithmetic education now a requirement for every child in the extended period of compulsory schooling. Money promised to free time and technology was now widely accepted as being the answer to drudgery. Further still, there was a social acceptance of life-long change, and an emerging concept of the desirability of 'life-long learning'. The new consumer calculators were increasingly cheap, required little knowledge to use, displaced the mental effort of recall of multiplication tables and mental and written arithmetic. Printers attached to them produced now comparatively permanent records. And the whole increasingly seamlessly fitted a world which would soon be interconnected through computers and telecommunications into an ever more pervasive communications web. Calculators had not only reached a desired end. They also had found their moment when that end was widely required.

One might ask if there is any lesson in this for the future. Clearly the technology of calculation is now passing not only the first but perhaps even towards the second vanishing point where it converges and merges with other electronic devices which themselves have become so much part of the habitude of daily life, especially in the developed world, that their presence is sinking into the invisibility of the routine environment of human experience. But in doing so much of habit had to be relearned, and in the consequence human thinking, as well as collective culture has transformed.

This is of course a history of one area of innovation. So it may have some relevance to other areas of innovation in the world in which we now live. It is perhaps appropriate to remember that humans have reached the point where their innovation is actually destabilising the physical world in which they live - a situation unimaginable for most of the time in which the developments discussed here have taken place. But it is the case that humans are now challenged with the requirement to achieve an unprecedented level of innovation if the planet is to remain stable. The story of innovation in calculators tells us that whilst the time may be ripe for us to accept a great deal of change, it will require re-learning to be comfortable with the many innovations that will be needed to achieve it. Getting there will require people to re-learn and reshape many attitudes, hidden assumptions and habitual ways of living. In seeking to make those changes, we might reflect on the many challenges overcome in the simpler long history of how humans have learned to calculate, and what that means for the learning and innovation that will now be required.

09 March 2014 by 124.168.111.64 -

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~~In short,~~ the ~~use of a calculating technology is not just intellectual. It~~ is ~~what~~ Jean-François Gauvin[^Jean-François Gauvin , Habits of Knowledge: Artisans, Savants and Mechanical Devices in Seventeenth-Century French Natural Philosophy, The Department of the History of Science, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of History of Science, Harvard University, Cambridge, Mass., USA, November 2008, pp. 113. ^] refers to as "gestural". Gestural knowledge is the embodied knowledge that artisans rely on when they execute work of high craft skill. The first time someone looks at a Thomas de Colmar arithmometer learning how to add and subtract takes some time. Doing division and multiplication is much more challenging, especially if attempted without a good knowledge of how it can be done on paper. The first time is slow and subject to mistakes. It is only after repeated practice that the gestures required become so practiced that they are quick, instinctive and reliable. It is only then that the potential for calculation with such a device can be can be judged. And it would only have been after this sort of practice that one could credit the Gentleman's Magazine of 1857 claim that:

to:

This leads to the following observation: to learn how to use a calculating technology is not just a matter of understanding its concept. It also requires the acquisition of a type of knowledge which Jean-François Gauvin[^Jean-François Gauvin , Habits of Knowledge: Artisans, Savants and Mechanical Devices in Seventeenth-Century French Natural Philosophy, The Department of the History of Science, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of History of Science, Harvard University, Cambridge, Mass., USA, November 2008, pp. 113. ^] refers to as "gestural". Gestural knowledge is the embodied knowledge that artisans rely on when they execute work of high craft skill. The first time someone looks at a Thomas de Colmar arithmometer learning how to add and subtract takes some time. Doing division and multiplication is much more challenging, especially if attempted without a good knowledge of how it can be done on paper. The first time is slow and subject to mistakes. It is only after repeated practice that the gestures required become so practiced that they are quick, instinctive and reliable. It is only then that the potential for calculation with such a device can be can be judged. And it would only have been after this sort of practice that one could credit the Gentleman's Magazine of 1857 claim that:

09 March 2014 by 124.168.111.64 -

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||1920||Addo adder||Aktiebolaget Addo||Rod||%height=125px%[[Site.Addo1922|http://meta-studies.net/pmwiki/uploads/~~Scribola150~~.~~jpg~~]]||
||1922||Scribola\\10 column\\printing adding machine||Addiator Gesellschaft||Rod||%height=150px%[[Site.Scribola1922 |http://meta-studies.net/pmwiki/uploads/~~AddoW150~~.~~png~~]]||

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||1922||Scribola\\10 column\\printing adding machine||Addiator Gesellschaft||Rod||%height=150px%[[Site.Scribola1922 |http://meta-studies.net/pmwiki/uploads/Scribola150.jpg]]||

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||1920||Addo adder||Aktiebolaget Addo||Rod||%height=125px%[[Site.Addo1922|http://meta-studies.net/pmwiki/uploads/Scribola150.jpg]]||

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||1920||Addo adder||Aktiebolaget Addo||Rod||%height=150px%[[Site.Addo1922 |http://meta-studies.net/pmwiki/uploads/Scribola150.jpg]]||
||1922||Scribola\\10 column\\printing adding machine||Addiator Gesellschaft||Rod||%height=150px%[[Site.Scribola1922 |http://meta-studies.net/pmwiki/uploads/AddoW150.png]]||

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||%center% %height=200px% http://meta-studies.net/pmwiki/uploads/~~Mercedes~~.~~png~~||%center% %height=200px% http://meta-studies.net/pmwiki/uploads/MercedesDemoH200.jpg||

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As with previous calculating machines that commercial success of this machine was far from assured. The aesthetics of the design still reflects the high status market where it could have become just another prestigious mathematical machine in the cabinets of curiosities of those of elevated status. The somewhat circuitous route to that later success is described by Stephen Johnston. [^Stephen Johnston, "Making the arithmometer count", //Bulletin of the Scientific Instrument Society//, Volume 52, 1997, pp. 12-21.^] As Johnston notes, Thomas did not of course make these early machines. The first of his machines to survive was made by in Paris by Devrine, as usual a local clock (and instrument) maker.

to:

As with previous calculating machines that commercial success of this machine was far from assured. The aesthetics of the design still reflects the high status market where it could have become just another prestigious mathematical machine in the cabinets of curiosities of those of elevated status. The somewhat circuitous route to that later success is described by Stephen Johnston.[^Stephen Johnston, "Making the arithmometer count", //Bulletin of the Scientific Instrument Society//, Volume 52, 1997, pp. 12-21.^] As Johnston notes, Thomas did not of course make these early machines. The first of his machines to survive was made by in Paris by Devrine, as usual a local clock (and instrument) maker.

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These machines thus constitute the pinacle reached in the development of the personal hand-operated mechanical digital calculator - able to carry out all four functions by means of a crank operated machine of exquisite miniaturised workmanship and design. Production ceased in November 1970 although sales continued through 1973. At least 150,000 of the various calculator models were made. [^//An Interview with Curt Herzstark//^] For more on the Curta see the marvellous collection of documents and simulations at //The Curta Caclulator Page//.[^//The CURTA Calculator Page//, [[http://www.vcalc.net/cu.htm]], viewed 25 July 2013.^]

to:

These machines thus constitute the pinacle reached in the development of the personal hand-operated mechanical digital calculator - able to carry out all four functions by means of a crank operated machine of exquisite miniaturised workmanship and design. Production ceased in November 1970 although sales continued through 1973. At least 150,000 of the various calculator models were made.[^//An Interview with Curt Herzstark//^] For more on the Curta see the marvellous collection of documents and simulations at //The Curta Caclulator Page//.[^//The CURTA Calculator Page//, [[http://www.vcalc.net/cu.htm]], viewed 25 July 2013.^]

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||1910 ||Adall Adding Machine||Dreyfus\\and Levy ||~~Key input\\~~Concentric \\toothed disk\\and groove||%height=125px%[[Site.Adall1910| http://meta-studies.net/pmwiki/uploads/AdallH125.jpg]]||

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||1910 ||Adall Adding Machine||Dreyfus\\and Levy ||Concentric \\toothed disk\\and groove||%height=125px%[[Site.Adall1910| http://meta-studies.net/pmwiki/uploads/AdallH125.jpg]]||

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||1903 ||Adix Adding Machine Original model||Manheim||Key input~~\\lever~~ &\\gears||%height=175px% http://meta-studies.net/pmwiki/uploads/AdixH175.jpg||
||1910 ||Adall Adding Machine||Dreyfus and Levy ||~~Key input\\Concentric \\toothed~~ disk~~\\and~~ groove||%height=125px% http://meta-studies.net/pmwiki/uploads/AdallH125.jpg||
||~1946 ||Lightning Portable Adding Machine||Lightning~~\\Adding~~ Machine\\Co. L.A.||7 Wheels||%height=125px% http://meta-studies.net/pmwiki/uploads/LightningH125.jpg||
||1968 ||SEE Demonstration Adding Machine||Selective Educational\\Equipment Corporation||4 Wheels||%height=75px% http://meta-studies.net/pmwiki/uploads/SEE-1H75.jpg||

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||1903 ||Adix Adding Machine Original model||Manheim||Key input lever & gears||%height=175px% http://meta-studies.net/pmwiki/uploads/AdixH175.jpg||
||1910 ||Adall Adding Machine||Dreyfus and Levy ||Concentric toothed disk and groove||%height=125px% http://meta-studies.net/pmwiki/uploads/AdallH125.jpg||
||~1946 ||Lightning Portable Adding Machine||Lightning Adding Machine Co. L.A.||7 Wheels||%height=125px% http://meta-studies.net/pmwiki/uploads/LightningH125.jpg||
||1968 ||SEE Demonstration Adding Machine||Selective Educational Equipment Corporation||4 Wheels||%height=75px% http://meta-studies.net/pmwiki/uploads/SEE-1H75.jpg||

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||1937||Add-O-Matic Adding Machine||Allied MFG. Co.||Chain||%height=125px%[[Site.Add-O-Matic1937 |http://meta-studies.net/pmwiki/uploads/AddOMatic1_125.jpg]]||

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||1937||Add-O-Matic\\Adding Machine||Allied MFG. Co.||Chain||%height=125px%[[Site.Add-O-Matic1937 |http://meta-studies.net/pmwiki/uploads/AddOMatic1_125.jpg]]||

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||1922||Scribola 10 column printing adding machine||Addiator Gesellschaft||Rod||%height=150px%[[Site.Scribola1922 |http://meta-studies.net/pmwiki/uploads/Scribola150.jpg]]||

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||1922||Scribola\\10 column\\printing adding machine||Addiator Gesellschaft||Rod||%height=150px%[[Site.Scribola1922 |http://meta-studies.net/pmwiki/uploads/Scribola150.jpg]]||

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||1890-1900 ||A. M. Stevenson Adder||Joliet, Ill.\\||2 Wheel||%height=75px%[[Stevenson1890| http://meta-studies.net/pmwiki/uploads/StevensonH75.jpg]]||

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||1890-1900 ||A. M. Stevenson\\Adder||Joliet, Ill.\\||2 Wheel||%height=75px%[[Stevenson1890| http://meta-studies.net/pmwiki/uploads/StevensonH75.jpg]]||

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||~1913 ||Bunzel-Denton Arithmometer||Bunzel||Prototype\\Front Crank||%height=150px%[[Site.BunzelPrototype1913| http://meta-studies.net/pmwiki/uploads/BunzelH150.jpg]]||

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||~1913 ||Bunzel-Denton\\Arithmometer||Bunzel||Prototype\\Front Crank||%height=150px%[[Site.BunzelPrototype1913| http://meta-studies.net/pmwiki/uploads/BunzelH150.jpg]]||

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||1945 ||Facit ~~Model~~ S Calculator\\serial 210652||Facit||Pinwheel||%height=150px%[[Site.Facit1945| http://meta-studies.net/pmwiki/uploads/FacitH150.jpg]]||
||~1951||Original Ohdner Model 39\\serial 39-288965||Ohdner||Pinwheel||%height=100px%[[Site.OriginalOhdner39-1951| http://meta-studies.net/pmwiki/uploads/Ohdner1951H150.jpg]]||

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||1945 ||Facit\\Model S Calculator\\serial 210652||Facit||Pinwheel||%height=150px%[[Site.Facit1945| http://meta-studies.net/pmwiki/uploads/FacitH150.jpg]]||
||~1951||Original Ohdner\\Model 39\\serial 39-288965||Ohdner||Pinwheel||%height=100px%[[Site.OriginalOhdner39-1951| http://meta-studies.net/pmwiki/uploads/Ohdner1951H150.jpg]]||

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||~1915||Golden Gem Automatic Adding Machine||H. & H. Goldmann||Chain||%height=100px%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem100.jpg]]||

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||~1915||Golden Gem\\Automatic Adding Machine||H. & H. Goldmann||Chain||%height=100px%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem100.jpg]]||

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||1910-20s||Comptator (9 col)||Schubert~~\\&~~ Salzer||Chain||%height=125px% http://meta-studies.net/pmwiki/uploads/Comptator125.jpg||
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||1910-20s||Comptator (9 col)||Schubert & Salzer||Chain||%height=125px% http://meta-studies.net/pmwiki/uploads/Comptator125.jpg||
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||1922||Scribola 10 column\\printing~~\\Adding~~ Machine||Addiator Gesellschaft||Rod||%height=150px% http://meta-studies.net/pmwiki/uploads/Scribola150.jpg||
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||1922||Scribola 10 column printing Adding Machine||Addiator Gesellschaft||Rod||%height=150px% http://meta-studies.net/pmwiki/uploads/Scribola150.jpg||
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||1890-1900 ||A. M. Stevenson Adder||Joliet, Ill.\\||2 Wheel||%height=75px% http://meta-studies.net/pmwiki/uploads/StevensonH75.jpg||
||1903 ||Adix Adding Machine~~\\Original~~ model||Manheim||Key input\\lever &\\gears||%height=175px% http://meta-studies.net/pmwiki/uploads/AdixH175.jpg||
||1910 ||Adall Adding Machine||Dreyfus~~\\and~~ Levy ||Key input\\Concentric \\toothed disk\\and groove||%height=125px% http://meta-studies.net/pmwiki/uploads/AdallH125.jpg||
||~1946 ||Lightning Portable~~\\Adding~~ Machine||Lightning\\Adding Machine\\Co. L.A.||7 Wheels||%height=125px% http://meta-studies.net/pmwiki/uploads/LightningH125.jpg||
||1968 ||SEE Demonstration\\Adding Machine||Selective Educational\\Equipment Corporation||4 Wheels||%height=75px% http://meta-studies.net/pmwiki/uploads/SEE-1H75.jpg||

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||1890-1900 ||A. M. Stevenson Adder||Joliet, Ill. ||2 Wheel||%height=75px% http://meta-studies.net/pmwiki/uploads/StevensonH75.jpg||
||1903 ||Adix Adding Machine Original model||Manheim||Key input\\lever &\\gears||%height=175px% http://meta-studies.net/pmwiki/uploads/AdixH175.jpg||
||1910 ||Adall Adding Machine||Dreyfus and Levy ||Key input\\Concentric \\toothed disk\\and groove||%height=125px% http://meta-studies.net/pmwiki/uploads/AdallH125.jpg||
||~1946 ||Lightning Portable Adding Machine||Lightning\\Adding Machine\\Co. L.A.||7 Wheels||%height=125px% http://meta-studies.net/pmwiki/uploads/LightningH125.jpg||
||1968 ||SEE Demonstration Adding Machine||Selective Educational\\Equipment Corporation||4 Wheels||%height=75px% http://meta-studies.net/pmwiki/uploads/SEE-1H75.jpg||

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||1909 ||TIM (Time is Money)\\ Arithmometer||Ludwig Spitz\\ & Co||Arithmometer||%height=150px% http://meta-studies.net/pmwiki/uploads/TIMH150.jpg||

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||1909 ||TIM (Time is Money) Arithmometer||Ludwig Spitz\\ & Co||Arithmometer||%height=150px% http://meta-studies.net/pmwiki/uploads/TIMH150.jpg||

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||%center%A single pinwheel||%center% Mechanism of the~~\\Walther~~ pinwheel calculator\\(parts removed for demonstration)||

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||%center%A single pinwheel||%center% Mechanism of the Walther pinwheel calculator (parts removed for demonstration)||

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||1945 ||Facit Model S Calculator~~\\serial~~ 210652||Facit||Pinwheel||%height=150px% http://meta-studies.net/pmwiki/uploads/FacitH150.jpg||
||~1951||Original Ohdner Model 39~~\\serial~~ 39-288965||Ohdner||Pinwheel||%height=100px% http://meta-studies.net/pmwiki/uploads/Ohdner1951H150.jpg]||
||~1957 ||Walther WSR160~~\\Pinwheel~~ Calculator||Walther||Pinwheel||%height=150px% http://meta-studies.net/pmwiki/uploads/WaltherH150.jpg||
||~1957 ||Walther WSR160\\Demonstration\\Pinwheel Calculator||Walther||Demonstration\\Pinwheel||%height=150px% http://meta-studies.net/pmwiki/uploads/WaltherDemoH150.jpg||

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||1945 ||Facit Model S Calculator serial 210652||Facit||Pinwheel||%height=150px% http://meta-studies.net/pmwiki/uploads/FacitH150.jpg||
||~1951||Original Ohdner Model 39 serial 39-288965||Ohdner||Pinwheel||%height=100px% http://meta-studies.net/pmwiki/uploads/Ohdner1951H150.jpg]||
||~1957 ||Walther WSR160 Pinwheel Calculator||Walther||Pinwheel||%height=150px% http://meta-studies.net/pmwiki/uploads/WaltherH150.jpg||
||~1957 ||Walther WSR160 Demonstration Pinwheel Calculator||Walther||Demonstration\\Pinwheel||%height=150px% http://meta-studies.net/pmwiki/uploads/WaltherDemoH150.jpg||

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||%center% 1923: Mercedes-Euklid~~\\Model~~ 29 calculator||%center% 1923: Mercedes-Euklid Model 29\\Demonstration calculator||

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||%center% 1923: Mercedes-Euklid Model 29 calculator||%center% 1923: Mercedes-Euklid Model 29 Demonstration calculator||

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%center%%height=250px%%Woodie% http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg"1896 comptometer"|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491\\

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%center%%height=250px%%Woodie% http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg"1896 comptometer"|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491

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||~1955||Bell Punch Sumlock ||Bell Punch||Demonstration\\Comptometer||%height=250px%[[Site.SumlockDemonstrator1955| http://meta-studies.net/pmwiki/uploads/BellPunchDemoH250.jpg]]||

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||~1955||Bell Punch Sumlock ||Bell Punch||Demonstration Comptometer||%height=250px%[[Site.SumlockDemonstrator1955| http://meta-studies.net/pmwiki/uploads/BellPunchDemoH250.jpg]]||

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||~1955||Bell Punch Sumlock ||Bell Punch||Demonstration\\Comptometer||%height=250px% http://meta-studies.net/pmwiki/uploads/BellPunchDemoH250.jpg||

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||~1955||Bell Punch Sumlock ||Bell Punch||Demonstration Comptometer||%height=250px% http://meta-studies.net/pmwiki/uploads/BellPunchDemoH250.jpg||

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||%center% ~July 1948: CURTA Type 1~~\\(pin~~ sliders) earliest~~\\model~~ calculator~~\\serial~~ 5424||%center% 1967: CURTA Type I~~\\calculator~~ serial 76436~~\\&~~ cardboard box||%center% 1963: CURTA Type II\\calculator||

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||%center% ~July 1948: CURTA Type 1 (pin sliders) earliest model calculator serial 5424||%center% 1967: CURTA Type I calculator serial 76436 & cardboard box||%center% 1963: CURTA Type II calculator||

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||1623: ~~Recreation~~ of ||1904-1905: Bamberger's Omega||

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||1623: Re-creation of ||1904-1905: Bamberger's Omega||

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Other simple linear devices in this collection are shown ~~in TAB~~(~~SimpleLinearCalcs)~~ below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)

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Other simple linear devices in this collection are shown (:if equal {Site.PrintBook$:PSW} "True":)in TAB(SimpleLinearCalcs) (:ifend:)below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)

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||1910-20s||Comptator (9 col)||Schubert~~\\&~~ Salzer||Chain||%height=125px%[[Site.Comptator1910|http://meta-studies.net/pmwiki/uploads/Comptator125.jpg]]||
||~1915||Golden Gem Automatic\\Adding Machine||H. & H. Goldmann||Chain||%height=100px%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem100.jpg]]||

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||1910-20s||Comptator (9 col)||Schubert & Salzer||Chain||%height=125px%[[Site.Comptator1910|http://meta-studies.net/pmwiki/uploads/Comptator125.jpg]]||
||~1915||Golden Gem Automatic Adding Machine||H. & H. Goldmann||Chain||%height=100px%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem100.jpg]]||

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||1922||Scribola 10 column\\printing~~\\Adding~~ Machine||Addiator Gesellschaft||Rod||%height=150px%[[Site.Scribola1922 |http://meta-studies.net/pmwiki/uploads/Scribola150.jpg]]||
||1937||Add-O-Matic\\Adding Machine||Allied MFG. Co.||Chain||%height=125px%[[Site.Add-O-Matic1937 |http://meta-studies.net/pmwiki/uploads/AddOMatic1_125.jpg]]||

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||1922||Scribola 10 column printing Adding Machine||Addiator Gesellschaft||Rod||%height=150px%[[Site.Scribola1922 |http://meta-studies.net/pmwiki/uploads/Scribola150.jpg]]||
||1937||Add-O-Matic Adding Machine||Allied MFG. Co.||Chain||%height=125px%[[Site.Add-O-Matic1937 |http://meta-studies.net/pmwiki/uploads/AddOMatic1_125.jpg]]||

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Other simple rotational adding devices in this collection are shown in (:if equal {Site.PrintBook$:PSW} "True":)TAB(SimpleRotationalCalcs)(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)

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Other simple rotational adding devices in this collection are shown (:if equal {Site.PrintBook$:PSW} "True":)in TAB(SimpleRotationalCalcs)(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)

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Other simple rotational adding devices in this collection are shown in ~~TAB~~(~~SimpleRotationalCalcs)~~ below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)

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Other simple rotational adding devices in this collection are shown in (:if equal {Site.PrintBook$:PSW} "True":)TAB(SimpleRotationalCalcs)(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)

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Ready reckoners were in widespread use by shopkeepers and many others from the C17 on. They presented tables of precalculated results of many kinds of multiplication. These included the much needed calculations of the price for multiples of an item for sale, or per unit of weight. They could also be used to look up the calculations needed for wages and interest.[^see Bruce O.B. Williams and Roger G. Johnson, "Ready Reckoners", //IEEE Annals of the History of Computing//, October-December, 2005, pp. 64-80.^] One such, from 1892 is "Ropp's Commercial Calculator: a practical arithmetic for practical purposes, containing a complete system of useful, accurate, and convenient tables, together with simple, short, and practical methods for rapid calculation", published in the US and used widely into the early C20. This one, shown below (:if equal {Site.PrintBook$:PSW} "True":)in ~~FIG(ThomasDe)as~~ FIG(Ropp)(:ifend:), is the 1892 World's Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.

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Ready reckoners were in widespread use by shopkeepers and many others from the C17 on. They presented tables of precalculated results of many kinds of multiplication. These included the much needed calculations of the price for multiples of an item for sale, or per unit of weight. They could also be used to look up the calculations needed for wages and interest.[^see Bruce O.B. Williams and Roger G. Johnson, "Ready Reckoners", //IEEE Annals of the History of Computing//, October-December, 2005, pp. 64-80.^] One such, from 1892 is "Ropp's Commercial Calculator: a practical arithmetic for practical purposes, containing a complete system of useful, accurate, and convenient tables, together with simple, short, and practical methods for rapid calculation", published in the US and used widely into the early C20. This one, shown below(:if equal {Site.PrintBook$:PSW} "True":) in FIG(Ropp)(:ifend:), is the 1892 World's Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.

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Ready reckoners were in widespread use by shopkeepers and many others from the C17 on. They presented tables of precalculated results of many kinds of multiplication. These included the much needed calculations of the price for multiples of an item for sale, or per unit of weight. They could also be used to look up the calculations needed for wages and interest.[^see Bruce O.B. Williams and Roger G. Johnson, "Ready Reckoners", //IEEE Annals of the History of Computing//, October-December, 2005, pp. 64-80.^] One such, from 1892 is "Ropp's Commercial Calculator: a practical arithmetic for practical purposes, containing a complete system of useful, accurate, and convenient tables, together with simple, short, and practical methods for rapid calculation", published in the US and used widely into the early C20. This one, shown below ~~as FIG~~(~~Ropp),~~ is the 1892 World's Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.

to:

Ready reckoners were in widespread use by shopkeepers and many others from the C17 on. They presented tables of precalculated results of many kinds of multiplication. These included the much needed calculations of the price for multiples of an item for sale, or per unit of weight. They could also be used to look up the calculations needed for wages and interest.[^see Bruce O.B. Williams and Roger G. Johnson, "Ready Reckoners", //IEEE Annals of the History of Computing//, October-December, 2005, pp. 64-80.^] One such, from 1892 is "Ropp's Commercial Calculator: a practical arithmetic for practical purposes, containing a complete system of useful, accurate, and convenient tables, together with simple, short, and practical methods for rapid calculation", published in the US and used widely into the early C20. This one, shown below (:if equal {Site.PrintBook$:PSW} "True":)in FIG(ThomasDe)as FIG(Ropp)(:ifend:), is the 1892 World's Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.

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Other early new mathematical devices to gain broader use were simple adaptations of the sorts of tables that might be found in ready reckoners. There was an ever more extensive need to be able to measure and compare especially in the expanding processes of trade and commerce. The bane of earlier centuries (and even still) is lack of standardisation across localities in which trade took place. In particular, quantities were often not measured in the same units. As a result, special purpose devices, basically just forms of mechanical look-up tables were devised to enable conversion, needed not the least since performing associated conversion calculations each time was not only time consuming but beyond the skill of many who might need them. A particularly stark need for such devices was created, following the French Revolution, when the Revolutionary Government introduced metric measures. A "Convertisseur" from (1780–1810) designed by clock maker Gabrielle Chaix in Paris to assist in converting between the old measure of distance (the "Aune") to the new metric metre that was introduced in 1791, is shown ~~in FIG~~(~~convertiseur)~~ below.

to:

Other early new mathematical devices to gain broader use were simple adaptations of the sorts of tables that might be found in ready reckoners. There was an ever more extensive need to be able to measure and compare especially in the expanding processes of trade and commerce. The bane of earlier centuries (and even still) is lack of standardisation across localities in which trade took place. In particular, quantities were often not measured in the same units. As a result, special purpose devices, basically just forms of mechanical look-up tables were devised to enable conversion, needed not the least since performing associated conversion calculations each time was not only time consuming but beyond the skill of many who might need them. A particularly stark need for such devices was created, following the French Revolution, when the Revolutionary Government introduced metric measures. A "Convertisseur" from (1780–1810) designed by clock maker Gabrielle Chaix in Paris to assist in converting between the old measure of distance (the "Aune") to the new metric metre that was introduced in 1791, is shown (:if equal {Site.PrintBook$:PSW} "True":)in FIG(convertiseur)(:ifend:) below.

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~~[[<<]]~~

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%center%%height=200px%%CalculantStepDrum% http://meta-studies.net/pmwiki/uploads/TIMDrumH200.jpg"Step drum"|Step drum (in a later 'TIM' arithmometer)\\

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%center%%height=200px%%id=CalculantStepDrum% http://meta-studies.net/pmwiki/uploads/TIMDrumH200.jpg"Step drum"|Step drum (in a later 'TIM' arithmometer)\\

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In the left lower corner of the above can be seen the motor, now coupled to the characteristic step drums of an arithmometer (bottom center and right), with the carry mechanism above. This puts paid to any simple story of the linear development of innovation in the calculator. Here the most modern device of the motor is being coupled to the longest serving commercial system of an arithmometer.~~[[<<]]~~

to:

In the left lower corner of the above can be seen the motor, now coupled to the characteristic step drums of an arithmometer (bottom center and right), with the carry mechanism above. This puts paid to any simple story of the linear development of innovation in the calculator. Here the most modern device of the motor is being coupled to the longest serving commercial system of an arithmometer.

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Changed lines 38-39 from:

Ready reckoners were in widespread use by shopkeepers and many others from the C17 on. They presented tables of precalculated results of many kinds of multiplication. These included the much needed calculations of the price for multiples of an item for sale, or per unit of weight. They could also be used to look up the calculations needed for wages and interest.[^see Bruce O.B. Williams and Roger G. Johnson, "Ready Reckoners", //IEEE Annals of the History of Computing//, October-December, 2005, pp. 64-80.^] One such, from 1892~~, shown below in FIG(Ropp) is "Ropp's Commercial Calculator: a~~ practical ~~arithmetic for practical purposes, containing a complete system of useful, accurate~~, ~~and convenient tables~~, ~~together with simple, short, and practical methods for rapid~~ calculation", a published in the US and used widely into the early C20. This one is the 1892 World's Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.

to:

Ready reckoners were in widespread use by shopkeepers and many others from the C17 on. They presented tables of precalculated results of many kinds of multiplication. These included the much needed calculations of the price for multiples of an item for sale, or per unit of weight. They could also be used to look up the calculations needed for wages and interest.[^see Bruce O.B. Williams and Roger G. Johnson, "Ready Reckoners", //IEEE Annals of the History of Computing//, October-December, 2005, pp. 64-80.^] One such, from 1892 is "Ropp's Commercial Calculator: a practical arithmetic for practical purposes, containing a complete system of useful, accurate, and convenient tables, together with simple, short, and practical methods for rapid calculation", published in the US and used widely into the early C20. This one, shown below as FIG(Ropp), is the 1892 World's Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.

Deleted line 44:

~~[[<<]]~~

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%center%%height=200px%%id=Ropp% http://meta-studies.net/pmwiki/uploads/Ropp200.jpg"Ropp"|1892: Ropp's Commercial Calculator\\

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%center%%height=200px%%id=Ropp% http://meta-studies.net/pmwiki/uploads/Ropp200.jpg"Ropp's Calculator"|1892: Ropp's Commercial Calculator\\

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%center%%height=200px%%id=convertiseur% http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg"~~Convertiseur~~"|~1790: Conversion device\\

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%center%%height=200px%%id=convertiseur% http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg"Conversion device"|~1790: Conversion device\\

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Whether or not Thomas reinvented the step drum, even in this first design, the four integers to be added (or subtracted) were set by sliding four corresponding cogs to the appropriate position on such drums. The cogs were moved by sliding nobs along four (square section) axles which were in turn attached to output dial wheels which showed the correct number through small windows. A carry mechanism was incorporated. Rather than being turned by a crank handle the stepped drums were turned by a ribbon that was pulled out from the side. All later designs used a crank handle to turn the drums as is shown in the diagram by Franz Reuleaux in 1862.

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Whether or not Thomas reinvented the step drum, even in this first design, the four integers to be added (or subtracted) were set by sliding four corresponding cogs to the appropriate position on such drums. The cogs were moved by sliding nobs along four (square section) axles which were in turn attached to output dial wheels which showed the correct number through small windows. A carry mechanism was incorporated. Rather than being turned by a crank handle the stepped drums were turned by a ribbon that was pulled out from the side. All later designs used a crank handle to turn the drums as is shown in the diagram by Franz Reuleaux in 1862 shown (:if equal {Site.PrintBook$:PSW} "True":)in FIG(Reuleaux)(:ifend:) below.

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%center%1862: Diagram of the Thomas de Colmar arithmometer mechanism.[^ Franz Reuleaux, //Die Thomas'sche Rechenmaschine//, Freiberg, 1862 reproduced in Reuleaux's article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^]\\ (~~:if equal {Site.PrintBook$:PSW} "False":)(Click on the image for an~~ enlargement.~~)(:ifend:~~)\\(Source: Museum of the History of Science, University of Oxford.)

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%center%1862: Diagram of the Thomas de Colmar arithmometer mechanism.[^ Franz Reuleaux, //Die Thomas'sche Rechenmaschine//, Freiberg, 1862 reproduced in Reuleaux's article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^]\\ (Click on the image for an enlargement.)\\(Source: Museum of the History of Science, University of Oxford.)

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%center%%height=200px% http://meta-studies.net/pmwiki/uploads/Misc/ThomasMechRelH200.jpg|1862: Thomas de Colmar arithmometer mechanism\\
diagram.[^ Franz Reuleaux, //Die Thomas'sche Rechenmaschine//, Freiberg, 1862 reproduced in Reuleaux's article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^] ~~(:if equal {Site.PrintBook$:PSW} "False":)(Click on the image for an enlargement.)(:ifend:)~~\\(Source: Museum of the History of Science, University of Oxford.)

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%center%%height=200px%%id=Reuleaux% http://meta-studies.net/pmwiki/uploads/Misc/ThomasMechRelH200.jpg"Thomas mechanism"|1862: Thomas de Colmar arithmometer mechanism\\
diagram.[^ Franz Reuleaux, //Die Thomas'sche Rechenmaschine//, Freiberg, 1862 reproduced in Reuleaux's article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^] \\(Source: Museum of the History of Science, University of Oxford.)

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The above diagram shows the crank handle on the right top which drives the rotation of the step drum (shown centre right). In front of the crank handle can be seen a "slider nob" which moves the cog along the axle to engage with correct number of teeth of the step drum. To the left is a reversing mechanism connected to an output dial. The reversing mechanism allows the output dial to be rotated in the opposite direction, if the nob that activates it (situated above) is shifted from the "addition" to the "subtraction" position.~~[[<<]]~~

Immediately below is a picture of a step drum from a later arithmometer, but based on the Thomas mechanism, showing the slider, drum with its 'counting gear' positioned for the input of '5'. In this arithmometer the input number selected shows in the immediately adjacent window. Note the square section axle on which the counting gear moves.

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The above diagram shows the crank handle on the right top which drives the rotation of the step drum (shown centre right). In front of the crank handle can be seen a "slider nob" which moves the cog along the axle to engage with correct number of teeth of the step drum. To the left is a reversing mechanism connected to an output dial. The reversing mechanism allows the output dial to be rotated in the opposite direction, if the nob that activates it (situated above) is shifted from the "addition" to the "subtraction" position.

Immediately below (:if equal {Site.PrintBook$:PSW} "True":)in FIG(CalculantStepDrum)(:ifend:) is a picture of a step drum from a later arithmometer, but based on the Thomas mechanism, showing the slider, drum with its 'counting gear' positioned for the input of '5'. In this arithmometer the input number selected shows in the immediately adjacent window. Note the square section axle on which the counting gear moves.

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%center%%height=200px% http://meta-studies.net/pmwiki/uploads/TIMDrumH200.jpg|Step drum (in a later 'TIM' arithmometer)\\

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%center%%height=200px%%CalculantStepDrum% http://meta-studies.net/pmwiki/uploads/TIMDrumH200.jpg"Step drum"|Step drum (in a later 'TIM' arithmometer)\\

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By the time Thomas died, in May 1870, some 800 arithmometers had been made. His son, Thomas de Bojano then took over manufacturing. Thomas de Bojano died in 1881 and Thomas's grandson, the Compte de Ronseray, continued manufacturing arithmometers under the management of Payen. By 1878 some 1500 Thomas arithmometers had been constructed. Some 180 Thomas arithmometers are known to have survived to the present, of which 110 are in public collections and 50 in private collections. Below is the Thomas Arithmometer in this collection, which is from 1884.

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By the time Thomas died, in May 1870, some 800 arithmometers had been made. His son, Thomas de Bojano then took over manufacturing. Thomas de Bojano died in 1881 and Thomas's grandson, the Compte de Ronseray, continued manufacturing arithmometers under the management of Payen. By 1878 some 1500 Thomas arithmometers had been constructed. Some 180 Thomas arithmometers are known to have survived to the present, of which 110 are in public collections and 50 in private collections. Below (:if equal {Site.PrintBook$:PSW} "True":)in FIG(ThomasDe)(:ifend:) is the Thomas Arithmometer in this collection, which is from 1884.

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%center%%height=300px% http://meta-studies.net/pmwiki/uploads/ThomasDeColmarH300.jpg|1884: Thomas de Colmar Arithmometer\\

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%center%%height=300px%%id=ThomasDe% http://meta-studies.net/pmwiki/uploads/ThomasDeColmarH300.jpg"Thomas Arithmometer"|1884: Thomas de Colmar Arithmometer\\

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The time was ripe for others to attempt to produce improved machines. The Thomas concept was developed and improved by a number of other engineers and marketed from different countries.[^P. A. Kidwell, "American Scientists and Calculating Machines- From Novelty to Commonplace", Annals of the History of Computing, Volume 12, Number 1, 1990, pp. 31^] From 1880, other European manufacturers - Burkhardt, Layton, Saxonia, Egli, Bunzel, etc entered the market. The three arithmometers from this collection, below, are products of this now enlarging set of competing manufacturers and designers.

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The time was ripe for others to attempt to produce improved machines. The Thomas concept was developed and improved by a number of other engineers and marketed from different countries.[^P. A. Kidwell, "American Scientists and Calculating Machines- From Novelty to Commonplace", Annals of the History of Computing, Volume 12, Number 1, 1990, pp. 31^] From 1880, other European manufacturers - Burkhardt, Layton, Saxonia, Egli, Bunzel, etc entered the market. The three arithmometers from this collection, shown below (:if equal {Site.PrintBook$:PSW} "True":)in TAB(Arithmometers)(:ifend:), are products of this now enlarging set of competing manufacturers and designers.

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The pinwheel calculator was developed as an improvement on the arithmometer more or less simultaneously in Russia in 1878 by Swedish engineer Willgodt Theophil Odhner (1845-1905) and in the US in 1874, by Frank Stephen Baldwin (1838-1925). Although they worked independently of each there machines were so similar that the 'Ohdner' or 'Baldwin' machine became more or less interchangeable terms.[^Diana H. Hook and Jeremy M. Norman, //Origins of Cyberspace//, Novato, California, 2002, p. 255.^]. The designs utilised a clever 'counting gear' in which the number of teeth protruding could be adjusted by sliders (and later a push-down keyboard). A pinwheel and the internal mechanism (with some pinwheels removed) from a Walther pinwheel calculator in this collection is shown below.

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The pinwheel calculator was developed as an improvement on the arithmometer more or less simultaneously in Russia in 1878 by Swedish engineer Willgodt Theophil Odhner (1845-1905) and in the US in 1874, by Frank Stephen Baldwin (1838-1925). Although they worked independently of each there machines were so similar that the 'Ohdner' or 'Baldwin' machine became more or less interchangeable terms.[^Diana H. Hook and Jeremy M. Norman, //Origins of Cyberspace//, Novato, California, 2002, p. 255.^]. The designs utilised a clever 'counting gear' in which the number of teeth protruding could be adjusted by sliders (and later a push-down keyboard). A pinwheel and the internal mechanism (with some pinwheels removed) from a Walther pinwheel calculator in this collection is shown (:if equal {Site.PrintBook$:PSW} "True":)in TAB(DemoPinwheels)(:ifend:) below.

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As can be seen above, the pinwheel (left, above) is a thin disk with the slider shown protruding in the top right corner. It is in the '3' position, with the cam slot rotated pushing 3 teeth out (seen between and behind the fixed teeth at the bottom). These then are the teeth that are added by the counting wheel. (:if equal {Site.PrintBook$:PSW} "False":)(Click on the image to enlarge.)(:ifend:)~~[[<<]]~~

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As can be seen above, the pinwheel (left, above) is a thin disk with the slider shown protruding in the top right corner. It is in the '3' position, with the cam slot rotated pushing 3 teeth out (seen between and behind the fixed teeth at the bottom). These then are the teeth that are added by the counting wheel. (:if equal {Site.PrintBook$:PSW} "False":)(Click on the image to enlarge.)(:ifend:)

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Ohdner began manufacture of his machines in 1886 under the name "Original Ohdner" but sold his rights also to Grimme, Natalis and Co., Braunsweig, who began marketing the machines under the name Brunsviga.[^ibid^] In turn they also licenced agents such as Schuster to sell them. Reflecting a later start these machines were made from a wider range of materials than the arithmometers, including iron and nickel alloys as well as brass and steel. The Brunsviga was a quick success selling 20,000 units between 1892 and 1912.[[^Hook and Norman, //Origins of Cyberspace//, p. 255.^] Below ~~is the very early~~ Brunsviga~~-Schuster pinwheel calculator from 1896~~ in this collection.

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Ohdner began manufacture of his machines in 1886 under the name "Original Ohdner" but sold his rights also to Grimme, Natalis and Co., Braunsweig, who began marketing the machines under the name Brunsviga.[^ibid^] In turn they also licenced agents such as Schuster to sell them. Reflecting a later start these machines were made from a wider range of materials than the arithmometers, including iron and nickel alloys as well as brass and steel. The Brunsviga was a quick success selling 20,000 units between 1892 and 1912.[[^Hook and Norman, //Origins of Cyberspace//, p. 255.^] Below (:if equal {Site.PrintBook$:PSW} "True":)in FIG(Brunsviga)(:ifend:) is the very early Brunsviga-Schuster pinwheel calculator from 1896, followed (:if equal {Site.PrintBook$:PSW} "True":)in TAB(PinwheelCalcs)(:ifend:) by the other pinwheel calculators in this collection.

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%center%%height=250px% http://meta-studies.net/pmwiki/uploads/Brunsviga1896H250.jpg|

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%center%%height=250px%%id=Brunsviga% http://meta-studies.net/pmwiki/uploads/Brunsviga1896H250.jpg"Brunsviga Calculator"|

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One helpful development in design was the development of a proportional rack which moved cogs through a series of increments depending on the length of a toothed rack with which they engaged. Shown below is the rack mechanism of such a calculator. Note how successive racks have moved increasing distances as the crank handle is turned (creating the diagonal pattern). The loose cogs seen on the square section axle are an example of the nine such cogs under each column of keys. Normally lying between the racks when a key is depressed it moves the corresponding cog sideways on the axle to engage with the appropriate rack for the number of the key depressed.

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One helpful development in design was the development of a proportional rack which moved cogs through a series of increments depending on the length of a toothed rack with which they engaged. Shown below (:if equal {Site.PrintBook$:PSW} "True":)in FIG(Rack)(:ifend:) is the rack mechanism of such a calculator. Note how successive racks have moved increasing distances as the crank handle is turned (creating the diagonal pattern). The loose cogs seen on the square section axle are an example of the nine such cogs under each column of keys. Normally lying between the racks when a key is depressed it moves the corresponding cog sideways on the axle to engage with the appropriate rack for the number of the key depressed.

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%center%%height=200px% http://meta-studies.net/pmwiki/uploads/Misc/RackMechH200.jpg|Rack mechanism\\

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%center%%height=200px%%id=Rack% http://meta-studies.net/pmwiki/uploads/Misc/RackMechH200.jpg"Rack mechanism"|Rack mechanism\\

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In 1906 Christel Haman founded the Mercedes-Euklid company who adopted the rack mechanism. In 1910 he incorporated the mechanism patented by Alexander Rechnitzer, referred to earlier, which enabled his machine to automatically perform the process of division, thus becoming the first mass produced machine with this capacity. The fully working Mercedes-Euklid 29 can be seen below (left) and a demonstration Mercedes-Euklid (model 29 from 1934) can be seen below (right).

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In 1906 Christel Haman founded the Mercedes-Euklid company who adopted the rack mechanism. In 1910 he incorporated the mechanism patented by Alexander Rechnitzer, referred to earlier, which enabled his machine to automatically perform the process of division, thus becoming the first mass produced machine with this capacity. The fully working Mercedes-Euklid 29 can be seen below (left) and a demonstration Mercedes-Euklid (model 29 from 1934) can be seen below (right)(:if equal {Site.PrintBook$:PSW} "True":) in TAB(RackCalcs)(:ifend:).

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Felt first demonstrated this famously with a model constructed in a wooden macaroni box in 1885. He patented his design in 1887 and began selling it from his manufacturing company in Chicago. In 1890 he gave it the name "the Comptometer" and energetically promoted it.[^//Origins of Cyberspace, p. 244.^] Below ~~is the Comptometer in this collections~~ - an example from 1896 of the first model, cased in wood, and one of the 40 oldest known to still be in existence. Remarkably with a drop of oil on the springs it still works perfectly.

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Felt first demonstrated this famously with a model constructed in a wooden macaroni box in 1885. He patented his design in 1887 and began selling it from his manufacturing company in Chicago. In 1890 he gave it the name "the Comptometer" and energetically promoted it.[^//Origins of Cyberspace, p. 244.^] Below (:if equal {Site.PrintBook$:PSW} "True":)in FIG(Woodie)(:ifend:) is the Comptometer in this collection - an example from 1896 of the first model, cased in wood, and one of the 40 oldest known to still be in existence. Remarkably with a drop of oil on the springs it still works perfectly.

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%center%%height=250px% http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491\\

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%center%%height=250px%%Woodie% http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg"1896 comptometer"|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491\\

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The comptometer was a highly successful innovation and was sufficiently cheap and useful to reach a broad market. Characterised by extremely effective marketing and capable of being mass produced the device continued to be marketed for some 80 years unusually for such innovations leaving its inventor extremely wealthy. By then its essential mechanism was being utilised by more than one company. Shown below is the remaining comptometer in this collection, this time made of plastic in the 1950s by the British Bell Punch company. Also shown is a demonstration model showing the keys and lever system used in the Bell Punch machine.~~[[<<]]~~

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The comptometer was a highly successful innovation and was sufficiently cheap and useful to reach a broad market. Characterised by extremely effective marketing and capable of being mass produced the device continued to be marketed for some 80 years unusually for such innovations leaving its inventor extremely wealthy. By then its essential mechanism was being utilised by more than one company. Shown below (:if equal {Site.PrintBook$:PSW} "True":)in TAB(Comptometers)(:ifend:) is the remaining comptometer in this collection, this time made of plastic in the 1950s by the British Bell Punch company. Also shown is a demonstration model showing the keys and lever system used in the Bell Punch machine.

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Finally there is the last and most beautifully miniaturised of the four function manual mechanical calculators designed by Curt Herzstark. Curt was born in 1902 as the son of Samuel Herzstark who had established a calculator manufacturing company in Vienna in 1905-6. Curt's father died in 1937 but by then Curt was both Director of the company and a highly competent designer in his own right. He recognised the need for a miniaturised four function calculator which could be carried in an engineer's pocket. He began to design this as a cylindrical calculator which could be held in one hand and operated with the other. It could utilise the modern new light weight alloys of aluminium, magnesium, etc. By the end of 1937 he had the form of what he wished to accomplish firmly in his mind. It would be compact, lightweight, and in order to allow a carry mechanism which would allow the crank to be turned only one way, it would use and internal process of complementary arithmetic for subtraction. Then came Hitler. Herzstark found himself in 1943 arrested and imprisoned in Buchenwald concentration camp where he was placed in a small technical camp to manufacture components to assist the Nazi war effort (in particular, parts of the V I and II missile bombs).~~[[<<]]~~

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Finally there is the last and most beautifully miniaturised of the four function manual mechanical calculators designed by Curt Herzstark. Curt was born in 1902 as the son of Samuel Herzstark who had established a calculator manufacturing company in Vienna in 1905-6. Curt's father died in 1937 but by then Curt was both Director of the company and a highly competent designer in his own right. He recognised the need for a miniaturised four function calculator which could be carried in an engineer's pocket. He began to design this as a cylindrical calculator which could be held in one hand and operated with the other. It could utilise the modern new light weight alloys of aluminium, magnesium, etc. By the end of 1937 he had the form of what he wished to accomplish firmly in his mind. It would be compact, lightweight, and in order to allow a carry mechanism which would allow the crank to be turned only one way, it would use and internal process of complementary arithmetic for subtraction. Then came Hitler. Herzstark found himself in 1943 arrested and imprisoned in Buchenwald concentration camp where he was placed in a small technical camp to manufacture components to assist the Nazi war effort (in particular, parts of the V I and II missile bombs).

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The first model (the Model 1) began production in 1947. Below left is a (rare) example of the Model I Curta ( with pin sliders which were soon improved upon) in mint condition coming from the first 5500 made in ~July 1948, the year after production began and in the first 5,500 made. As can be seen the sliders are pins which were used by Curta before he introduced bakelite handles on them. Centre is a later Curta from 1967 complete with the original box in which it was sold and its instructions, all in mint condition. On the right is a Curta Model II from 1962. The Model II was a larger machine capable of a number input to 11 significant figures, compared with the more compact Model I which could accept a number accurate to 8 significant figures. Note the very 'modern' anodised aluminium sliders on the Model II which comes also with an optional leather carry case (not shown).

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The first model (the Model 1) began production in 1947. Below left (:if equal {Site.PrintBook$:PSW} "True":)in TAB(CurtaCalcs)(:ifend:) is a (rare) example of the Model I Curta ( with pin sliders which were soon improved upon) in mint condition coming from the first 5500 made in ~July 1948, the year after production began and in the first 5,500 made. As can be seen the sliders are pins which were used by Curta before he introduced bakelite handles on them. Centre is a later Curta from 1967 complete with the original box in which it was sold and its instructions, all in mint condition. On the right is a Curta Model II from 1962. The Model II was a larger machine capable of a number input to 11 significant figures, compared with the more compact Model I which could accept a number accurate to 8 significant figures. Note the very 'modern' anodised aluminium sliders on the Model II which comes also with an optional leather carry case (not shown).

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The earliest of these machines had been that of Schickard (below, left). In the upper part is a set of rotatable Napier's rods revealed by windows to give partial products. In the lower part is the world's first known stylus operated adding machine to add these partial products up. A late and unique expression of these in this collection (below, right) is Justin Bamberger's Omega Calculating Machine (1903-6). In the upper section is a set of Napier's bones revealed by moveable windows for discovering the partial products of two multiplied numbers. In the lower section is a Locke adding machine for adding them up.

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~~%center% %height=250px% http://meta-studies~~.~~net/pmwiki/uploads/Schickard1H250.jpg|1623:~~ Recreation of Wilhelm Schickard's calculating machine\\

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The earliest of these machines had been that of Schickard (immediately below in FIG(Schickardreminder)). In the upper part of it is a set of rotatable Napier's rods revealed by windows to give partial products. In the lower part is the world's first known stylus operated adding machine to add these partial products up.

%center% %height=250px%%id=Schickardreminder% http://meta-studies.net/pmwiki/uploads/Schickard1H250.jpg"Schickard's Calculator"|1623: Recreation of Wilhelm Schickard's calculating machine\\

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\\

%center% %height=250px% http://meta-~~studies~~.~~net/pmwiki/uploads/BambergerOmegaH250.jpg|1904-1905:~~ Bamberger's Omega calculating machine\\

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A late and unique expression of the same principle in this collection is Justin Bamberger's Omega Calculating Machine (1903-6), shown in FIG(Bamberger) below. In the upper section is a set of Napier's bones revealed by moveable windows for discovering the partial products of two multiplied numbers. In the lower section is a Locke adding machine for adding them up.

%center% %height=250px%%id=Bamberger% http://meta-studies.net/pmwiki/uploads/BambergerOmegaH250.jpg"Bamberger Omega"|1904-1905: Bamberger's Omega calculating machine\\

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A much heavier and complex mechanical approach was also explored. First it was embodied in Léon Bollée's calculating machine which won a gold medal at the Paris Exposition of 1889. One surviving example of this bulky but beautiful machine can be seen at the Musée des Arts et Métiers in Paris. This collection has only an article on this "New Calculating Machine of very General Applicability" from the Manufacturer and Builder of 1890.

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A much heavier and complex mechanical approach was also explored. First it was embodied in Léon Bollée's calculating machine which won a gold medal at the Paris Exposition of 1889. One surviving example of this bulky but beautiful machine can be seen at the Musée des Arts et Métiers in Paris. This collection has only an article on this "New Calculating Machine of very General Applicability" from the Manufacturer and Builder of 1890, see (:if equal {Site.PrintBook$:PSW} "True":) FIG(Bollee)(:ifend:) below.

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%center%%height=250px% http://meta-studies.net/pmwiki/uploads/BolleeMAB1890H250.jpg|Leon Bollée Calculating Machine\\

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%center%%height=250px%%id=Bollee% http://meta-studies.net/pmwiki/uploads/BolleeMAB1890H250.jpg"Bollée calculator"|Leon Bollée Calculating Machine\\

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Similar principles were however utilised by Otto Steiger in Switzerland who in 1895 patented a rather more practical "Millionaire calculating machine" which had a simple enough mechanism to enable production on a commercial scale.~~[[<<]]~~

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Similar principles were however utilised by Otto Steiger in Switzerland who in 1895 patented a rather more practical "Millionaire calculating machine" which had a simple enough mechanism to enable production on a commercial scale (see (:if equal {Site.PrintBook$:PSW} "True":) FIG(Millionaire)(:ifend:)below).

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%center%%height=300px% http://meta-studies.net/pmwiki/uploads/MillionairH300.jpg|1912: Millionaire Calculating Machine, serial 2015 (10x10x20)\\

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%center%%height=300px%%id=Millionaire% http://meta-studies.net/pmwiki/uploads/MillionairH300.jpg"Millionaire calculator"|1912: Millionaire Calculating Machine, serial 2015 (10x10x20)\\

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The deck of the Millionaire in this collection is shown below with the selector on the left which picks the multiplying factor, and the selector on the right which sets it for addition, subtraction, multiplication and division (AMDS). The ten sliders for setting the number to be operated on are obvious, as are the result windows, and on the far right, the crank handle.

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The deck of the Millionaire in this collection is shown below (:if equal {Site.PrintBook$:PSW} "True":)in FIG(MillionaireDeck)(:ifend:) with the selector on the left which picks the multiplying factor, and the selector on the right which sets it for addition, subtraction, multiplication and division (AMDS). The ten sliders for setting the number to be operated on are obvious, as are the result windows, and on the far right, the crank handle.

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%center%%height=230px% http://meta-studies.net/pmwiki/uploads/MillionaireDeckH230.jpg|Deck of the Millionaire Calculating Machine\\

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%center%%height=230px%%id=MillionaireDeck% http://meta-studies.net/pmwiki/uploads/MillionaireDeckH230.jpg"Millionaire deck"|Deck of the Millionaire Calculating Machine\\

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Samuel Herzstark (1867-1937), the father of Curt Herzstark who built the Curta, also was a pioneer in calculator construction and together with Gustav Perger established the Austria Calculator Machines Manufacturing Company in Vienna in 1905-6. In an interview in 1987 Curt Herzstark reports that in 1907 Samuel became the first to attach an electric motor to an arithmometer, which he equipped also with a keyboard. Curt also notes that this machine was equipped with automatic division.[^//An Interview with Curt Herzstark//, OH 140, conducted by Erwin Tomash on 10-11 September 1987, Nendeln, Liechtenstein, (English Translation).^] However after the 1914-18 War Herzstark returned to a demolished business. He restarted with a combination of importing and selling calculators from other manufacturers, assembling old stock of his own design, and then as the business built up designing new machines. Below is an arithmometer in this collection branded by Samuel Herzstark from 1929. It is actually a Badenia (manufactured by the German Company Math. Bauerle in the Black Forest) which Herzstark was at that time re-badging and selling.

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Samuel Herzstark (1867-1937), the father of Curt Herzstark who built the Curta, also was a pioneer in calculator construction and together with Gustav Perger established the Austria Calculator Machines Manufacturing Company in Vienna in 1905-6. In an interview in 1987 Curt Herzstark reports that in 1907 Samuel became the first to attach an electric motor to an arithmometer, which he equipped also with a keyboard. Curt also notes that this machine was equipped with automatic division.[^//An Interview with Curt Herzstark//, OH 140, conducted by Erwin Tomash on 10-11 September 1987, Nendeln, Liechtenstein, (English Translation).^] However after the 1914-18 War Herzstark returned to a demolished business. He restarted with a combination of importing and selling calculators from other manufacturers, assembling old stock of his own design, and then as the business built up designing new machines. Below (:if equal {Site.PrintBook$:PSW} "True":)in FIG(Herzstark)(:ifend:) is an arithmometer in this collection branded by Samuel Herzstark from 1929. It is actually a Badenia (manufactured by the German Company Math. Bauerle in the Black Forest) which Herzstark was at that time re-badging and selling.

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%center%%height=250px% http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometerH250.jpg|~1929: "Herzstark" electric Calculating Machine serial 6549\\

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%center%%height=250px%%id=Herzstark% http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometerH250.jpg"Herzstark arithmometer"|~1929: "Herzstark" electric Calculating Machine serial 6549\\

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This calculator features its original electric motor, still in good working order, and with a keyboard instead of sliders for input. The features of it were not only that it had a keyboard for input, but also a control mechanism consisting of a column of keys which enabled a number to be entered and then added through 0 to 8 repeats representing multiplication by one to nine. A view of the mechanism of this machine is shown below.~~[[<<]]~~

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This calculator features its original electric motor, still in good working order, and with a keyboard instead of sliders for input. The features of it were not only that it had a keyboard for input, but also a control mechanism consisting of a column of keys which enabled a number to be entered and then added through 0 to 8 repeats representing multiplication by one to nine. A view of the mechanism of this machine is shown below (:if equal {Site.PrintBook$:PSW} "True":)in FIG(HerzstarkMech)(:ifend:).

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%center%%height=250px% http://meta-studies.net/pmwiki/uploads/HerzstarkMechH250.jpg|1950s-1960s: Underneath view of the Herzstark mechanism (note the stepped drums)\\

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%center%%height=250px%%id=HerzstarkMech% http://meta-studies.net/pmwiki/uploads/HerzstarkMechH250.jpg"Herzstark mechanism"|1950s-1960s: Underneath view of the Herzstark mechanism (note the stepped drums)\\

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%center%%height=250px% http://meta-studies.net/pmwiki/uploads/MADAS_SmallerH250.jpg|1950s-1960s: MADAS\\

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%center%%height=250px%%id=MADAS20BTG% http://meta-studies.net/pmwiki/uploads/MADAS_SmallerH250.jpg"MADAS 20BTG"|1950s-1960s: MADAS\\

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The late MADAS 20BTG calculator, seen above~~, which is part of this collection represents a classic exemplar of the late stages~~ of this evolutionary development. Now fully utilising an electric motor it could fluently perform all the operations of arithmetic, complete with automatic clearing and moving the carriage entirely automatically as necessary. It could also be further extended to automatically extract square roots. Its mechanism was also adopted in its essentials, then with many innovations (but with ~~less of the Swiss robust construction~~ of the ~~Madas), in the US Frieden calculators. As it turned out, this final class of machines represented the pinacle~~ of ~~achievement in motorised mechanical~~ calculation.~~[[<<]]~~

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The late MADAS 20BTG calculator, seen above (:if equal {Site.PrintBook$:PSW} "True":)in FIG(MADAS20BTG)(:ifend:), which is part of this collection represents a classic exemplar of the late stages of this evolutionary development. Now fully utilising an electric motor it could fluently perform all the operations of arithmetic, complete with automatic clearing and moving the carriage entirely automatically as necessary. It could also be further extended to automatically extract square roots. Its mechanism was also adopted in its essentials, then with many innovations (but with less of the Swiss robust construction of the Madas), in the US Frieden calculators. As it turned out, this final class of machines represented the pinacle of achievement in motorised mechanical calculation.

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It was in July 1972, that the old ways for scientists and citizen alike were definitively undermined. In that month, to some astonishment, the Hewlett Packard company produced the HP-35 electronic 'pocket' calculator. It was an extraordinary leap forward, equipped not only with a red lit showing smooth performance of the arithmetic functions but also reciprocals, powers, square roots, logarithms and anti-logarithms (base e and 10), the trigonometric functions, pi, and a system of registers which enabled chain operations without having to write down intermediate results. For those of a technical orientation who could afford it, all else was now as obsolete as gaslight. Hewlett Packard followed quickly with the HP-45 appearing in the following year with a configurable display, more functions and registers, a variety of constants, and a more compact shape, more suited for the male shirt top pocket. A year later in 1974 the HP-65 was launched with all that could be done by the HP-45 but with the added feature of being user-programmable through a small built in magnetic strip reader. With that the diminutive HP calculator had taken a huge step towards the first mass-marketed personal computers (the TRS-80 - the author wrote his second book on one of these in 1981 - launched by Tandy, and the Apple-II by Apple, both launched in 1977).

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It was in July 1972, that the old ways for scientists and citizen alike were definitively undermined. In that month, to some astonishment, the Hewlett Packard company produced the HP-35 electronic 'pocket' calculator (see (:if equal {Site.PrintBook$:PSW} "True":)in TAB(HPCacl)(:ifend:) below). It was an extraordinary leap forward, equipped not only with a red lit showing smooth performance of the arithmetic functions but also reciprocals, powers, square roots, logarithms and anti-logarithms (base e and 10), the trigonometric functions, pi, and a system of registers which enabled chain operations without having to write down intermediate results. For those of a technical orientation who could afford it, all else was now as obsolete as gaslight. Hewlett Packard followed quickly with the HP-45 appearing in the following year with a configurable display, more functions and registers, a variety of constants, and a more compact shape, more suited for the male shirt top pocket. A year later in 1974 the HP-65 was launched with all that could be done by the HP-45 but with the added feature of being user-programmable through a small built in magnetic strip reader. With that the diminutive HP calculator had taken a huge step towards the first mass-marketed personal computers (the TRS-80 - the author wrote his second book on one of these in 1981 - launched by Tandy, and the Apple-II by Apple, both launched in 1977).

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Ready reckoners were in widespread use by shopkeepers and many others from the C17 on. They presented tables of precalculated results of many kinds of multiplication. These included the much needed calculations of the price for multiples of an item for sale, or per unit of weight. They could also be used to look up the calculations needed for wages and interest.[^see Bruce O.B. Williams and Roger G. Johnson, "Ready Reckoners", //IEEE Annals of the History of Computing//, October-December, 2005, pp. 64-80.^] One such, from 1892, shown below ~~is "~~Ropp~~'s Commercial~~ Calculator: a practical arithmetic for practical purposes, containing a complete system of useful, accurate, and convenient tables, together with simple, short, and practical methods for rapid calculation", a published in the US and used widely into the early C20. This one is the 1892 World's Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.

%center%%height=200px% http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp's Commercial Calculator\\

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Ready reckoners were in widespread use by shopkeepers and many others from the C17 on. They presented tables of precalculated results of many kinds of multiplication. These included the much needed calculations of the price for multiples of an item for sale, or per unit of weight. They could also be used to look up the calculations needed for wages and interest.[^see Bruce O.B. Williams and Roger G. Johnson, "Ready Reckoners", //IEEE Annals of the History of Computing//, October-December, 2005, pp. 64-80.^] One such, from 1892, shown below in FIG(Ropp) is "Ropp's Commercial Calculator: a practical arithmetic for practical purposes, containing a complete system of useful, accurate, and convenient tables, together with simple, short, and practical methods for rapid calculation", a published in the US and used widely into the early C20. This one is the 1892 World's Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.

%center%%height=200px%%id=Ropp% http://meta-studies.net/pmwiki/uploads/Ropp200.jpg"Ropp"|1892: Ropp's Commercial Calculator\\

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Other early new mathematical devices to gain broader use were simple adaptations of the sorts of tables that might be found in ready reckoners. There was an ever more extensive need to be able to measure and compare especially in the expanding processes of trade and commerce. The bane of earlier centuries (and even still) is lack of standardisation across localities in which trade took place. In particular, quantities were often not measured in the same units. As a result, special purpose devices, basically just forms of mechanical look-up tables were devised to enable conversion, needed not the least since performing associated conversion calculations each time was not only time consuming but beyond the skill of many who might need them. A particularly stark need for such devices was created, following the French Revolution, when the Revolutionary Government introduced metric measures. A "Convertisseur" from (1780–1810) designed by clock maker Gabrielle Chaix in Paris to assist in converting between the old measure of distance (the "Aune") to the new metric metre that was introduced in 1791, is shown ~~below.~~

%center%%height=200px% http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg|~1790: Conversion device\\

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Other early new mathematical devices to gain broader use were simple adaptations of the sorts of tables that might be found in ready reckoners. There was an ever more extensive need to be able to measure and compare especially in the expanding processes of trade and commerce. The bane of earlier centuries (and even still) is lack of standardisation across localities in which trade took place. In particular, quantities were often not measured in the same units. As a result, special purpose devices, basically just forms of mechanical look-up tables were devised to enable conversion, needed not the least since performing associated conversion calculations each time was not only time consuming but beyond the skill of many who might need them. A particularly stark need for such devices was created, following the French Revolution, when the Revolutionary Government introduced metric measures. A "Convertisseur" from (1780–1810) designed by clock maker Gabrielle Chaix in Paris to assist in converting between the old measure of distance (the "Aune") to the new metric metre that was introduced in 1791, is shown in FIG(convertiseur) below.

%center%%height=200px%%id=convertiseur% http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg"Convertiseur"|~1790: Conversion device\\

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One such line of development was based on the possibility of adding linear displacements of strips of metal. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe, later to be known as the Addiator (of which there is one in this collection), of which a bewildering number of different designs appeared in the late C19 and early C20. Some used strips or rods, and some used chains which were more versatile. A rather beautiful Locke Adder which uses strips moved by knobs, from 1905-10, sold by Clarence Locke, is shown below.

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One such line of development was based on the possibility of adding linear displacements of strips of metal. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe, later to be known as the Addiator (of which there is one in this collection), of which a bewildering number of different designs appeared in the late C19 and early C20. Some used strips or rods, and some used chains which were more versatile. A rather beautiful Locke Adder which uses strips moved by knobs, from 1905-10, sold by Clarence Locke, is shown (:if equal {Site.PrintBook$:PSW} "True":)in FIG(Locke)(:ifend:) below.

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%center% http://meta-studies.net/pmwiki/uploads/Locke170.jpg|The Locke Adder\\(collection Calculant)

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%center%%id=Locke% http://meta-studies.net/pmwiki/uploads/Locke170.jpg"The Locke Adder"|The Locke Adder\\(collection Calculant)

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Other simple linear devices in this collection are shown below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)

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Other simple linear devices in this collection are shown in TAB(SimpleLinearCalcs) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)

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The above relied either on the movement by a stylus or knobs of strips, rods or chains to create addition. Some (such as the Locke adder) used a simplified form of complementary arithmetic for subtraction,t others allowed a such as the Golden Gem allowed reverse motion, and others again such as the Addiator could be turned over to perform the subtraction. Most (but not the Locke Adder) had a simple provision for carries and some (such as the Scribola - which also had a very early printout) had clearing levers to bring the display back to zero for the next calculation. All however, whilst affordable, were cumbersome and slow to use since each digit had to be individually entered by performing a sliding motion. It was much quicker to add the numbers on paper using mental arithmetic, but of course, here that capability was lacking, or where the effort of doing it was considered tedious, then these devices began to find a market in the first half of the C20, and thousands were produced and sold across the more industrialised countries of Europe, the British Empire and the USA.~~[[<<]]~~

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The above relied either on the movement by a stylus or knobs of strips, rods or chains to create addition. Some (such as the Locke adder) used a simplified form of complementary arithmetic for subtraction,t others allowed a such as the Golden Gem allowed reverse motion, and others again such as the Addiator could be turned over to perform the subtraction. Most (but not the Locke Adder) had a simple provision for carries and some (such as the Scribola - which also had a very early printout) had clearing levers to bring the display back to zero for the next calculation. All however, whilst affordable, were cumbersome and slow to use since each digit had to be individually entered by performing a sliding motion. It was much quicker to add the numbers on paper using mental arithmetic, but of course, here that capability was lacking, or where the effort of doing it was considered tedious, then these devices began to find a market in the first half of the C20, and thousands were produced and sold across the more industrialised countries of Europe, the British Empire and the USA.

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Similar simple devices were developed which utilised simple rotation of cogs, with a crude carry process (usually along the lines of that used by Schickard). They relied for their success on having but a small number of interacting cogs, so that the carry mechanism would not jam, or adopting the use of springs (in place of Pascal's weights) which would store rotary motion to then be utilised when a carry was required. The device shown below was the first model made by C.H. Webb (from New York) who began marketing it in 1869. It is made of brass and is set on a heavy wooden base.

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Similar simple devices were developed which utilised simple rotation of cogs, with a crude carry process (usually along the lines of that used by Schickard). They relied for their success on having but a small number of interacting cogs, so that the carry mechanism would not jam, or adopting the use of springs (in place of Pascal's weights) which would store rotary motion to then be utilised when a carry was required. The device shown below (:if equal {Site.PrintBook$:PSW} "True":) in FIG(Webb)(:ifend:) was the first model made by C.H. Webb (from New York) who began marketing it in 1869. It is made of brass and is set on a heavy wooden base.

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%center%~~Web~~ Patent Adder and Talley Board 1869\\

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%center%Webb Patent Adder and Talley Board 1869\\

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%center%%height=200px% http://meta-studies.net/pmwiki/uploads/WebbH200.jpg|1869:~~Web~~ Patent Adder and Talley Board\\

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%center%%height=200px%%id=Webb% http://meta-studies.net/pmwiki/uploads/WebbH200.jpg"Webb Adder"|1869:Webb Patent Adder and Talley Board\\

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Other simple rotational adding devices in this collection are shown below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)

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Other simple rotational adding devices in this collection are shown in TAB(SimpleRotationalCalcs) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)

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The main advantage of these devices was that they were cheap to manufacture and could be easily mass-produced. We can of course see a lot of innovation in the detail of these machines. A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which simply used successive rotations of a wheel to wind on successive numbers whilst a ball bearing, moving in a spiral groove, tracked the successive rotations. Early experiments with keyboards can be seen in the Adix adding machine of 1903.~~[[<<]]~~

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The main advantage of these devices was that they were cheap to manufacture and could be easily mass-produced. We can of course see a lot of innovation in the detail of these machines. A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which simply used successive rotations of a wheel to wind on successive numbers whilst a ball bearing, moving in a spiral groove, tracked the successive rotations. Early experiments with keyboards can be seen in the Adix adding machine of 1903.

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||~1951||Original Ohdner Model 39\\serial 39-288965||Ohdner||Pinwheel||%height=100px%[[Site.OriginalOhdner39-1951|~~Add Picture~~]]||

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||~1951||Original Ohdner Model 39\\serial 39-288965||Ohdner||Pinwheel||%height=100px%[[Site.OriginalOhdner39-1951| http://meta-studies.net/pmwiki/uploads/Ohdner1951H150.jpg]]||

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||~1951||Original Ohdner Model 39\\serial 39-288965||Ohdner||Pinwheel||%height=100px% ~~Add Picture~~||

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||~1951||Original Ohdner Model 39\\serial 39-288965||Ohdner||Pinwheel||%height=100px% http://meta-studies.net/pmwiki/uploads/Ohdner1951H150.jpg]||

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(:ifend:)

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(:ifend:)

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||~1917 ||Madas IX Maxima||Madas||Auto Division||%width=~~225px~~%[[Site.Madas-IX-Maxima| http://meta-studies.net/pmwiki/uploads/MADAS-~~1917H125~~.jpg]]||

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||~1917 ||Madas IX Maxima||Madas||Auto Division||%width=250px%[[Site.Madas-IX-Maxima| http://meta-studies.net/pmwiki/uploads/MADAS-1917W250.jpg]]||

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->By the ~~1860’s~~, the favorite device for lessening the work of the computer (human), the mathematical table, had become an object whose dizzying rows of printed figures would fascinate the Victorian public. These tables displayed the limitless fecundity of numbers, and transformed them into a commodity that would bring the power of calculation within the reach of the ordinary citizen. The centrality of tables of numbers and calculation to mid-Victorian life was famously portrayed by Charles ~~Dickens’~~ character Thomas Gradgrind, who always had a rule and a pair of scales and the multiplication table in his pocket.[^M.N. Wise, //The Values of Precision//, Princeton University Press, USA, 1995, p. 318.^]

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->By the 1860's, the favorite device for lessening the work of the computer (human), the mathematical table, had become an object whose dizzying rows of printed figures would fascinate the Victorian public. These tables displayed the limitless fecundity of numbers, and transformed them into a commodity that would bring the power of calculation within the reach of the ordinary citizen. The centrality of tables of numbers and calculation to mid-Victorian life was famously portrayed by Charles Dickens' character Thomas Gradgrind, who always had a rule and a pair of scales and the multiplication table in his pocket.[^M.N. Wise, //The Values of Precision//, Princeton University Press, USA, 1995, p. 318.^]

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Other early new mathematical devices to gain broader use were simple adaptations of the sorts of tables that might be found in ready reckoners. There was an ever more extensive need to be able to measure and compare especially in the expanding processes of trade and commerce. The bane of earlier centuries (and even still) is lack of standardisation across localities in which trade took place. In particular, quantities were often not measured in the same units. As a result, special purpose devices, basically just forms of mechanical look-up tables were devised to enable conversion, needed not the least since performing associated conversion calculations each time was not only time consuming but beyond the skill of many who might need them. A particularly stark need for such devices was created, following the French Revolution, when the Revolutionary Government introduced metric measures. A ~~“Convertisseur”~~ from (~~1780–1810~~) designed by clock maker Gabrielle Chaix in Paris to assist in converting between the old measure of distance (the ~~“Aune”~~) to the new metric metre that was introduced in 1791, is shown below.

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Other early new mathematical devices to gain broader use were simple adaptations of the sorts of tables that might be found in ready reckoners. There was an ever more extensive need to be able to measure and compare especially in the expanding processes of trade and commerce. The bane of earlier centuries (and even still) is lack of standardisation across localities in which trade took place. In particular, quantities were often not measured in the same units. As a result, special purpose devices, basically just forms of mechanical look-up tables were devised to enable conversion, needed not the least since performing associated conversion calculations each time was not only time consuming but beyond the skill of many who might need them. A particularly stark need for such devices was created, following the French Revolution, when the Revolutionary Government introduced metric measures. A "Convertisseur" from (1780–1810) designed by clock maker Gabrielle Chaix in Paris to assist in converting between the old measure of distance (the "Aune") to the new metric metre that was introduced in 1791, is shown below.

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*something else that can be moved (for example, although it was barely used,[^An exception is the ingenious MONIAC hydraulic computer used to demonstrate macroeconomic theory. See for example, Anna Corkhill ‘A superb explanatory ~~device’~~ //University of Melbourne Collections//, issue 10, June 2012^] the height of columns of water).

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*something else that can be moved (for example, although it was barely used,[^An exception is the ingenious MONIAC hydraulic computer used to demonstrate macroeconomic theory. See for example, Anna Corkhill 'A superb explanatory device' //University of Melbourne Collections//, issue 10, June 2012^] the height of columns of water).

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One such line of development was based on the possibility of adding linear displacements of strips of metal. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (~~1613–88~~) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe, later to be known as the Addiator (of which there is one in this collection), of which a bewildering number of different designs appeared in the late C19 and early C20. Some used strips or rods, and some used chains which were more versatile. A rather beautiful Locke Adder which uses strips moved by knobs, from 1905-10, sold by Clarence Locke, is shown below.

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One such line of development was based on the possibility of adding linear displacements of strips of metal. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe, later to be known as the Addiator (of which there is one in this collection), of which a bewildering number of different designs appeared in the late C19 and early C20. Some used strips or rods, and some used chains which were more versatile. A rather beautiful Locke Adder which uses strips moved by knobs, from 1905-10, sold by Clarence Locke, is shown below.

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Popular though some of these were as they became cheaper and more accessible not only to shopkeepers but ordinary citizens who might value the assistance they offered, for example in their role as taxpayers,[^See for example, A.P. Kidwell, "~~‘Yours~~ for ~~Improvement’—The~~ Adding Machines of Chicago, ~~1884–1930~~", //IEEE Annals of the History of Computing//, July-September, 2001, pp. 3-6.^] they suffered from the same problems of clumsy input and slow operation that afflicted the simple linear machines. Some such as the Adall could only add, others had no provision for zeroing, and all were slow to use. Further, such adders, whilst simple in concept and cheap to manufacture, were so slow to use for repetitive calculation that they were virtually useless for the key arithmetic operations of multiplication and division. A quick method repeated addition and subtraction was required at minimum to achieve these other two functions. That required a more expensive approach and a much more elaborate machine, the first commercial variant of which was designed and sold as the "Arithmometer" by Thomas de Colmar.

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Popular though some of these were as they became cheaper and more accessible not only to shopkeepers but ordinary citizens who might value the assistance they offered, for example in their role as taxpayers,[^See for example, A.P. Kidwell, "'Yours for Improvement'—The Adding Machines of Chicago, 1884–1930", //IEEE Annals of the History of Computing//, July-September, 2001, pp. 3-6.^] they suffered from the same problems of clumsy input and slow operation that afflicted the simple linear machines. Some such as the Adall could only add, others had no provision for zeroing, and all were slow to use. Further, such adders, whilst simple in concept and cheap to manufacture, were so slow to use for repetitive calculation that they were virtually useless for the key arithmetic operations of multiplication and division. A quick method repeated addition and subtraction was required at minimum to achieve these other two functions. That required a more expensive approach and a much more elaborate machine, the first commercial variant of which was designed and sold as the "Arithmometer" by Thomas de Colmar.

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Thomas de Colmar first made public his design for a calculating machine capable of doing all four functions (addition, subtraction, multiplication and division) when he was granted a patent for it in 1820.[^Patent no. 1420, 18 November 1820^]. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.[^For the most authoritative website on the Thomas de Colmar machines and history see ~~Valéry~~ Monier's magisterial site [[http://www.arithmometre.org]], viewed 20 July 2013.^] The first design consisted of four step drums (along the lines invented by Leibniz, but not necessarily based on having ever heard of, let alone seen the internal mechanism of Leibniz's invention[^see Friedrich W. Kistermann, "When Could Anyone Have Seen ~~Leibniz’s~~ Stepped Wheel?", //IEEE Annals of the History of Computing//, Volume 21, Number 2, 1999, pp. 68-72. However, as Stephen Johnston (see reference below) points out, images of Leibniz's machine were available from the late C18, see for example 1744 engraving in Annegret Kehrbaum and Bernhard Korte, //Calculi: Bilder des Rechnens einst und heute (Images of Computing in Olden and Modern Times)//, Opladen, 1995, p. 61.^]).

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Thomas de Colmar first made public his design for a calculating machine capable of doing all four functions (addition, subtraction, multiplication and division) when he was granted a patent for it in 1820.[^Patent no. 1420, 18 November 1820^]. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.[^For the most authoritative website on the Thomas de Colmar machines and history see Valéry Monier's magisterial site [[http://www.arithmometre.org]], viewed 20 July 2013.^] The first design consisted of four step drums (along the lines invented by Leibniz, but not necessarily based on having ever heard of, let alone seen the internal mechanism of Leibniz's invention[^see Friedrich W. Kistermann, "When Could Anyone Have Seen Leibniz's Stepped Wheel?", //IEEE Annals of the History of Computing//, Volume 21, Number 2, 1999, pp. 68-72. However, as Stephen Johnston (see reference below) points out, images of Leibniz's machine were available from the late C18, see for example 1744 engraving in Annegret Kehrbaum and Bernhard Korte, //Calculi: Bilder des Rechnens einst und heute (Images of Computing in Olden and Modern Times)//, Opladen, 1995, p. 61.^]).

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%center%1862: Diagram of the Thomas de Colmar arithmometer mechanism.[^ Franz Reuleaux, //Die ~~Thomas’sche~~ Rechenmaschine//, Freiberg, 1862 reproduced in ~~Reuleaux’s~~ article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^]\\ (:if equal {Site.PrintBook$:PSW} "False":)(Click on the image for an enlargement.)(:ifend:)\\(Source: Museum of the History of Science, University of Oxford.)

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%center%1862: Diagram of the Thomas de Colmar arithmometer mechanism.[^ Franz Reuleaux, //Die Thomas'sche Rechenmaschine//, Freiberg, 1862 reproduced in Reuleaux's article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^]\\ (:if equal {Site.PrintBook$:PSW} "False":)(Click on the image for an enlargement.)(:ifend:)\\(Source: Museum of the History of Science, University of Oxford.)

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diagram.[^ Franz Reuleaux, //Die ~~Thomas’sche~~ Rechenmaschine//, Freiberg, 1862 reproduced in ~~Reuleaux’s~~ article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^] (:if equal {Site.PrintBook$:PSW} "False":)(Click on the image for an enlargement.)(:ifend:)\\(Source: Museum of the History of Science, University of Oxford.)

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diagram.[^ Franz Reuleaux, //Die Thomas'sche Rechenmaschine//, Freiberg, 1862 reproduced in Reuleaux's article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^] (:if equal {Site.PrintBook$:PSW} "False":)(Click on the image for an enlargement.)(:ifend:)\\(Source: Museum of the History of Science, University of Oxford.)

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Thomas de Colmar himself was the director of an insurance company. In the 1820s the insurance industry was rapidly expanding as a consequence of free trade and the transport revolution, and France had become international centres of the industry.[^Peter Borscheid, "Europe: Overview", in Peter Borscheid and Niels Vigo Haueter (eds), //World Insurance: The Evolution of a Global Risk Network//, Oxford University Press, Oxford, 2012, p. 39.^] The likely consequent intensification of work no doubt galvanised Thomas's interest in finding an efficient way of handling multiple calculations. But given his responsibilities in an intense commercial environment is unlikely that he would have been able to spend all or even a great deal of his time on designing and building more arithmometers over the next several decades. Indeed it was not until several decades later that, in 1844, the arithmometer, very much re-designed, appeared at a French national exhibition. There it could be found amongst precision instruments in a category of ~~‘diverse~~ measures, counters and calculating ~~machines’~~.[^ibid.^] Johnston thus argues that far from being a lone pioneer, the machines of Thomas were in competition (and regarded initially as a poor second) to others. However, over a half century, the machines of Thomas, as they evolved, prevailed.[^As cited by Johnston, Jean Marguin, //Histoire des instruments et machines à calculer//, Paris, 1994, p. 111: ~~‘Pendant~~ un demi-~~siècle~~, la machine y ~~régna~~ seule.’^] Johnston notes that to achieve this "Thomas campaigned both through the press and in commissioned publications. He also engaged in the rituals of patronage, rituals that we might more readily associate with the decoratively elaborate calculating machines of the 18th century."[^Johnston, "Making the arithmometer count".^] However, the design of the Thomas machine was sufficiently beautifully executed to make it an appropriate gift to persons of high standing, a property essential to its successful promotion.

Indeed the Thomas arithmometer did take off as a consumer product in France, the UK and Europe and variants continued to sell right up to the first world war. They were not cheap. For example, in 1872 British engineer Henry Brunel wrote that "I have just got what my mother irreverently calls ‘a new ~~toy’ –~~ to wit a calculating machine price £12 which does all the common operations of arithmetic viz addition, multiplication, subtraction & division in the twinkling of an eye. It is really a very useful article worth its weight in brass."[^ Brunel to Adams, 18 March 1866, Bristol University Library, Brunel Collection, Letter Book VII, f. 106, cited in Johnston, ibid.^] In terms of today's purchasing power, £12 from 1872 was the equivalent of £5,840 (~US$8,900) in 2013 (based on average earnings).[^Calculated using the [[http://www.measuringworth.com]] calculator on 21 July 2013^]

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Thomas de Colmar himself was the director of an insurance company. In the 1820s the insurance industry was rapidly expanding as a consequence of free trade and the transport revolution, and France had become international centres of the industry.[^Peter Borscheid, "Europe: Overview", in Peter Borscheid and Niels Vigo Haueter (eds), //World Insurance: The Evolution of a Global Risk Network//, Oxford University Press, Oxford, 2012, p. 39.^] The likely consequent intensification of work no doubt galvanised Thomas's interest in finding an efficient way of handling multiple calculations. But given his responsibilities in an intense commercial environment is unlikely that he would have been able to spend all or even a great deal of his time on designing and building more arithmometers over the next several decades. Indeed it was not until several decades later that, in 1844, the arithmometer, very much re-designed, appeared at a French national exhibition. There it could be found amongst precision instruments in a category of 'diverse measures, counters and calculating machines'.[^ibid.^] Johnston thus argues that far from being a lone pioneer, the machines of Thomas were in competition (and regarded initially as a poor second) to others. However, over a half century, the machines of Thomas, as they evolved, prevailed.[^As cited by Johnston, Jean Marguin, //Histoire des instruments et machines à calculer//, Paris, 1994, p. 111: 'Pendant un demi-siècle, la machine y régna seule.'^] Johnston notes that to achieve this "Thomas campaigned both through the press and in commissioned publications. He also engaged in the rituals of patronage, rituals that we might more readily associate with the decoratively elaborate calculating machines of the 18th century."[^Johnston, "Making the arithmometer count".^] However, the design of the Thomas machine was sufficiently beautifully executed to make it an appropriate gift to persons of high standing, a property essential to its successful promotion.

Indeed the Thomas arithmometer did take off as a consumer product in France, the UK and Europe and variants continued to sell right up to the first world war. They were not cheap. For example, in 1872 British engineer Henry Brunel wrote that "I have just got what my mother irreverently calls 'a new toy' – to wit a calculating machine price £12 which does all the common operations of arithmetic viz addition, multiplication, subtraction & division in the twinkling of an eye. It is really a very useful article worth its weight in brass."[^ Brunel to Adams, 18 March 1866, Bristol University Library, Brunel Collection, Letter Book VII, f. 106, cited in Johnston, ibid.^] In terms of today's purchasing power, £12 from 1872 was the equivalent of £5,840 (~US$8,900) in 2013 (based on average earnings).[^Calculated using the [[http://www.measuringworth.com]] calculator on 21 July 2013^]

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The above three arithmometers demonstrate the sorts of improvements to the basic arithmometer design which now emerged. The first, a TIM (~~“Time~~ is ~~Money”~~ ) arithmometer manufactured by Ludwig Spitz and Co. of Berlin-Tempelhof in 1909 was greatly strengthened from the Thomas design to create a much more robust and reliable machine. First produced in a wooden box it was later made much stronger by installing it in a cast iron frame which held all parts rigidly.[^See Ernst Martin, //The Calculating Machines (Die Rechenmaschinen): Their History and Development//, ed. and trs. by Peggy Aldridge Kidwell and Michael R. Williams, MIT Press, Mass., 1992, p. ~~191–4~~^] Beginning a change in style that would be emulated in many other machines the brass panels were now enamelled black consistent with the management, industrial and commercial settings where it was intended to find its market. The other two machines in this set would also originally have had a similar black finish. (Unfortunately, there was a tendency in the late C20 to "take the machines back to brass" in the same way that in the 1960s there was a trend to remove the original finish from wood on vintage furniture, and plaster from brick walls in old houses.)[[<<]]

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The above three arithmometers demonstrate the sorts of improvements to the basic arithmometer design which now emerged. The first, a TIM ("Time is Money" ) arithmometer manufactured by Ludwig Spitz and Co. of Berlin-Tempelhof in 1909 was greatly strengthened from the Thomas design to create a much more robust and reliable machine. First produced in a wooden box it was later made much stronger by installing it in a cast iron frame which held all parts rigidly.[^See Ernst Martin, //The Calculating Machines (Die Rechenmaschinen): Their History and Development//, ed. and trs. by Peggy Aldridge Kidwell and Michael R. Williams, MIT Press, Mass., 1992, p. 191–4^] Beginning a change in style that would be emulated in many other machines the brass panels were now enamelled black consistent with the management, industrial and commercial settings where it was intended to find its market. The other two machines in this set would also originally have had a similar black finish. (Unfortunately, there was a tendency in the late C20 to "take the machines back to brass" in the same way that in the 1960s there was a trend to remove the original finish from wood on vintage furniture, and plaster from brick walls in old houses.)[[<<]]

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The above principle was incorporated into a MADAS arithmometer, developed by Erwin Janz and manufactured by Egli in Zurich, starting in 1913. The acronym MADAS was short for ~~“Multiplication~~, Addition, Division - Automatically, ~~Substraction”~~). The achievement of an entirely automatic division process - the first ever for an arithmometer style calculator. In this collection there is a MADAS IX Maxima calculator (produced in 1917), an ambitious machine also in that it could accept 9 digits, up to one thousand million, as input and could display 16 digits (representing numbers up to ten thousand trillion) in its results register. Two MADAS models were produced and by 1920 about 1,000 were being produced with some 7,000 having been sold from countries as wide apart as Europe and Australia.[^Martin Reese, Hamburg, //55 erfolgreiche Jahre: MADAS-Rechenautomaten aus der Schweiz 1913 - 1968//, http://www.rechnerlexikon.de/files/~~MADAS—8~~-2010.pdf, viewed 18 February 2012.^]

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The above principle was incorporated into a MADAS arithmometer, developed by Erwin Janz and manufactured by Egli in Zurich, starting in 1913. The acronym MADAS was short for "Multiplication, Addition, Division - Automatically, Substraction"). The achievement of an entirely automatic division process - the first ever for an arithmometer style calculator. In this collection there is a MADAS IX Maxima calculator (produced in 1917), an ambitious machine also in that it could accept 9 digits, up to one thousand million, as input and could display 16 digits (representing numbers up to ten thousand trillion) in its results register. Two MADAS models were produced and by 1920 about 1,000 were being produced with some 7,000 having been sold from countries as wide apart as Europe and Australia.[^Martin Reese, Hamburg, //55 erfolgreiche Jahre: MADAS-Rechenautomaten aus der Schweiz 1913 - 1968//, http://www.rechnerlexikon.de/files/MADAS—8-2010.pdf, viewed 18 February 2012.^]

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The pinwheel calculator was developed as an improvement on the arithmometer more or less simultaneously in Russia in 1878 by Swedish engineer Willgodt Theophil Odhner (1845-1905) and in the US in 1874, by Frank Stephen Baldwin (1838-1925). Although they worked independently of each there machines were so similar that the 'Ohdner' or 'Baldwin' machine became more or less interchangeable terms.[^Diana H. Hook and Jeremy M. Norman, //Origins of Cyberspace//, Novato, California, 2002, p. 255.^]. The designs utilised a clever ~~‘counting gear’~~ in which the number of teeth protruding could be adjusted by sliders (and later a push-down keyboard). A pinwheel and the internal mechanism (with some pinwheels removed) from a Walther pinwheel calculator in this collection is shown below.

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The pinwheel calculator was developed as an improvement on the arithmometer more or less simultaneously in Russia in 1878 by Swedish engineer Willgodt Theophil Odhner (1845-1905) and in the US in 1874, by Frank Stephen Baldwin (1838-1925). Although they worked independently of each there machines were so similar that the 'Ohdner' or 'Baldwin' machine became more or less interchangeable terms.[^Diana H. Hook and Jeremy M. Norman, //Origins of Cyberspace//, Novato, California, 2002, p. 255.^]. The designs utilised a clever 'counting gear' in which the number of teeth protruding could be adjusted by sliders (and later a push-down keyboard). A pinwheel and the internal mechanism (with some pinwheels removed) from a Walther pinwheel calculator in this collection is shown below.

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Notably no crank handle is needed. The small force required for the addition comes simply from the key press. The process of multiplication is done by multiple presses of the appropriate key. This is fast, not the least because with two hands up to ten keys can be pressed at once. But subtraction must be carried out by addition of complementary numbers. Carrying of ~~“tens”~~ is implemented between the accumulating read-out wheels.

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Notably no crank handle is needed. The small force required for the addition comes simply from the key press. The process of multiplication is done by multiple presses of the appropriate key. This is fast, not the least because with two hands up to ten keys can be pressed at once. But subtraction must be carried out by addition of complementary numbers. Carrying of "tens" is implemented between the accumulating read-out wheels.

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An entirely different evolutionary path (mentioned earlier) attempted to solving the problem of mechanising the four arithmetic operations (+, -, x, /). The emphasis was on finding ways to directly perform the more difficult two operations of multiplication and division. The approach was a development from ~~Napier’s~~ rods - or ~~“bones”~~ (developed by John Napier (~~1550–1617~~). As already mentioned calculational approaches had been designed around these principles by Wilhelm Schickard in 1623, Charles Cotterel in 1667, Gaspard Schott in 1668, and Samuel Morland between 1625 and 1695.

The earliest of these machines had been that of Schickard (below, left). In the upper part is a set of rotatable Napier's rods revealed by windows to give partial products. In the lower part is the world's first known stylus operated adding machine to add these partial products up. A late and unique expression of these in this collection (below, right) is Justin ~~Bamberger’s~~ Omega Calculating Machine (1903-6). In the upper section is a set of Napier's bones revealed by moveable windows for discovering the partial products of two multiplied numbers. In the lower section is a Locke adding machine for adding them up.

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An entirely different evolutionary path (mentioned earlier) attempted to solving the problem of mechanising the four arithmetic operations (+, -, x, /). The emphasis was on finding ways to directly perform the more difficult two operations of multiplication and division. The approach was a development from Napier's rods - or "bones" (developed by John Napier (1550–1617). As already mentioned calculational approaches had been designed around these principles by Wilhelm Schickard in 1623, Charles Cotterel in 1667, Gaspard Schott in 1668, and Samuel Morland between 1625 and 1695.

The earliest of these machines had been that of Schickard (below, left). In the upper part is a set of rotatable Napier's rods revealed by windows to give partial products. In the lower part is the world's first known stylus operated adding machine to add these partial products up. A late and unique expression of these in this collection (below, right) is Justin Bamberger's Omega Calculating Machine (1903-6). In the upper section is a set of Napier's bones revealed by moveable windows for discovering the partial products of two multiplied numbers. In the lower section is a Locke adding machine for adding them up.

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||1623: Recreation of ||1904-1905: ~~Bamberger’s~~ Omega||

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||1623: Recreation of ||1904-1905: Bamberger's Omega||

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%center% %height=250px% http://meta-studies.net/pmwiki/uploads/BambergerOmegaH250.jpg|1904-1905: ~~Bamberger’s~~ Omega calculating machine\\

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%center% %height=250px% http://meta-studies.net/pmwiki/uploads/BambergerOmegaH250.jpg|1904-1905: Bamberger's Omega calculating machine\\

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A much heavier and complex mechanical approach was also explored. First it was embodied in ~~Léon Bollée’s~~ calculating machine which won a gold medal at the Paris Exposition of 1889. One surviving example of this bulky but beautiful machine can be seen at the ~~Musée~~ des Arts et ~~Métiers~~ in Paris. This collection has only an article on this ~~“New~~ Calculating Machine of very General ~~Applicability”~~ from the Manufacturer and Builder of 1890.

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A much heavier and complex mechanical approach was also explored. First it was embodied in Léon Bollée's calculating machine which won a gold medal at the Paris Exposition of 1889. One surviving example of this bulky but beautiful machine can be seen at the Musée des Arts et Métiers in Paris. This collection has only an article on this "New Calculating Machine of very General Applicability" from the Manufacturer and Builder of 1890.

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%center% Leon ~~Bollée~~ Calculating Machine "A New Calculating Machine of very General ~~Applicability”~~\\//The Manufacturer and Builder 1890//[^1890: Leon ~~Bollée~~ Calculating Machine, “A New Calculating Machine of very General ~~Applicability”~~, //The Manufacturer and Builder//, July 1890, p. 156. Original print article.^]\\

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%center% Leon Bollée Calculating Machine "A New Calculating Machine of very General Applicability"\\//The Manufacturer and Builder 1890//[^1890: Leon Bollée Calculating Machine, "A New Calculating Machine of very General Applicability", //The Manufacturer and Builder//, July 1890, p. 156. Original print article.^]\\

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%center%%height=250px% http://meta-studies.net/pmwiki/uploads/BolleeMAB1890H250.jpg|Leon ~~Bollée~~ Calculating Machine\\
"A New Calculating Machine of very General ~~Applicability”~~\\
//The Manufacturer and Builder 1890//[^1890: Leon ~~Bollée~~ Calculating Machine, “A New Calculating Machine of very General ~~Applicability”~~, //The Manufacturer and Builder//, July 1890, p. 156. Original print article.^]\\

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%center%%height=250px% http://meta-studies.net/pmwiki/uploads/BolleeMAB1890H250.jpg|Leon Bollée Calculating Machine\\
"A New Calculating Machine of very General Applicability"\\
//The Manufacturer and Builder 1890//[^1890: Leon Bollée Calculating Machine, "A New Calculating Machine of very General Applicability", //The Manufacturer and Builder//, July 1890, p. 156. Original print article.^]\\

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Similar principles were however utilised by Otto Steiger in Switzerland who in 1895 patented a rather more practical ~~“Millionaire~~ calculating ~~machine”~~ which had a simple enough mechanism to enable production on a commercial scale.[[<<]]

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Similar principles were however utilised by Otto Steiger in Switzerland who in 1895 patented a rather more practical "Millionaire calculating machine" which had a simple enough mechanism to enable production on a commercial scale.[[<<]]

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Manufactured by H.W. Egli, some 4,655 Millionaires were sold between 1895 and 1935[^//Origins of Cyberspace// p. 242.^] at a 1912 price of about US$480[^Price list in Edmonds Collins, //The Millionaire Calculating Machine//, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. See also price of US$500 at 1914 prices given by Luc de Brabandere cited in B.O.B. Williams," Check ~~Figures—A~~ Once Ubiquitous Tool for Book-keepers, published in //Slide Rule and Calculation monographs//, Slide Rule Circle, UK, 2002, pp. 59-98.^] (about $11,700 in 2013 US dollars[^Calculated using the [[http://www.measuringworth.com]] calculator on 24 July 2013^]). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,[^Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant).^] and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones. The machine still operates reliably after more than 100 years.

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Manufactured by H.W. Egli, some 4,655 Millionaires were sold between 1895 and 1935[^//Origins of Cyberspace// p. 242.^] at a 1912 price of about US$480[^Price list in Edmonds Collins, //The Millionaire Calculating Machine//, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. See also price of US$500 at 1914 prices given by Luc de Brabandere cited in B.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, published in //Slide Rule and Calculation monographs//, Slide Rule Circle, UK, 2002, pp. 59-98.^] (about $11,700 in 2013 US dollars[^Calculated using the [[http://www.measuringworth.com]] calculator on 24 July 2013^]). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,[^Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant).^] and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones. The machine still operates reliably after more than 100 years.

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%center% ~1929: ~~“Herzstark”~~ electric Calculating Machine serial 6549\\badged by Herzstark, Vienna\\(essentially a Badenia Model TE 13 Duplex)\\

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%center% ~1929: "Herzstark" electric Calculating Machine serial 6549\\badged by Herzstark, Vienna\\(essentially a Badenia Model TE 13 Duplex)\\

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%center%%height=250px% http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometerH250.jpg|~1929: ~~“Herzstark”~~ electric Calculating Machine serial 6549\\

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%center%%height=250px% http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometerH250.jpg|~1929: "Herzstark" electric Calculating Machine serial 6549\\

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In short, the use of a calculating technology is not just intellectual. It is what Jean-~~François~~ Gauvin[^Jean-~~François~~ Gauvin , Habits of Knowledge: Artisans, Savants and Mechanical Devices in Seventeenth-Century French Natural Philosophy, The Department of the History of Science, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of History of Science, Harvard University, Cambridge, Mass., USA, November 2008, pp. 113. ^] refers to as "gestural". Gestural knowledge is the embodied knowledge that artisans rely on when they execute work of high craft skill. The first time someone looks at a Thomas de Colmar arithmometer learning how to add and subtract takes some time. Doing division and multiplication is much more challenging, especially if attempted without a good knowledge of how it can be done on paper. The first time is slow and subject to mistakes. It is only after repeated practice that the gestures required become so practiced that they are quick, instinctive and reliable. It is only then that the potential for calculation with such a device can be can be judged. And it would only have been after this sort of practice that one could credit the Gentleman's Magazine of 1857 claim that:

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In short, the use of a calculating technology is not just intellectual. It is what Jean-François Gauvin[^Jean-François Gauvin , Habits of Knowledge: Artisans, Savants and Mechanical Devices in Seventeenth-Century French Natural Philosophy, The Department of the History of Science, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of History of Science, Harvard University, Cambridge, Mass., USA, November 2008, pp. 113. ^] refers to as "gestural". Gestural knowledge is the embodied knowledge that artisans rely on when they execute work of high craft skill. The first time someone looks at a Thomas de Colmar arithmometer learning how to add and subtract takes some time. Doing division and multiplication is much more challenging, especially if attempted without a good knowledge of how it can be done on paper. The first time is slow and subject to mistakes. It is only after repeated practice that the gestures required become so practiced that they are quick, instinctive and reliable. It is only then that the potential for calculation with such a device can be can be judged. And it would only have been after this sort of practice that one could credit the Gentleman's Magazine of 1857 claim that:

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These overblown claims are reminiscent of similar claims for their inventions by Pascal (with this machine the user can do with ease, "without effort of memory" and "without even thinking of it", every possible arithmetic operation[^Pascal, ~~ligé~~ de retenir ou ~~d’emprunter~~ les nombres ~~nécessaires~~, et combien ~~d’erreurs~~ se glissent dans ces ~~rétentions~~ et emprunts, à mois ~~d’une très~~ longue habitude et, en outre, ~~d’une~~ attention profonde et qui fatigue ~~l’esprit~~ en peu de temps. Cette machine ~~délivre~~ celui qui ~~opère~~ par elle de cette vexation; il suffit ~~qu’il~~ ait le jugement, elle le ~~relève~~ du ~~défaut~~ de la ~~mémoire~~; et, sans rien retenir ni emprunter, elle fait ~~d’elle~~-~~même~~ ce ~~qu’il désire~~, sans ~~même qu’il~~ y pense.” p. 337^]) and Moreland (allowing addition and subtraction "without charging the memory or disturbing the mind[^S. Moreland, //A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence// 1672, title page.^]). They show the hope, that the mental activity could be replaced by the machine. But in reality, for all of these machines it was not just a question of the high cost of obtaining it, but the learning and practice required to use it.

to:

These overblown claims are reminiscent of similar claims for their inventions by Pascal (with this machine the user can do with ease, "without effort of memory" and "without even thinking of it", every possible arithmetic operation[^Pascal, ligé de retenir ou d'emprunter les nombres nécessaires, et combien d'erreurs se glissent dans ces rétentions et emprunts, à mois d'une très longue habitude et, en outre, d'une attention profonde et qui fatigue l'esprit en peu de temps. Cette machine délivre celui qui opère par elle de cette vexation; il suffit qu'il ait le jugement, elle le relève du défaut de la mémoire; et, sans rien retenir ni emprunter, elle fait d'elle-même ce qu'il désire, sans même qu'il y pense." p. 337^]) and Moreland (allowing addition and subtraction "without charging the memory or disturbing the mind[^S. Moreland, //A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence// 1672, title page.^]). They show the hope, that the mental activity could be replaced by the machine. But in reality, for all of these machines it was not just a question of the high cost of obtaining it, but the learning and practice required to use it.

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%center%%height=250px% http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer\\
earliest wood-cased model, serial 2491\\

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%center%%height=250px% http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491\\

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%center% %height=250px% http://meta-studies.net/pmwiki/uploads/Schickard1H250.jpg|1623: Recreation of Wilhelm Schickard's\\
calculating machine\\

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%center% %height=250px% http://meta-studies.net/pmwiki/uploads/Schickard1H250.jpg|1623: Recreation of Wilhelm Schickard's calculating machine\\

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%center% %height=250px% http://meta-studies.net/pmwiki/uploads/BambergerOmegaH250.jpg|1904-1905: Bamberger’s Omega\\
calculating machine\\

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%center% %height=250px% http://meta-studies.net/pmwiki/uploads/BambergerOmegaH250.jpg|1904-1905: Bamberger’s Omega calculating machine\\

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%center% Leon Bollée Calculating Machine\\"A New Calculating Machine of very General Applicability”\\//The Manufacturer and Builder 1890//[^1890: Leon Bollée Calculating Machine, “A New Calculating Machine of very General Applicability”, //The Manufacturer and Builder//, July 1890, p. 156. Original print article.^]\\

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%center% Leon Bollée Calculating Machine "A New Calculating Machine of very General Applicability”\\//The Manufacturer and Builder 1890//[^1890: Leon Bollée Calculating Machine, “A New Calculating Machine of very General Applicability”, //The Manufacturer and Builder//, July 1890, p. 156. Original print article.^]\\

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%center%%height=300px% http://meta-studies.net/pmwiki/uploads/MillionairH300.jpg|1912: Millionaire Calculating Machine\\
serial 2015 (10x10x20)\\

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%center%%height=300px% http://meta-studies.net/pmwiki/uploads/MillionairH300.jpg|1912: Millionaire Calculating Machine, serial 2015 (10x10x20)\\

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%center%%height=250px% http://meta-studies.net/pmwiki/uploads/HerzstarkMechH250.jpg|1950s-1960s: Underneath view\\
the Herzstark mechanism - note the stepped drums\\

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%center%%height=250px% http://meta-studies.net/pmwiki/uploads/HerzstarkMechH250.jpg|1950s-1960s: Underneath view of the Herzstark mechanism (note the stepped drums)\\

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Model 20BTG serial 94046\\
electric calculator with true automatic division\\

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Model 20BTG serial 94046 electric calculator with true automatic division\\

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%center%%height=200px% http://meta-studies.net/pmwiki/uploads/Misc/ThomasMechRelH200.jpg|1862: ~~Diagram of the Thomas de Colmar arithmometer~~ mechanism.[^ Franz Reuleaux, //Die Thomas’sche Rechenmaschine//, Freiberg, 1862 reproduced in Reuleaux’s article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^] (:if equal {Site.PrintBook$:PSW} "False":)(Click on the image for an enlargement.)(:ifend:)\\(Source: Museum of the History of Science, University of Oxford.)

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%center%%height=200px% http://meta-studies.net/pmwiki/uploads/Misc/ThomasMechRelH200.jpg|1862: Thomas de Colmar arithmometer mechanism\\
diagram.[^ Franz Reuleaux, //Die Thomas’sche Rechenmaschine//, Freiberg, 1862 reproduced in Reuleaux’s article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^] (:if equal {Site.PrintBook$:PSW} "False":)(Click on the image for an enlargement.)(:ifend:)\\(Source: Museum of the History of Science, University of Oxford.)

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~~Earliest -~~ wood-cased model, serial 2491\\

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earliest wood-cased model, serial 2491\\

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%center% %height=250px% http://meta-studies.net/pmwiki/uploads/Schickard1H250.jpg||1623: Recreation of Wilhelm Schickard's\\

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%center% %height=250px% http://meta-studies.net/pmwiki/uploads/Schickard1H250.jpg|1623: Recreation of Wilhelm Schickard's\\

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calculating machine|\\

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calculating machine\\

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||align=center cellpadding=6 border=1 tableclass=long id=HPCacl"Hewlett Packard Pocket Scientific Calculators"

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||align=center cellpadding=6 border=0 tableclass=long id=HPCacl"Hewlett Packard Pocket Scientific Calculators"

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(:if equal {Site.PrintBook$:PSW} "True":)
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||align=center cellpadding=6 border=1 tableclass=long id=CurtaCalcs"Curta Calculators"

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||align=center cellpadding=6 border=0 tableclass=long id=CurtaCalcs"Curta Calculators"

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||align=center cellpadding=6 border=0 tableclass=long id=CurtaCalcs"Curta Calculators"

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%center%%height=250px% http://meta-studies.net/pmwiki/uploads/~~HerzstarkArithmometer250~~.jpg|~1929: “Herzstark” electric Calculating Machine serial 6549\\

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%center%%height=250px% http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometerH250.jpg|~1929: “Herzstark” electric Calculating Machine serial 6549\\

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||%center% %height=200px% http://meta-studies.net/pmwiki/uploads/Curta1-1948H200.jpg||%center% %height=200px% http://meta-studies.net/pmwiki/uploads/Curta1-1967H200.jpg]]||%center% %height=200px% http://meta-studies.net/pmwiki/uploads/Curta2H200.jpg||

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||%center% %height=200px% http://meta-studies.net/pmwiki/uploads/Curta1-1948H200.jpg||%center% %height=200px% http://meta-studies.net/pmwiki/uploads/Curta1-1967H200.jpg||%center% %height=200px% http://meta-studies.net/pmwiki/uploads/Curta2H200.jpg||

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%center%%height=250px% http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometer250.jpg|~1929: “Herzstark” electric Calculating Machine serial 6549\\badged by Herzstark, Vienna\\

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%center%%height=250px% http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometer250.jpg|~1929: “Herzstark” electric Calculating Machine serial 6549\\
badged by Herzstark, Vienna\\

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(:if equal {Site.PrintBook$:PSW} "False":)

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(:ifend:)

(:if equal {Site.PrintBook$:PSW} "True":)
||align=center cellpadding=6 border=0 tableclass=long id=DemoPinwheels"Demonstration Pinwheel Calculator"
||%center% %height=200px% http://meta-studies.net/pmwiki/uploads/PinWheelSingleH200.jpg||%center% %height=200px% http://meta-studies.net/pmwiki/uploads/PinwheelDemoH200.jpg||
||%center%A single pinwheel||%center% Mechanism of the\\Walther pinwheel calculator\\(parts removed for demonstration)||
||(collection Calculant)||(collection Calculant)||
||tableend
(:ifend:)

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%center% ~~Brunsviga Schuster Pinwheel Calculator ~1896~~

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%center% ~1896: Brunsviga Schuster Pinwheel Calculator

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(:ifend:)

(:if equal {Site.PrintBook$:PSW} "True":)
%center%%height=250px% http://meta-studies.net/pmwiki/uploads/Brunsviga1896H250.jpg|
~1896: Brunsviga Schuster Pinwheel Calculator\\
Serial 3406\\
(collection Calculant)
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||(collection Calculant - all above)||

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||(collection Calculant ||- all above)||

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(:ifend:)

(:if equal {Site.PrintBook$:PSW} "True":)
||align=center cellpadding=6 border=0 tableclass=long id=PinwheelCalcs"Pinwheel Calculators"
||Date||Description||Maker||Type||Device (click for greater detail)||
||1945 ||Facit Model S Calculator\\serial 210652||Facit||Pinwheel||%height=150px% http://meta-studies.net/pmwiki/uploads/FacitH150.jpg||
||~1951||Original Ohdner Model 39\\serial 39-288965||Ohdner||Pinwheel||%height=100px% Add Picture||
||~1957 ||Walther WSR160\\Pinwheel Calculator||Walther||Pinwheel||%height=150px% http://meta-studies.net/pmwiki/uploads/WaltherH150.jpg||
||~1957 ||Walther WSR160\\Demonstration\\Pinwheel Calculator||Walther||Demonstration\\Pinwheel||%height=150px% http://meta-studies.net/pmwiki/uploads/WaltherDemoH150.jpg||
||(collection Calculant ||- all above)||
||tableend
(:ifend:)

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(:if equal {Site.PrintBook$:PSW} "True":)
%center%%height=200px% http://meta-studies.net/pmwiki/uploads/Misc/RackMechH200.jpg|Rack mechanism\\
of a Mercedes-Euklid 29 calculator.\\
(collection Calculant)
(:ifend:)

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(:if equal {Site.PrintBook$:PSW} "True":)
||align=center cellpadding=6 border=0 tableclass=long id=RackCalcs"Proportional Rack Calculators"
||%center% %height=200px% http://meta-studies.net/pmwiki/uploads/Mercedes.png||%center% %height=200px% http://meta-studies.net/pmwiki/uploads/MercedesDemoH200.jpg||
||%center% 1923: Mercedes-Euklid\\Model 29 calculator||%center% 1923: Mercedes-Euklid Model 29\\Demonstration calculator||
||(collection Calculant)||(collection Calculant)||
||tableend
(:ifend:)

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(:if equal {Site.PrintBook$:PSW} "True":)
(:table align=center :)
%center%%height=250px% http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer\\
Earliest - wood-cased model, serial 2491\\
(collection Calculant)
(:ifend:)

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(:if equal {Site.PrintBook$:PSW} "True":)
||align=center cellpadding=6 border=0 tableclass=long id=Comptometers"Comptometers"
||Date||Description||Maker||Type||Device||
||1950s ||Bell Sumlock Comptometer||Bell Sumlock||Model 909/S/117.878||%height=250px% http://meta-studies.net/pmwiki/uploads/SumlockH250.jpg||
||~1955||Bell Punch Sumlock ||Bell Punch||Demonstration\\Comptometer||%height=250px% http://meta-studies.net/pmwiki/uploads/BellPunchDemoH250.jpg||
||(collection Calculant ||- all above)||
||tableend
(:ifend:)

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(:if equal {Site.PrintBook$:PSW} "True":)
||align=center cellpadding=6 border=1 tableclass=long id=CurtaCalcs"Curta Calculators"
||%center% %height=200px% http://meta-studies.net/pmwiki/uploads/Curta1-1948H200.jpg||%center% %height=200px% http://meta-studies.net/pmwiki/uploads/Curta1-1967H200.jpg]]||%center% %height=200px% http://meta-studies.net/pmwiki/uploads/Curta2H200.jpg||
||%center% ~July 1948: CURTA Type 1\\(pin sliders) earliest\\model calculator\\serial 5424||%center% 1967: CURTA Type I\\calculator serial 76436\\& cardboard box||%center% 1963: CURTA Type II\\calculator||
||(collection Calculant)||(collection Calculant) ||(collection Calculant)||
||tableend
(:ifend:)

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(:if equal {Site.PrintBook$:PSW} "True":)
%center% %height=250px% http://meta-studies.net/pmwiki/uploads/Schickard1H250.jpg||1623: Recreation of Wilhelm Schickard's\\
calculating machine\\
(collection Calculant)

\\

%center% %height=250px% http://meta-studies.net/pmwiki/uploads/BambergerOmegaH250.jpg|1904-1905: Bamberger’s Omega\\
calculating machine|\\
(collection Calculant)
(:ifend:)

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(:if equal {Site.PrintBook$:PSW} "True":)
%center%%height=250px% http://meta-studies.net/pmwiki/uploads/BolleeMAB1890H250.jpg|Leon Bollée Calculating Machine\\
"A New Calculating Machine of very General Applicability”\\
//The Manufacturer and Builder 1890//[^1890: Leon Bollée Calculating Machine, “A New Calculating Machine of very General Applicability”, //The Manufacturer and Builder//, July 1890, p. 156. Original print article.^]\\
(collection Calculant)
(:ifend:)

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(:if equal {Site.PrintBook$:PSW} "True":)
%center%%height=300px% http://meta-studies.net/pmwiki/uploads/MillionairH300.jpg|1912: Millionaire Calculating Machine\\
serial 2015 (10x10x20)\\
(collection Calculant)
(:ifend:)

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(:if equal {Site.PrintBook$:PSW} "True":)
%center%%height=230px% http://meta-studies.net/pmwiki/uploads/MillionaireDeckH230.jpg|Deck of the Millionaire Calculating Machine\\
(collection Calculant)
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(:if equal {Site.PrintBook$:PSW} "True":)
%center%%height=250px% http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometer250.jpg|~1929: “Herzstark” electric Calculating Machine serial 6549\\badged by Herzstark, Vienna\\
(essentially a Badenia Model TE 13 Duplex)\\
(collection Calculant)
(:ifend:)

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(:if equal {Site.PrintBook$:PSW} "True":)
%center%%height=250px% http://meta-studies.net/pmwiki/uploads/HerzstarkMechH250.jpg|1950s-1960s: Underneath view\\
the Herzstark mechanism - note the stepped drums\\
(collection Calculant)
(:ifend:)

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(:if equal {Site.PrintBook$:PSW} "True":)
%center%%height=250px% http://meta-studies.net/pmwiki/uploads/MADAS_SmallerH250.jpg|1950s-1960s: MADAS\\
Model 20BTG serial 94046\\
electric calculator with true automatic division\\
(collection Calculant)
(:ifend:)

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:if equal {Site.PrintBook$:PSW} "True":)
||align=center cellpadding=6 border=1 tableclass=long id=HPCacl"Hewlett Packard Pocket Scientific Calculators"
||%center% %height=250px% http://meta-studies.net/pmwiki/uploads/HP35H250.jpg||%center% %height=250px% http://meta-studies.net/pmwiki/uploads/HP-45H250.jpg||
||%center% July1972\\Hewlett Packard\\HP 35 Calculator\\serial 1230A 79429, 1972||%center% December 1973\\Hewlett Packard\\HP 45 Calculator\\serial 1350A 36719, 1973||
||(collection Calculant)|| ||
||tableend
(:ifend:)

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(:if equal {Site.PrintBook$:PSW} "True":)
%center%%height=200px% http://meta-studies.net/pmwiki/uploads/TIMDrumH200.jpg|Step drum (in a later 'TIM' arithmometer)\\
(collection Calculant)
(:ifend:)

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(:if equal {Site.PrintBook$:PSW} "True":)
%center%%height=300px% http://meta-studies.net/pmwiki/uploads/ThomasDeColmarH300.jpg|1884: Thomas de Colmar Arithmometer\\
Serial 2083 Model T1878 B\\
%center% (collection Calculant)
(:ifend:)

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(:if equal {Site.PrintBook$:PSW} "True":)
||align=center cellpadding=6 border=0 tableclass=long id=Arithmometers"Arithmometers"
||Date||Description||Maker||Type||Device||
||1909 ||TIM (Time is Money)\\ Arithmometer||Ludwig Spitz\\ & Co||Arithmometer||%height=150px% http://meta-studies.net/pmwiki/uploads/TIMH150.jpg||
||~1913 ||Bunzel-Denton Arithmometer||Bunzel||Prototype\\Front Crank||%height=150px% http://meta-studies.net/pmwiki/uploads/BunzelH150.jpg||
||~1917 ||Madas IX Maxima||Madas||Auto Division||%height=125px% http://meta-studies.net/pmwiki/uploads/MADAS-1917H125.jpg||
||(collection Calculant - all above)||
||tableend
(:ifend:)

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%center%%height=200px% http://meta-studies.net/pmwiki/uploads/Misc/ThomasMechRelH200.jpg|1862: Diagram of the Thomas de Colmar arithmometer mechanism.[^ Franz Reuleaux, //Die Thomas’sche Rechenmaschine//, Freiberg, 1862 reproduced in Reuleaux’s article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^] (:if equal {Site.PrintBook$:PSW} "False":)(Click on the image for an enlargement.)(:ifend:)\\(Source: Museum of the History of Science, University of Oxford.)
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Other simple linear devices in this collection are shown below. (~~Clicking on the image will take you to a larger image on the description~~ page.)

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Other simple linear devices in this collection are shown below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)

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~~Other simple rotational adding devices in this collection are shown below~~. ~~(Once more, clicking on the image will take you to a larger image on the description page~~.)

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(:if equal {Site.PrintBook$:PSW} "True":)
%center%%height=200px% http://meta-studies.net/pmwiki/uploads/WebbH200.jpg|1869:Web Patent Adder and Talley Board\\
(collection Calculant)
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Other simple rotational adding devices in this collection are shown below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)

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||align=center cellpadding=6 border=0 tableclass=long id=SimpleRotationalCalcs"Simple Rotational Calculators"
||Date||Description||Maker||Type||Device||
||1890-1900 ||A. M. Stevenson Adder||Joliet, Ill.\\||2 Wheel||%height=75px% http://meta-studies.net/pmwiki/uploads/StevensonH75.jpg||
||1903 ||Adix Adding Machine\\Original model||Manheim||Key input\\lever &\\gears||%height=175px% http://meta-studies.net/pmwiki/uploads/AdixH175.jpg||
||1910 ||Adall Adding Machine||Dreyfus\\and Levy ||Key input\\Concentric \\toothed disk\\and groove||%height=125px% http://meta-studies.net/pmwiki/uploads/AdallH125.jpg||
||~1946 ||Lightning Portable\\Adding Machine||Lightning\\Adding Machine\\Co. L.A.||7 Wheels||%height=125px% http://meta-studies.net/pmwiki/uploads/LightningH125.jpg||
||1968 ||SEE Demonstration\\Adding Machine||Selective Educational\\Equipment Corporation||4 Wheels||%height=75px% http://meta-studies.net/pmwiki/uploads/SEE-1H75.jpg||
|| (collection Calculant - all above)||
||tablend
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%center%1862: Diagram of the Thomas de Colmar arithmometer mechanism.[^ Franz Reuleaux, //Die Thomas’sche Rechenmaschine//, Freiberg, 1862 reproduced in Reuleaux’s article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^]\\ (~~click on the image for an~~ enlargement)\\(Source: Museum of the History of Science, University of Oxford.)

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%center%1862: Diagram of the Thomas de Colmar arithmometer mechanism.[^ Franz Reuleaux, //Die Thomas’sche Rechenmaschine//, Freiberg, 1862 reproduced in Reuleaux’s article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^]\\ (:if equal {Site.PrintBook$:PSW} "False":)(Click on the image for an enlargement.)(:ifend:)\\(Source: Museum of the History of Science, University of Oxford.)

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As can be seen above, the pinwheel (left, above) is a thin disk with the slider shown protruding in the top right corner. It is in the '3' position, with the cam slot rotated pushing 3 teeth out (seen between and behind the fixed teeth at the bottom). These then are the teeth that are added by the counting wheel. (~~Click on the image to enlarge~~.)[[<<]]

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As can be seen above, the pinwheel (left, above) is a thin disk with the slider shown protruding in the top right corner. It is in the '3' position, with the cam slot rotated pushing 3 teeth out (seen between and behind the fixed teeth at the bottom). These then are the teeth that are added by the counting wheel. (:if equal {Site.PrintBook$:PSW} "False":)(Click on the image to enlarge.)(:ifend:)[[<<]]

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%center%%height=200px% http://meta-studies.net/pmwiki/uploads/~~Ropp200~~.jpg|~1790: Conversion device\\

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%center%%height=200px% http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg|~1790: Conversion device\\

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||align=center cellpadding=6 border=0 tableclass=long id=SimpleLinearCalcs"Simple Linear Calculators"
||Date||Description||Maker||Type||Device (click for greater detail)
||1910-20s||Comptator (9 col)||Schubert\\& Salzer||Chain||%height=125px% http://meta-studies.net/pmwiki/uploads/Comptator125.jpg||
||~1915||Golden Gem Automatic\\Adding Machine||H. & H. Goldmann||Chain||%height=100px% http://meta-studies.net/pmwiki/uploads/GoldenGem100.jpg||
||1920||Addiator Troncet adder||Ruthard & Co||Chain||%height=125px% http://meta-studies.net/pmwiki/uploads/Addiator125.jpg||
||1922||Scribola 10 column\\printing\\Adding Machine||Addiator Gesellschaft||Rod||%height=150px% http://meta-studies.net/pmwiki/uploads/Scribola150.jpg||
||1937||Add-O-Matic\\Adding Machine||Allied MFG. Co.||Chain||%height=125px% http://meta-studies.net/pmwiki/uploads/AddOMatic1_125.jpg||
|| (collection Calculant - all above)||
||tableend
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~~||table align=~~center ~~cellpadding~~=3 border=0 tableclass=long id=Convertiseur"Convertiseur"
||[[Site.CHAIX1790|%height=200px%http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg]]||
||~1790: Conversion device||
||(from Aunes to Metres)||
||(collection Calculant)||
||tableend

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%center%%height=200px% http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|~1790: Conversion device\\
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%height=200px% http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp's Commercial Calculator\\

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||table align=center id=ReadyR"1892: Ropp's Commercial Calculator"
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%center% %height=200px% http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp's Commercial Calc. (collection Calculant)

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%center% %height=200px% http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|Ropp's Commercial ~~Calculator, 1892\\~~(collection Calculant)

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(:if equal {Site.PrintBook$:PSW} "False":)
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[[<<]]

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[[<<]]

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The above relied either on the movement by a stylus or knobs of strips, rods or chains to create addition. Some (such as the Locke adder) used a simplified form of complementary arithmetic for subtraction,t others allowed a such as the Golden Gem allowed reverse motion, and others again such as the Addiator could be turned over to perform the subtraction. Most (but not the Locke Adder) had a simple provision for carries and some (such as the Scribola - which also had a very early printout) had clearing levers to bring the display back to zero for the next calculation. All however, whilst affordable, were cumbersome and slow to use since each digit had to be individually entered by performing a sliding motion. It was much quicker to add the numbers on paper using mental arithmetic, but of course, here that capability was lacking, or where the effort of doing it was considered tedious, then these devices began to find a market in the first half of the C20, and thousands were produced and sold across the more industrialised countries of Europe, the British Empire and the USA.

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The above relied either on the movement by a stylus or knobs of strips, rods or chains to create addition. Some (such as the Locke adder) used a simplified form of complementary arithmetic for subtraction,t others allowed a such as the Golden Gem allowed reverse motion, and others again such as the Addiator could be turned over to perform the subtraction. Most (but not the Locke Adder) had a simple provision for carries and some (such as the Scribola - which also had a very early printout) had clearing levers to bring the display back to zero for the next calculation. All however, whilst affordable, were cumbersome and slow to use since each digit had to be individually entered by performing a sliding motion. It was much quicker to add the numbers on paper using mental arithmetic, but of course, here that capability was lacking, or where the effort of doing it was considered tedious, then these devices began to find a market in the first half of the C20, and thousands were produced and sold across the more industrialised countries of Europe, the British Empire and the USA.[[<<]]

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The main advantage of these devices was that they were cheap to manufacture and could be easily mass-produced. We can of course see a lot of innovation in the detail of these machines. A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which simply used successive rotations of a wheel to wind on successive numbers whilst a ball bearing, moving in a spiral groove, tracked the successive rotations. Early experiments with keyboards can be seen in the Adix adding machine of 1903.

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The main advantage of these devices was that they were cheap to manufacture and could be easily mass-produced. We can of course see a lot of innovation in the detail of these machines. A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which simply used successive rotations of a wheel to wind on successive numbers whilst a ball bearing, moving in a spiral groove, tracked the successive rotations. Early experiments with keyboards can be seen in the Adix adding machine of 1903.[[<<]]

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The above diagram shows the crank handle on the right top which drives the rotation of the step drum (shown centre right). In front of the crank handle can be seen a "slider nob" which moves the cog along the axle to engage with correct number of teeth of the step drum. To the left is a reversing mechanism connected to an output dial. The reversing mechanism allows the output dial to be rotated in the opposite direction, if the nob that activates it (situated above) is shifted from the "addition" to the "subtraction" position.

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The above diagram shows the crank handle on the right top which drives the rotation of the step drum (shown centre right). In front of the crank handle can be seen a "slider nob" which moves the cog along the axle to engage with correct number of teeth of the step drum. To the left is a reversing mechanism connected to an output dial. The reversing mechanism allows the output dial to be rotated in the opposite direction, if the nob that activates it (situated above) is shifted from the "addition" to the "subtraction" position.[[<<]]

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The above arithmometer demonstrates the high level of usability that the firm of Thomas had now achieved. It allows the multiplication of two numbers each as large as 9 million and the result can be read out to 16 places. Ivory markers are provided for the decimal point (and to delineate hundreds, thousands and millions for ease of use). The clearing and carry mechanisms are entirely reliable. Indeed, still bearing its original varnish, this particular machine operates reliably some 125 years after it was made. Indicating that its owner was serious about its use in practice the machine appears to have been re-mounted by the famous instrument maker, Stanley, (sometime after 1900) in a better quality and stronger box fixed to a cast iron frame. This allows the machine to be tilted at a suitable angle for easy use. As the only surviving Thomas known to have this improvement, this machine seems to stand as a precursor to later innovations under Payen when he added a (rather less robust) hinged tilt base to his machines.

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The above arithmometer demonstrates the high level of usability that the firm of Thomas had now achieved. It allows the multiplication of two numbers each as large as 9 million and the result can be read out to 16 places. Ivory markers are provided for the decimal point (and to delineate hundreds, thousands and millions for ease of use). The clearing and carry mechanisms are entirely reliable. Indeed, still bearing its original varnish, this particular machine operates reliably some 125 years after it was made. Indicating that its owner was serious about its use in practice the machine appears to have been re-mounted by the famous instrument maker, Stanley, (sometime after 1900) in a better quality and stronger box fixed to a cast iron frame. This allows the machine to be tilted at a suitable angle for easy use. As the only surviving Thomas known to have this improvement, this machine seems to stand as a precursor to later innovations under Payen when he added a (rather less robust) hinged tilt base to his machines.[[<<]]

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The above three arithmometers demonstrate the sorts of improvements to the basic arithmometer design which now emerged. The first, a TIM (“Time is Money” ) arithmometer manufactured by Ludwig Spitz and Co. of Berlin-Tempelhof in 1909 was greatly strengthened from the Thomas design to create a much more robust and reliable machine. First produced in a wooden box it was later made much stronger by installing it in a cast iron frame which held all parts rigidly.[^See Ernst Martin, //The Calculating Machines (Die Rechenmaschinen): Their History and Development//, ed. and trs. by Peggy Aldridge Kidwell and Michael R. Williams, MIT Press, Mass., 1992, p. 191–4^] Beginning a change in style that would be emulated in many other machines the brass panels were now enamelled black consistent with the management, industrial and commercial settings where it was intended to find its market. The other two machines in this set would also originally have had a similar black finish. (Unfortunately, there was a tendency in the late C20 to "take the machines back to brass" in the same way that in the 1960s there was a trend to remove the original finish from wood on vintage furniture, and plaster from brick walls in old houses.)

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The above three arithmometers demonstrate the sorts of improvements to the basic arithmometer design which now emerged. The first, a TIM (“Time is Money” ) arithmometer manufactured by Ludwig Spitz and Co. of Berlin-Tempelhof in 1909 was greatly strengthened from the Thomas design to create a much more robust and reliable machine. First produced in a wooden box it was later made much stronger by installing it in a cast iron frame which held all parts rigidly.[^See Ernst Martin, //The Calculating Machines (Die Rechenmaschinen): Their History and Development//, ed. and trs. by Peggy Aldridge Kidwell and Michael R. Williams, MIT Press, Mass., 1992, p. 191–4^] Beginning a change in style that would be emulated in many other machines the brass panels were now enamelled black consistent with the management, industrial and commercial settings where it was intended to find its market. The other two machines in this set would also originally have had a similar black finish. (Unfortunately, there was a tendency in the late C20 to "take the machines back to brass" in the same way that in the 1960s there was a trend to remove the original finish from wood on vintage furniture, and plaster from brick walls in old houses.)[[<<]]

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As can be seen above, the pinwheel (left, above) is a thin disk with the slider shown protruding in the top right corner. It is in the '3' position, with the cam slot rotated pushing 3 teeth out (seen between and behind the fixed teeth at the bottom). These then are the teeth that are added by the counting wheel. (Click on the image to enlarge.)

to:

As can be seen above, the pinwheel (left, above) is a thin disk with the slider shown protruding in the top right corner. It is in the '3' position, with the cam slot rotated pushing 3 teeth out (seen between and behind the fixed teeth at the bottom). These then are the teeth that are added by the counting wheel. (Click on the image to enlarge.)[[<<]]

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As the range of dates for the set of pinwheel calculators in this collection suggests, the pinwheel design was highly successful and capable of being improved on for the better part of three quarters of a century. The second Ohdner in the collection is from 1938, and although possessing some improvements (such as the capacity to move the carriage back and forth with tab keys), was little different in concept. The same can be said for the Facit calculator from around 1945, and even from the 1950s, near the end of the production of such machines, despite its more modern finish and use of plastic fittings (and some improvements such as clearing levers), the Walther 160 remains quite similar in operation to the Brunsviga of 1896, which, significantly, still works as smoothly as the Walther.

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As the range of dates for the set of pinwheel calculators in this collection suggests, the pinwheel design was highly successful and capable of being improved on for the better part of three quarters of a century. The second Ohdner in the collection is from 1938, and although possessing some improvements (such as the capacity to move the carriage back and forth with tab keys), was little different in concept. The same can be said for the Facit calculator from around 1945, and even from the 1950s, near the end of the production of such machines, despite its more modern finish and use of plastic fittings (and some improvements such as clearing levers), the Walther 160 remains quite similar in operation to the Brunsviga of 1896, which, significantly, still works as smoothly as the Walther.[[<<]]

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A further approach to the problem of the four functions is found in the American invention by Felt, of a device that he called the comptometer and patented in 1887. It performs the task of addition by a system of keys and levers. The keys press down rods which from key 1 to key 9 increase incrementally in length for each successive key. This difference in displacement, magnified by a lever turns an accumulating gear through 1 to 9 teeth as appropriate.

to:

A further approach to the problem of the four functions is found in the American invention by Felt, of a device that he called the comptometer and patented in 1887. It performs the task of addition by a system of keys and levers. The keys press down rods which from key 1 to key 9 increase incrementally in length for each successive key. This difference in displacement, magnified by a lever turns an accumulating gear through 1 to 9 teeth as appropriate.[[<<]]

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The comptometer was a highly successful innovation and was sufficiently cheap and useful to reach a broad market. Characterised by extremely effective marketing and capable of being mass produced the device continued to be marketed for some 80 years unusually for such innovations leaving its inventor extremely wealthy. By then its essential mechanism was being utilised by more than one company. Shown below is the remaining comptometer in this collection, this time made of plastic in the 1950s by the British Bell Punch company. Also shown is a demonstration model showing the keys and lever system used in the Bell Punch machine.

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The comptometer was a highly successful innovation and was sufficiently cheap and useful to reach a broad market. Characterised by extremely effective marketing and capable of being mass produced the device continued to be marketed for some 80 years unusually for such innovations leaving its inventor extremely wealthy. By then its essential mechanism was being utilised by more than one company. Shown below is the remaining comptometer in this collection, this time made of plastic in the 1950s by the British Bell Punch company. Also shown is a demonstration model showing the keys and lever system used in the Bell Punch machine.[[<<]]

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Finally there is the last and most beautifully miniaturised of the four function manual mechanical calculators designed by Curt Herzstark. Curt was born in 1902 as the son of Samuel Herzstark who had established a calculator manufacturing company in Vienna in 1905-6. Curt's father died in 1937 but by then Curt was both Director of the company and a highly competent designer in his own right. He recognised the need for a miniaturised four function calculator which could be carried in an engineer's pocket. He began to design this as a cylindrical calculator which could be held in one hand and operated with the other. It could utilise the modern new light weight alloys of aluminium, magnesium, etc. By the end of 1937 he had the form of what he wished to accomplish firmly in his mind. It would be compact, lightweight, and in order to allow a carry mechanism which would allow the crank to be turned only one way, it would use and internal process of complementary arithmetic for subtraction. Then came Hitler. Herzstark found himself in 1943 arrested and imprisoned in Buchenwald concentration camp where he was placed in a small technical camp to manufacture components to assist the Nazi war effort (in particular, parts of the V I and II missile bombs).

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Finally there is the last and most beautifully miniaturised of the four function manual mechanical calculators designed by Curt Herzstark. Curt was born in 1902 as the son of Samuel Herzstark who had established a calculator manufacturing company in Vienna in 1905-6. Curt's father died in 1937 but by then Curt was both Director of the company and a highly competent designer in his own right. He recognised the need for a miniaturised four function calculator which could be carried in an engineer's pocket. He began to design this as a cylindrical calculator which could be held in one hand and operated with the other. It could utilise the modern new light weight alloys of aluminium, magnesium, etc. By the end of 1937 he had the form of what he wished to accomplish firmly in his mind. It would be compact, lightweight, and in order to allow a carry mechanism which would allow the crank to be turned only one way, it would use and internal process of complementary arithmetic for subtraction. Then came Hitler. Herzstark found himself in 1943 arrested and imprisoned in Buchenwald concentration camp where he was placed in a small technical camp to manufacture components to assist the Nazi war effort (in particular, parts of the V I and II missile bombs).[[<<]]

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On the Curta above, left we see the clearing ring protruding. Bringing all numbers to zero is achieved by lifting the top section and turning the clearing ring. Adding is achieved by setting successive numbers and turning the crank through a full turn. Ingeniously, pulling the crank up sets it for subtraction. Multiplication is done in the usual manner of multiplying by each successive integer of the multiplier with the upper register being advanced for each one by lifting the top section and rotating it one notch. Division is by the usual method of long division by repeated subtractions. Once more, for each partial product the operator must either correctly judge the correct number of times to turn the crank, or if an overflow is forced, reverse the operation by pushing in the crank and turning it one full turn. In short it is an excellent machine for addition and subtraction, but involves the normal acquired skill, and tedium, required by multiplication and division in any of the mechanical calculators not equipped to do it automatically.

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On the Curta above, left we see the clearing ring protruding. Bringing all numbers to zero is achieved by lifting the top section and turning the clearing ring. Adding is achieved by setting successive numbers and turning the crank through a full turn. Ingeniously, pulling the crank up sets it for subtraction. Multiplication is done in the usual manner of multiplying by each successive integer of the multiplier with the upper register being advanced for each one by lifting the top section and rotating it one notch. Division is by the usual method of long division by repeated subtractions. Once more, for each partial product the operator must either correctly judge the correct number of times to turn the crank, or if an overflow is forced, reverse the operation by pushing in the crank and turning it one full turn. In short it is an excellent machine for addition and subtraction, but involves the normal acquired skill, and tedium, required by multiplication and division in any of the mechanical calculators not equipped to do it automatically.[[<<]]

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Bamberger's Omega uses linear strips rather than the rotatable mechanisms of both halves of the Schickard. It also has some additional provision for storing intermediate results to assist long division, including the register on the top right, and the notebook. Otherwise the two machines are very similar in operation and both, with some considerable effort, can be used to perform all four functions of arithmetic. The fact that neither took off in the market place may be in part a factor of their difficulty of use and part a lack of adequately determined marketing.

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Bamberger's Omega uses linear strips rather than the rotatable mechanisms of both halves of the Schickard. It also has some additional provision for storing intermediate results to assist long division, including the register on the top right, and the notebook. Otherwise the two machines are very similar in operation and both, with some considerable effort, can be used to perform all four functions of arithmetic. The fact that neither took off in the market place may be in part a factor of their difficulty of use and part a lack of adequately determined marketing.[[<<]]

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Similar principles were however utilised by Otto Steiger in Switzerland who in 1895 patented a rather more practical “Millionaire calculating machine” which had a simple enough mechanism to enable production on a commercial scale.

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Similar principles were however utilised by Otto Steiger in Switzerland who in 1895 patented a rather more practical “Millionaire calculating machine” which had a simple enough mechanism to enable production on a commercial scale.[[<<]]

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The Millionaire calculating machine combines the idea of the physical embodiment of multiplication tables with that of the proportional rack. It is able to interrogate a multiplication table represented by metal rods, and in a single crank of the handle multiplies the multiplicand by a number set between 1 and 9 then advancing its internal carriage one place ready for the next multiplier to be set and applied. Thus, for example, to multiply 4689 x 2568 an arithmometer or pinwheel would take 21 cranks of the handle (8+6+5+2) whereas the Millionaire could achieve the same outcome with only four cranks of the handle. In the lid was a set of tables of factors to assist division, a brush to keep the machine clean, and a special bolt so when being transported the carriage was held clamped in place, since if the machine were dropped the carriage was heavy enough to punch through the end of the case.

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The Millionaire calculating machine combines the idea of the physical embodiment of multiplication tables with that of the proportional rack. It is able to interrogate a multiplication table represented by metal rods, and in a single crank of the handle multiplies the multiplicand by a number set between 1 and 9 then advancing its internal carriage one place ready for the next multiplier to be set and applied. Thus, for example, to multiply 4689 x 2568 an arithmometer or pinwheel would take 21 cranks of the handle (8+6+5+2) whereas the Millionaire could achieve the same outcome with only four cranks of the handle. In the lid was a set of tables of factors to assist division, a brush to keep the machine clean, and a special bolt so when being transported the carriage was held clamped in place, since if the machine were dropped the carriage was heavy enough to punch through the end of the case.[[<<]]

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This calculator features its original electric motor, still in good working order, and with a keyboard instead of sliders for input. The features of it were not only that it had a keyboard for input, but also a control mechanism consisting of a column of keys which enabled a number to be entered and then added through 0 to 8 repeats representing multiplication by one to nine. A view of the mechanism of this machine is shown below.

to:

This calculator features its original electric motor, still in good working order, and with a keyboard instead of sliders for input. The features of it were not only that it had a keyboard for input, but also a control mechanism consisting of a column of keys which enabled a number to be entered and then added through 0 to 8 repeats representing multiplication by one to nine. A view of the mechanism of this machine is shown below.[[<<]]

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In the left lower corner of the above can be seen the motor, now coupled to the characteristic step drums of an arithmometer (bottom center and right), with the carry mechanism above. This puts paid to any simple story of the linear development of innovation in the calculator. Here the most modern device of the motor is being coupled to the longest serving commercial system of an arithmometer.

to:

In the left lower corner of the above can be seen the motor, now coupled to the characteristic step drums of an arithmometer (bottom center and right), with the carry mechanism above. This puts paid to any simple story of the linear development of innovation in the calculator. Here the most modern device of the motor is being coupled to the longest serving commercial system of an arithmometer.[[<<]]

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The late MADAS 20BTG calculator, seen above, which is part of this collection represents a classic exemplar of the late stages of this evolutionary development. Now fully utilising an electric motor it could fluently perform all the operations of arithmetic, complete with automatic clearing and moving the carriage entirely automatically as necessary. It could also be further extended to automatically extract square roots. Its mechanism was also adopted in its essentials, then with many innovations (but with less of the Swiss robust construction of the Madas), in the US Frieden calculators. As it turned out, this final class of machines represented the pinacle of achievement in motorised mechanical calculation.

to:

The late MADAS 20BTG calculator, seen above, which is part of this collection represents a classic exemplar of the late stages of this evolutionary development. Now fully utilising an electric motor it could fluently perform all the operations of arithmetic, complete with automatic clearing and moving the carriage entirely automatically as necessary. It could also be further extended to automatically extract square roots. Its mechanism was also adopted in its essentials, then with many innovations (but with less of the Swiss robust construction of the Madas), in the US Frieden calculators. As it turned out, this final class of machines represented the pinacle of achievement in motorised mechanical calculation.[[<<]]

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The launch of the HP-35 marks what might be called the "First Vanishing Point" - the point at which all the arithmetic operations and common scientific functions required for calculation became available in a single small electronic calculator, capable of being carried on a belt or in a shirt pocket (albeit in serious peril of it falling out when one bent over to pick something up). Electronic calculators now proliferated throughout the developed and developing world displacing the rigours of mental arithmetic and caught in an 'arms race' to make them smaller, more powerful, easier to use, and find a niche in a highly competitive and very cluttered market.

to:

The launch of the HP-35 marks what might be called the "First Vanishing Point" - the point at which all the arithmetic operations and common scientific functions required for calculation became available in a single small electronic calculator, capable of being carried on a belt or in a shirt pocket (albeit in serious peril of it falling out when one bent over to pick something up). Electronic calculators now proliferated throughout the developed and developing world displacing the rigours of mental arithmetic and caught in an 'arms race' to make them smaller, more powerful, easier to use, and find a niche in a highly competitive and very cluttered market.[[<<]]

07 August 2013 by 203.166.245.137 -

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%center% http://meta-studies.net/pmwiki/uploads/Locke170.jpg|The Locke Adder\\(collection Calculant)
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(:cellnr:)%center% ~1790: Conversion device
(~~:cellnr:)%center% (from Aunes to~~ Metres)
~~(:cellnr:~~)%center% (collection Calculant)
(:tableend:)

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||[[Site.CHAIX1790|%height=200px%http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg]]||
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||(collection Calculant)||
||tableend

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||table align=center id=Convertiseur"Convertiseur
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|| ~~(from Aunes to~~ Metres)||
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||tableend

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||table align=center id=Convertiseur"Convertiseur
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|| ~1790: Conversion device||
|| (from Aunes to Metres)||
|| (collection Calculant)||
||tableend||

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(:table align=center :)
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(:cellnr:) ~1790: Conversion device
(:cellnr:) ~~(from~~ Aunes to Metres)
(:cellnr:) (collection Calculant)

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(:table align=center id=Convertiseur"Convertiseur:)
(:cellnr:) %center% %height=200px% [[http://meta-studies.net/pmwiki/pmwiki.php?n=Site.CHAIX1790|http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg]]%%
(:cellnr:)%center% ~1790: Conversion device
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(:~~cell~~:) ~1790: Conversion device
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(:~~cell~~:) (collection Calculant)

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(:cellnr:) ~1790: Conversion device
(:cellnr:) (from Aunes to Metres)
(:cellnr:) (collection Calculant)

06 August 2013 by 124.176.225.254 -

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~~%center% ~1790~~: Conversion device
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~~%center%~~ (collection Calculant)

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(:cell:) ~1790: Conversion device
(:cell:) (from Aunes to Metres)
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%center% ~1790: Conversion device\\(from Aunes to Metres)\\(collection Calculant)

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%center% ~1790: Conversion device
%center% (from Aunes to Metres)
%center% (collection Calculant)

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%center% Brunsviga Schuster Pinwheel Calculator ~1896\\Serial ~~3406\\~~

to:

%center% Brunsviga Schuster Pinwheel Calculator ~1896
%center% Serial 3406

06 August 2013 by 124.180.252.130 -

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||1909 ||TIM (Time is Money)\\ Arithmometer||Ludwig Spitz\\ & Co||Arithmometer||%height=150px%[[Site.TIM1909| http://meta-studies.net/pmwiki/uploads/TIMH150.~~JPG~~]]||

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||1909 ||TIM (Time is Money)\\ Arithmometer||Ludwig Spitz\\ & Co||Arithmometer||%height=150px%[[Site.TIM1909| http://meta-studies.net/pmwiki/uploads/TIMH150.jpg]]||

06 August 2013 by 124.180.252.130 -

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(:cellnr:) %height=200px% [[Site.Webb1869|%center% http://meta-studies.net/pmwiki/uploads/~~Webb~~.jpg]]%%

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(:cellnr:) %height=200px% [[Site.Webb1869|%center% http://meta-studies.net/pmwiki/uploads/WebbH200.jpg]]%%

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||1890-1900 ||A. M. Stevenson Adder||Joliet, Ill.\\||2 Wheel||%height=75px%[[Stevenson1890| http://meta-studies.net/pmwiki/uploads/~~Stevenson~~.~~png~~]]||
||1903 ||Adix Adding Machine\\Original model||Manheim||Key input\\lever &\\gears||%height=175px%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/~~Adix~~.~~png~~]]||
||1910 ||Adall Adding Machine||Dreyfus\\and Levy ||Key input\\Concentric \\toothed disk\\and groove||%height=125px%[[Site.Adall1910| http://meta-studies.net/pmwiki/uploads/~~Adall~~.jpg]]||
||~1946 ||Lightning Portable\\Adding Machine||Lightning\\Adding Machine\\Co. L.A.||7 Wheels||%height=125px%[[Site.Lightning1946| http://meta-studies.net/pmwiki/uploads/~~Lightning~~.~~png~~]]||
||1968 ||SEE Demonstration\\Adding Machine||Selective Educational\\Equipment Corporation||4 Wheels||%height=75px%[[Site.SEE1968| http://meta-studies.net/pmwiki/uploads/SEE-1.jpg]]||

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||1890-1900 ||A. M. Stevenson Adder||Joliet, Ill.\\||2 Wheel||%height=75px%[[Stevenson1890| http://meta-studies.net/pmwiki/uploads/StevensonH75.jpg]]||
||1903 ||Adix Adding Machine\\Original model||Manheim||Key input\\lever &\\gears||%height=175px%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/AdixH175.jpg]]||
||1910 ||Adall Adding Machine||Dreyfus\\and Levy ||Key input\\Concentric \\toothed disk\\and groove||%height=125px%[[Site.Adall1910| http://meta-studies.net/pmwiki/uploads/AdallH125.jpg]]||
||~1946 ||Lightning Portable\\Adding Machine||Lightning\\Adding Machine\\Co. L.A.||7 Wheels||%height=125px%[[Site.Lightning1946| http://meta-studies.net/pmwiki/uploads/LightningH125.jpg]]||
||1968 ||SEE Demonstration\\Adding Machine||Selective Educational\\Equipment Corporation||4 Wheels||%height=75px%[[Site.SEE1968| http://meta-studies.net/pmwiki/uploads/SEE-1H75.jpg]]||

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(:cellnr:) %height=200px% [[Site.ThomasMechanism|http://meta-studies.net/pmwiki/uploads/Misc/~~ThomasMechRel~~.jpg]]%%

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||1909 ||TIM (Time is Money)\\ Arithmometer||Ludwig Spitz\\ & Co||Arithmometer||%height=150px%[[Site.TIM1909| http://meta-studies.net/pmwiki/uploads/~~TIM~~.JPG]]||
||~1913 ||Bunzel-Denton Arithmometer||Bunzel||Prototype\\Front Crank||%height=150px%[[Site.BunzelPrototype1913| http://meta-studies.net/pmwiki/uploads/~~Bunzel~~.~~JPG~~]]||
||~1917 ||Madas IX Maxima||Madas||Auto Division||%height=125px%[[Site.Madas-IX-Maxima| http://meta-studies.net/pmwiki/uploads/MADAS-~~1917~~.jpg]]||

to:

||1909 ||TIM (Time is Money)\\ Arithmometer||Ludwig Spitz\\ & Co||Arithmometer||%height=150px%[[Site.TIM1909| http://meta-studies.net/pmwiki/uploads/TIMH150.JPG]]||
||~1913 ||Bunzel-Denton Arithmometer||Bunzel||Prototype\\Front Crank||%height=150px%[[Site.BunzelPrototype1913| http://meta-studies.net/pmwiki/uploads/BunzelH150.jpg]]||
||~1917 ||Madas IX Maxima||Madas||Auto Division||%height=125px%[[Site.Madas-IX-Maxima| http://meta-studies.net/pmwiki/uploads/MADAS-1917H125.jpg]]||

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||%center% %height=200px%[[Site.DemonstrationPinwheel|http://meta-studies.net/pmwiki/uploads/~~PinWheelSingle~~.jpg]]||%center% %height=200px%[[Site.DemonstrationPinwheelMechanism|http://meta-studies.net/pmwiki/uploads/~~PinwheelDemo~~.jpg]]||

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||%center% %height=200px%[[Site.DemonstrationPinwheel|http://meta-studies.net/pmwiki/uploads/PinWheelSingleH200.jpg]]||%center% %height=200px%[[Site.DemonstrationPinwheelMechanism|http://meta-studies.net/pmwiki/uploads/PinwheelDemoH200.jpg]]||

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(:cellnr:) %height=250px% [[Site.BrunsvigaSchuster1896|http://meta-studies.net/pmwiki/uploads/~~Brunsviga1896~~.~~png~~]]%%

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(:cellnr:) %height=250px% [[Site.BrunsvigaSchuster1896|http://meta-studies.net/pmwiki/uploads/Brunsviga1896H250.jpg]]%%

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||1945 ||Facit Model S Calculator\\serial 210652||Facit||Pinwheel||%height=150px%[[Site.Facit1945| http://meta-studies.net/pmwiki/uploads/~~Facit~~.~~png~~]]||

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||1945 ||Facit Model S Calculator\\serial 210652||Facit||Pinwheel||%height=150px%[[Site.Facit1945| http://meta-studies.net/pmwiki/uploads/FacitH150.jpg]]||

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||~1957 ||Walther WSR160\\Pinwheel Calculator||Walther||Pinwheel||%height=150px%[[Site.Walther1957| http://meta-studies.net/pmwiki/uploads/~~Walther~~.~~png~~]]||
||~1957 ||Walther WSR160\\Demonstration\\Pinwheel Calculator||Walther||Demonstration\\Pinwheel||%height=150px%[[Site.WaltherDemonstrator1957| http://meta-studies.net/pmwiki/uploads/~~WaltherDemo~~.~~png~~]]||

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||~1957 ||Walther WSR160\\Pinwheel Calculator||Walther||Pinwheel||%height=150px%[[Site.Walther1957| http://meta-studies.net/pmwiki/uploads/WaltherH150.jpg]]||
||~1957 ||Walther WSR160\\Demonstration\\Pinwheel Calculator||Walther||Demonstration\\Pinwheel||%height=150px%[[Site.WaltherDemonstrator1957| http://meta-studies.net/pmwiki/uploads/WaltherDemoH150.jpg]]||

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||%center% %height=200px%[[Site.Mercedes291923|http://meta-studies.net/pmwiki/uploads/Mercedes.png]]||%center% %height=200px%[[Site.Mercedes29Demonstrator1923|http://meta-studies.net/pmwiki/uploads/~~MercedesDemo~~.~~png~~]]||

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||%center% %height=200px%[[Site.Mercedes291923|http://meta-studies.net/pmwiki/uploads/Mercedes.png]]||%center% %height=200px%[[Site.Mercedes29Demonstrator1923|http://meta-studies.net/pmwiki/uploads/MercedesDemoH200.jpg]]||

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||1950s ||Bell Sumlock Comptometer||Bell Sumlock||Model 909/S/117.878||%height=250px%[[Site.SumlockComptometer1950s| http://meta-studies.net/pmwiki/uploads/~~Sumlock~~.~~png~~]]||
||~1955||Bell Punch Sumlock ||Bell Punch||Demonstration\\Comptometer||%height=250px%[[Site.SumlockDemonstrator1955| http://meta-studies.net/pmwiki/uploads/~~BellPunchDemo~~.~~png~~]]||

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||1950s ||Bell Sumlock Comptometer||Bell Sumlock||Model 909/S/117.878||%height=250px%[[Site.SumlockComptometer1950s| http://meta-studies.net/pmwiki/uploads/SumlockH250.jpg]]||
||~1955||Bell Punch Sumlock ||Bell Punch||Demonstration\\Comptometer||%height=250px%[[Site.SumlockDemonstrator1955| http://meta-studies.net/pmwiki/uploads/BellPunchDemoH250.jpg]]||

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||%center% %height=200px%[[Site.Curta-1-1948|http://meta-studies.net/pmwiki/uploads/Curta1-~~1948~~.~~png~~]]||%center% %height=200px%[[Site.Curta-1-1967|http://meta-studies.net/pmwiki/uploads/Curta1-~~1967~~.~~png~~]]||%center% %height=200px%[[Site.Curta-2-1963|http://meta-studies.net/pmwiki/uploads/~~Curta2~~.~~png~~]]||

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||%center% %height=250px%[[Site.HP-35-1972|http://meta-studies.net/pmwiki/uploads/HP35H250.jpg]]||%center% %height=250px%[[Site.HP-45-1973|http://meta-studies.net/pmwiki/uploads/HP-45H250.jpg]]||

05 August 2013 by 121.219.165.90 -

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||align=center cellpadding=6 border=1 tableclass=long id=SimpleLinearCalcs"Simple Linear Calculators"

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||align=center cellpadding=6 border=1 tableclass=long id=SimpleRotationalCalcs"Simple Rotational Calculators"

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||align=center cellpadding=6 border=0 tableclass=long id=SimpleRotationalCalcs"Simple Rotational Calculators"

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||align=center cellpadding=6 border=1 tableclass=long id=DemoPinwheels"Demonstration Pinwheel Calculator"

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||align=center cellpadding=6 border=0 tableclass=long id=DemoPinwheels"Demonstration Pinwheel Calculator"

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||align=center cellpadding=6 border=1 tableclass=long id=PinwheelCalcs"Pinwheel Calculators"

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||align=center cellpadding=6 border=0 tableclass=long id=PinwheelCalcs"Pinwheel Calculators"

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||align=center cellpadding=6 border=1 tableclass=long id=RackCalcs"Proportional Rack Calculators"

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||align=center cellpadding=6 border=0 tableclass=long id=RackCalcs"Proportional Rack Calculators"

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||align=center cellpadding=6 border=1 tableclass=long id=Comptometers"Comptometers"

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||align=center cellpadding=6 border=0 tableclass=long id=Comptometers"Comptometers"

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||align=center cellpadding=6 border=1 tableclass=long id=DirectMultiplier"Direct Multiplying Calculators"

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||align=center cellpadding=6 border=0 tableclass=long id=DirectMultiplier"Direct Multiplying Calculators"

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||align=center cellpadding=6 border=1 tableclass=long id=Arithmometers"~~Some~~ Arithmometers"

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||align=center cellpadding=6 border=1 tableclass=long id=Arithmometers"Arithmometers"

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||align=center cellpadding=6 border=1 tableclass=long id=~~SimpleLinearCalcs~~"~~Simple Linear~~ Calculators"

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||align=center cellpadding=6 border=1 tableclass=long id=PinwheelCalcs"Pinwheel Calculators"

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||align=center cellpadding=6 border=1 tableclass=long id=RackCalcs"Proportional Rack Calculators"

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||align=center cellpadding=6 border=1 tableclass=long id=CurtaCalcs"Curta Calculators"

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T earliest of these machines had been that of Schickard (below, left). In the upper part is a set of rotatable Napier's rods revealed by windows to give partial products. In the lower part is the world's first known stylus operated adding machine to add these partial products up. A late and unique expression of these in this collection (below, right) is Justin Bamberger’s Omega Calculating Machine (1903-6). In the upper section is a set of Napier's bones revealed by moveable windows for discovering the partial products of two multiplied numbers. In the lower section is a Locke adding machine for adding them up.

to:

The earliest of these machines had been that of Schickard (below, left). In the upper part is a set of rotatable Napier's rods revealed by windows to give partial products. In the lower part is the world's first known stylus operated adding machine to add these partial products up. A late and unique expression of these in this collection (below, right) is Justin Bamberger’s Omega Calculating Machine (1903-6). In the upper section is a set of Napier's bones revealed by moveable windows for discovering the partial products of two multiplied numbers. In the lower section is a Locke adding machine for adding them up.

||align=center cellpadding=6 border=1 tableclass=long id=DirectMultiplier"Direct Multiplying Calculators"

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||~~%center% %height=250px% 1623~~: ~~Recreation of \\Wilhelm~~ Schickard's machine~~\\(collection Calculant)~~||~~%center% 1904-1905: Bamberger’s Omega\\ Calculating~~ Machine~~\\(collection Calculant)~~||

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||1623: Recreation of ||1904-1905: Bamberger’s Omega||
||Wilhelm Schickard's machine|| Calculating Machine||
||(collection Calculant)||(collection Calculant)||
||tableend

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||align=center cellpadding=6 border=1 tableclass=long id=HPCacl"Hewlett Packard Pocket Scientific Calculators"

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||align=center cellpadding=6 border=1 tableclass=long id=SimpleRotationalCalcs"Simple Rotational Calculators"

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||align=center cellpadding=6 border=1 tableclass=long id=Arithmometers"Some Arithmometers"

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(:table align=center :)
(:cellnr:) [[Site.Locke1901|%center% http://meta-studies.net/pmwiki/uploads/Locke170.jpg]]%%
%center% 1905-10: Locke Adder\\
(collection Calculant)
(:tableend:)

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%height=200px%%center%http://meta-studies.net/pmwiki/pmwiki.php?n=Site.CHAIX1790|http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg|~1790: Conversion device (from Aunes to Metres)\\(collection Calculant)

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||align=center cellpadding=3 border=0 tableclass=long id=Locke"The Locke Adder"
||[[Site.Locke1901|%center% http://meta-studies.net/pmwiki/uploads/Locke170.jpg]]||
||(collection Calculant)||

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||align=center cellpadding=3 border=0 tableclass=long id=SimpleLinearCalcs"Simple Linear Calculators"

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%height=200px%%center%http://meta-studies.net/pmwiki/pmwiki.php?n=Site.CHAIX1790|http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg|~1790: Conversion device (from Aunes to Metres)\\(collection Calculant)

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||1910-20s||Comptator (9 col)||Schubert\\& Salzer||Chain||%height=125px%[[Site.Comptator1910|http://meta-studies.net/pmwiki/uploads/~~Comptator~~.~~png~~]]||
||~1915||Golden Gem Automatic\\Adding Machine||H. & H. Goldmann||Chain||%height=100px%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/~~GoldenGem~~.jpg]]||
||1920||Addiator Troncet adder||Ruthard & Co||Chain||%height=125px%[[Site.Addiator1920 |http://meta-studies.net/pmwiki/uploads/~~Addiator~~.~~png~~]]||
||1922||Scribola 10 column\\printing\\Adding Machine||Addiator Gesellschaft||Rod||%height=150px%[[Site.Scribola1922 |http://meta-studies.net/pmwiki/uploads/~~Scribola~~.jpg]]||
||1937||Add-O-Matic\\Adding Machine||Allied MFG. Co.||Chain||%height=125px%[[Site.Add-O-Matic1937 |http://meta-studies.net/pmwiki/uploads/AddOMatic1.jpg]]||

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||1910-20s||Comptator (9 col)||Schubert\\& Salzer||Chain||%height=125px%[[Site.Comptator1910|http://meta-studies.net/pmwiki/uploads/Comptator125.jpg]]||
||~1915||Golden Gem Automatic\\Adding Machine||H. & H. Goldmann||Chain||%height=100px%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem100.jpg]]||
||1920||Addiator Troncet adder||Ruthard & Co||Chain||%height=125px%[[Site.Addiator1920 |http://meta-studies.net/pmwiki/uploads/Addiator125.jpg]]||
||1922||Scribola 10 column\\printing\\Adding Machine||Addiator Gesellschaft||Rod||%height=150px%[[Site.Scribola1922 |http://meta-studies.net/pmwiki/uploads/Scribola150.jpg]]||
||1937||Add-O-Matic\\Adding Machine||Allied MFG. Co.||Chain||%height=125px%[[Site.Add-O-Matic1937 |http://meta-studies.net/pmwiki/uploads/AddOMatic1_125.jpg]]||

01 August 2013 by 203.166.245.137 -

01 August 2013 by 107.6.95.21 -

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The late MADAS 20BTG calculator, seen above, which is part of this collection represents a classic exemplar of the late stages of this evolutionary development. Now fully utilising an electric motor it could fluently perform all the operations of arithmetic, complete with automatic clearing and moving the carriage entirely automatically as necessary. It ~~and~~ could also be further extended to automatically extract square roots. Its mechanism was also adopted in its essentials, then with many innovations (but with less of the Swiss robust construction of the Madas), in the US Frieden calculators. As it turned out, this final class of machines represented the pinacle of achievement in motorised mechanical calculation.

to:

The late MADAS 20BTG calculator, seen above, which is part of this collection represents a classic exemplar of the late stages of this evolutionary development. Now fully utilising an electric motor it could fluently perform all the operations of arithmetic, complete with automatic clearing and moving the carriage entirely automatically as necessary. It could also be further extended to automatically extract square roots. Its mechanism was also adopted in its essentials, then with many innovations (but with less of the Swiss robust construction of the Madas), in the US Frieden calculators. As it turned out, this final class of machines represented the pinacle of achievement in motorised mechanical calculation.

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Another means of performing arithmetic had largely been neglected for calculators ~~although it~~ had already been employed in the enormous computers that had developed from earlier work by Babbage and Scheutz ~~(who devised remarkably complex special purpose "difference engines" for calculating~~ logarithms), ~~and then later work by Turing and others giving rise to the electronic computing machines developed in~~ the second world war for decoding. The electronic version initially used valves to control on/off electric circuits each representing a single binary digit (or bit). 1 was represented by 1, two by 10, three by 11 and so on. It has been recognised since Leibniz that arithmetic could be done with these (since they represented numbers). Indeed - the method is in retrospect obvious. 10 + 01 = 11. 11+01 = 100, etc.

Utilising switches it was therefore possible to build a very efficient calculating machine. Valves were too bulky, energy consuming, and unreliable for a consumer device but prior sales of mechanical calculators had by now established a massive potential market. The invention of the transistor in 1947 at Bell Telephone labs, based on the quantum properties of crystals, laid the way for "solid state" electric switches at tiny scale, able to be turned on and off by one another. Light emitting diodes (LEDs) - another solid state device which emitted light when electrons forced into a higher energy ("excited") state fell back to their stable energy - began to appear as practical output devices in 1962.

to:

Another means of performing arithmetic had largely been neglected for calculators. It had already been employed in the enormous computers that had developed from earlier work by Babbage and Scheutz. They had devised remarkably complex special purpose "difference engines" for calculating logarithms. It had also been utilised in later work by Turing and others giving rise to the electronic computing machines developed in the second world war for decoding. This was the use of binary arithmetic. The electronic version initially used valves to control on/off electric circuits each representing a single binary digit (or bit). 1 was represented by 1, two by 10, three by 11 and so on. It has been recognised since Leibniz that arithmetic could be done with these (since they represented numbers). Indeed - the method is in retrospect obvious. 10 + 01 = 11. 11+01 = 100, etc.

Using switches it was therefore possible to build a very efficient calculating machine. Valves were too bulky, energy consuming, and unreliable for a consumer device but prior sales of mechanical calculators had by now established a massive potential market. The invention of the transistor in 1947 at Bell Telephone labs, based on the quantum properties of crystals, laid the way for "solid state" electric switches at tiny scale, able to be turned on and off by one another. Light emitting diodes (LEDs) - another solid state device which emitted light when electrons forced into a higher energy ("excited") state fell back to their stable energy - began to appear as practical output devices in 1962.

01 August 2013 by 107.6.95.17 -

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An entirely different evolutionary path ~~which has already been mentioned was attempted to solving~~ the ~~problem of mechanising the four arithmetic operations (+, -, x, /), with emphasis on finding ways to directly perform the more difficult two operations of multiplication and~~ division. ~~This developed from the Napier’s rods - or “bones” (developed by John Napier (1550–1617) to which we have~~ already ~~referred. As already mentioned calculational approaches were designed around them by Wilhelm Schickard~~ in ~~1623~~, ~~Charles Cotterel~~ in ~~1667~~, ~~Gaspard Schott in 1668,~~ and Samuel Morland between 1625 and 1695.

As will be recalled, the earliest of these machines, that of Schickard (below, left). In the upper part is a set of rotatable Napier's rods in the ~~upper~~ part~~, revealed by windows to give partial products. In the lower part is the world's first known stylus operated adding machine to add them~~ up. A late and unique expression of these in this collection (below, right) is Justin Bamberger’s Omega Calculating Machine (1903-6). In the upper section is a set of Napier's bones revealed by moveable windows for discovering the partial products of two multiplied numbers. In the lower section is a Locke adding machine for adding them up.

to:

An entirely different evolutionary path (mentioned earlier) attempted to solving the problem of mechanising the four arithmetic operations (+, -, x, /). The emphasis was on finding ways to directly perform the more difficult two operations of multiplication and division. The approach was a development from Napier’s rods - or “bones” (developed by John Napier (1550–1617). As already mentioned calculational approaches had been designed around these principles by Wilhelm Schickard in 1623, Charles Cotterel in 1667, Gaspard Schott in 1668, and Samuel Morland between 1625 and 1695.

T earliest of these machines had been that of Schickard (below, left). In the upper part is a set of rotatable Napier's rods revealed by windows to give partial products. In the lower part is the world's first known stylus operated adding machine to add these partial products up. A late and unique expression of these in this collection (below, right) is Justin Bamberger’s Omega Calculating Machine (1903-6). In the upper section is a set of Napier's bones revealed by moveable windows for discovering the partial products of two multiplied numbers. In the lower section is a Locke adding machine for adding them up.

31 July 2013 by 203.166.245.137 -

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!!!!Curta: The peak of ~~minituarisation~~ (1947-1970)

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!!!!Curta: The peak of miniaturisation (1947-1970)

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These machines thus constitute the pinacle reached in the development of the personal hand-operated mechanical digital calculator - able to carry out all four functions by means of a crank operated machine of exquisite ~~minituarised~~ workmanship and design. Production ceased in November 1970 although sales continued through 1973. At least 150,000 of the various calculator models were made. [^//An Interview with Curt Herzstark//^] For more on the Curta see the marvellous collection of documents and simulations at //The Curta Caclulator Page//.[^//The CURTA Calculator Page//, [[http://www.vcalc.net/cu.htm]], viewed 25 July 2013.^]

to:

These machines thus constitute the pinacle reached in the development of the personal hand-operated mechanical digital calculator - able to carry out all four functions by means of a crank operated machine of exquisite miniaturised workmanship and design. Production ceased in November 1970 although sales continued through 1973. At least 150,000 of the various calculator models were made. [^//An Interview with Curt Herzstark//^] For more on the Curta see the marvellous collection of documents and simulations at //The Curta Caclulator Page//.[^//The CURTA Calculator Page//, [[http://www.vcalc.net/cu.htm]], viewed 25 July 2013.^]

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Finally there is the last and most beautifully ~~mintuarised~~ of the four function manual mechanical calculators designed by Curt ~~Hertzstark~~. Curt was born in 1902 as the son of Samuel ~~Hertzstark~~ who had established a calculator manufacturing company in Vienna in 1905-6. Curt's father died in 1937 but by then Curt was both Director of the company and a highly competent designer in his own right. He began to design his ideal calculator, which would utilise the modern new light weight alloys of aluminium, magnesium, etc. By the end of 1937 he had the form of what he wished to accomplish firmly in his mind. It would be compact, lightweight, and in order to solve a series of problems it would use complementary arithmetic for subtraction. Then came Hitler. Herzstark found himself in 1943 arrested and imprisoned in Buchenwald concentration camp where he was placed in a ~~small technical camp to manufacture instruments~~ to assist the Nazi war effort.

While Curta had been imprisoned at Buchenwald he had told the supervisor his idea for a minature calculating machine. Curta recounts the conversation as:

to:

Finally there is the last and most beautifully miniaturised of the four function manual mechanical calculators designed by Curt Herzstark. Curt was born in 1902 as the son of Samuel Herzstark who had established a calculator manufacturing company in Vienna in 1905-6. Curt's father died in 1937 but by then Curt was both Director of the company and a highly competent designer in his own right. He recognised the need for a miniaturised four function calculator which could be carried in an engineer's pocket. He began to design this as a cylindrical calculator which could be held in one hand and operated with the other. It could utilise the modern new light weight alloys of aluminium, magnesium, etc. By the end of 1937 he had the form of what he wished to accomplish firmly in his mind. It would be compact, lightweight, and in order to allow a carry mechanism which would allow the crank to be turned only one way, it would use and internal process of complementary arithmetic for subtraction. Then came Hitler. Herzstark found himself in 1943 arrested and imprisoned in Buchenwald concentration camp where he was placed in a small technical camp to manufacture components to assist the Nazi war effort (in particular, parts of the V I and II missile bombs).

While Curt Herzstark had been imprisoned at Buchenwald, the Germans had retreated from Italy and whilst doing so had seized some office machines of which two truckloads were delivered to the camp. After Curt unloaded them one of the local factory owners came over to inspect them. He turned out to be Fritz Walther, the son of Curt's father's competitor. The Walther company was now back to making weapons for the war effort. But Walther recognised Curt Herzstark and later told the Camp Commandant of Curt's high skills and background. Soon after his supervisor, Herr. Munich, called Curt over. Curt recounts the conversation as:

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~~Curta~~'s role gave him a relatively protected status and he survived to 1944 when the camp was liberated by US troops. His calculator plans drawn up in pencil, complete with all dimensions and tolerances were completed just as the war ended. He developed the prototypes with the Rheinmettalwerk typewriter and calculator factory which was still operating near Weimar where he was named a Director. However for a range of reasons after much exploration he agreed to a proposal by the Prince of Liechtenstein to produce the calculators there at a company established for the purpose which was named Contina AG. The financial arrangements did not live up to their promise, but because he owned the patents he was able to negotiate what was in the end a satisfactory outcome.

to:

Curt Herzstark's role gave him a relatively protected status and he survived to 1944 when the camp was liberated by US troops. His calculator plans drawn up in pencil, complete with all dimensions and tolerances were completed just as the war ended. He developed the prototypes with the Rheinmettalwerk typewriter and calculator factory which was still operating near Weimar where he was named a Director. However for a range of reasons after much exploration he agreed to a proposal by the Prince of Liechtenstein to produce the calculators there at a company established for the purpose which was named Contina AG. The financial arrangements did not live up to their promise, but because he owned the patents he was able to negotiate what was in the end a satisfactory outcome.

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!!!!Curta: The peak of minituarisation (~~1947–1970~~)

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!!!!Curta: The peak of minituarisation (1947-1970)

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%center%%height=200px%[[Site.ThomasMechanism|http://meta-studies.net/pmwiki/uploads/Misc/ThomasMechRel.jpg]]
%center%1862: Diagram of the Thomas de Colmar arithmometer mechanism.[^ Franz Reuleaux, //Die Thomas’sche Rechenmaschine//, Freiberg, 1862 reproduced in Reuleaux’s article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^]\\ (click on the image for an enlargement)\\(Source: Museum of the History of Science, University of Oxford.)

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(:cellnr:) %height=200px% [[Site.ThomasMechanism|http://meta-studies.net/pmwiki/uploads/Misc/ThomasMechRel.jpg]]%%
%center%1862: Diagram of the Thomas de Colmar arithmometer mechanism.[^ Franz Reuleaux, //Die Thomas’sche Rechenmaschine//, Freiberg, 1862 reproduced in Reuleaux’s article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^]\\ (click on the image for an enlargement)\\(Source: Museum of the History of Science, University of Oxford.)
(:tableend:)

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(collection Calculant)

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%center% Locke Adder ~~1905-10~~\\

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%center% 1905-10: Locke Adder\\

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(:table align=center :)
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%center% Locke Adder 1905-10\\
(collection Calculant)
(:tableend:)

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%center% Conversion device ~~(from~~ Aunes to Metres) ~~~1790~~\\(collection Calculant)

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%center% ~1790: Conversion device\\(from Aunes to Metres)\\(collection Calculant)

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Conversion device (from Aunes to Metres) ~1790\\(collection Calculant)

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%center% Conversion device (from Aunes to Metres) ~1790\\(collection Calculant)

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Locke Adder 1905-10\\

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%center% Locke Adder 1905-10\\

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~~||%~~center~~%%height=150px% [[ http~~://meta-studies.net/pmwiki/~~uploads/Locke~~.~~gif~~| http://meta-studies.net/pmwiki/uploads/Locke.gif]]||
||%center%Locke Adder 1905-10\\
~~%center%~~(collection Calculant)||

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(:table align=center :)
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Locke Adder 1905-10\\
(collection Calculant)
(:tableend:)

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||%center% Conversion device (from Aunes to Metres) ~1790\\(collection Calculant)||

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Conversion device (from Aunes to Metres) ~1790\\(collection Calculant)

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%center% ||Conversion device (from Aunes to Metres) ~1790\\(collection Calculant)||

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||[[http://meta-studies.net/pmwiki/pmwiki.php?n=Site.CHAIX1790|%center% %height=200px% http://meta-studies.net/pmwiki/uploads/Convertiseur.png]]||
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%center% ~~%height=200px%~~ [[http://meta-studies.net/pmwiki/pmwiki.php?n=Site.~~Locke1901~~| http://meta-studies.net/pmwiki/uploads/~~Locke~~.~~gif~~]]
%center%~~Conversion~~ device (from Aunes to Metres) ~1790\\(collection Calculant)

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%center% ||[[http://meta-studies.net/pmwiki/pmwiki.php?n=Site.CHAIX1790|%height=200px% http://meta-studies.net/pmwiki/uploads/Convertiseur.png]]||
%center% ||Conversion device (from Aunes to Metres) ~1790\\(collection Calculant)||

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%center%%height=150px% [[ http://meta-studies.net/pmwiki/uploads/Locke.gif| http://meta-studies.net/pmwiki/uploads/Locke.gif]]
%center%Locke Adder 1905-10\\
%center%(collection Calculant)

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||%center%Locke Adder 1905-10\\
%center%(collection Calculant)||

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||1910-20s||Comptator (9 col)||Schubert\\& Salzer||Chain||%height=125px%[[~~http://meta-studies~~.~~net/pmwiki/uploads/Comptator.png~~|http://meta-studies.net/pmwiki/uploads/Comptator.png]]||

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||1910-20s||Comptator (9 col)||Schubert\\& Salzer||Chain||%height=125px%[[Site.Comptator1910|http://meta-studies.net/pmwiki/uploads/Comptator.png]]||

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||1910-20s||Comptator (9 col)||Schubert\\& Salzer||Chain||%height=125px%[[~~Site~~.~~Comptator1910~~|http://meta-studies.net/pmwiki/uploads/Comptator.png]]||

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||1910-20s||Comptator (9 col)||Schubert\\& Salzer||Chain||%height=125px%[[http://meta-studies.net/pmwiki/uploads/Comptator.png|http://meta-studies.net/pmwiki/uploads/Comptator.png]]||

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These overblown claims are reminiscent of similar claims for their inventions by Pascal (with this machine the user can do with ease, "without effort of memory" and "without even thinking of it", every possible arithmetic operation[^Pascal, ligé de retenir ou d’emprunter les nombres nécessaires, et combien d’erreurs se glissent dans ces rétentions et emprunts, à mois d’une très longue habitude et, en outre, d’une attention profonde et qui fatigue l’esprit en peu de temps. Cette machine délivre celui qui opère par elle de cette vexation; il suffit qu’il ait le jugement, elle le relève du défaut de la mémoire; et, sans rien retenir ni emprunter, elle fait d’elle-même ce qu’il désire, sans même qu’il y pense.” p. 337^] and Moreland (allowing addition and subtraction "without charging the memory or disturbing the mind[^S. Moreland, //A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence// 1672, title page.^]). They show the hope, that the mental activity could be replaced by the machine. But in reality, for all of these machines it was not just a question of the high cost of obtaining it, but the learning and practice required to use it.

to:

These overblown claims are reminiscent of similar claims for their inventions by Pascal (with this machine the user can do with ease, "without effort of memory" and "without even thinking of it", every possible arithmetic operation[^Pascal, ligé de retenir ou d’emprunter les nombres nécessaires, et combien d’erreurs se glissent dans ces rétentions et emprunts, à mois d’une très longue habitude et, en outre, d’une attention profonde et qui fatigue l’esprit en peu de temps. Cette machine délivre celui qui opère par elle de cette vexation; il suffit qu’il ait le jugement, elle le relève du défaut de la mémoire; et, sans rien retenir ni emprunter, elle fait d’elle-même ce qu’il désire, sans même qu’il y pense.” p. 337^]) and Moreland (allowing addition and subtraction "without charging the memory or disturbing the mind[^S. Moreland, //A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence// 1672, title page.^]). They show the hope, that the mental activity could be replaced by the machine. But in reality, for all of these machines it was not just a question of the high cost of obtaining it, but the learning and practice required to use it.

27 July 2013 by 58.6.241.7 -

Changed lines 248-250 from:

The first model (the Model 1) began production in 1947. ~~Top~~ left is a (rare) example of the Model I Curta ( with pin sliders which were soon improved upon) in mint condition coming from the first 5500 made in ~July 1948, the year after production began and in the first 5,500 made. As can be seen the sliders are pins which were used by Curta before he introduced bakelite handles on them. Centre is a later Curta from 1967 complete with the original box in which it was sold and its instructions, all in mint condition. On the right is a Curta Model II from 1962. The Model II was a larger machine capable of a number input to 11 significant figures, compared with the more compact Model I which could accept a number accurate to 8 significant figures. Note the very 'modern' anodised aluminium sliders on the Model II which comes also with an optional leather carry case (not shown).

to:

The first model (the Model 1) began production in 1947. Below left is a (rare) example of the Model I Curta ( with pin sliders which were soon improved upon) in mint condition coming from the first 5500 made in ~July 1948, the year after production began and in the first 5,500 made. As can be seen the sliders are pins which were used by Curta before he introduced bakelite handles on them. Centre is a later Curta from 1967 complete with the original box in which it was sold and its instructions, all in mint condition. On the right is a Curta Model II from 1962. The Model II was a larger machine capable of a number input to 11 significant figures, compared with the more compact Model I which could accept a number accurate to 8 significant figures. Note the very 'modern' anodised aluminium sliders on the Model II which comes also with an optional leather carry case (not shown).

Changed lines 255-256 from:

On the ~~top~~ left ~~machine~~ we see the clearing ring protruding. Bringing all numbers to zero is achieved by lifting the top section and turning the clearing ring. Adding is achieved by setting successive numbers and turning the crank through a full turn. Ingeniously, pulling the crank up sets it for subtraction. Multiplication is done in the usual manner of multiplying by each successive integer of the multiplier with the upper register being advanced for each one by lifting the top section and rotating it one notch. Division is by the usual method of long division by repeated subtractions. Once more, for each partial product the operator must either correctly judge the correct number of times to turn the crank, or if an overflow is forced, reverse the operation by pushing in the crank and turning it one full turn. In short it is an excellent machine for addition and subtraction, but involves the normal acquired skill, and tedium, required by multiplication and division in any of the mechanical calculators not equipped to do it automatically.

to:

On the Curta above, left we see the clearing ring protruding. Bringing all numbers to zero is achieved by lifting the top section and turning the clearing ring. Adding is achieved by setting successive numbers and turning the crank through a full turn. Ingeniously, pulling the crank up sets it for subtraction. Multiplication is done in the usual manner of multiplying by each successive integer of the multiplier with the upper register being advanced for each one by lifting the top section and rotating it one notch. Division is by the usual method of long division by repeated subtractions. Once more, for each partial product the operator must either correctly judge the correct number of times to turn the crank, or if an overflow is forced, reverse the operation by pushing in the crank and turning it one full turn. In short it is an excellent machine for addition and subtraction, but involves the normal acquired skill, and tedium, required by multiplication and division in any of the mechanical calculators not equipped to do it automatically.

Changed line 286 from:

The deck of the Millionaire in this collection is shown below with the selector on the ~~right~~ which picks the multiplying factor, and the selector on the right which sets it for addition, subtraction, multiplication and division (AMDS). The ten sliders for setting the number to be operated on are obvious, as are the result windows, and on the far right, the crank handle.

to:

The deck of the Millionaire in this collection is shown below with the selector on the left which picks the multiplying factor, and the selector on the right which sets it for addition, subtraction, multiplication and division (AMDS). The ten sliders for setting the number to be operated on are obvious, as are the result windows, and on the far right, the crank handle.

26 July 2013 by 58.6.184.192 -

Changed lines 248-250 from:

The first model (the Model 1) began production in 1947. ~~A (rare) example of the Model I Curta ( with pin sliders which were soon improved upon) in mint condition coming from the first 5500 made in ~July 1948, is~~ in this collection along with another Model I (complete with its packing box and instructions) from 1967, and a Model II Curta from 1962 (with an ‘extra’ leather carrying case). These machines constitute the pinacle reached in the development of the personal hand-operated mechanical digital calculator - able to carry out all four functions by means of a crank operated machine of exquisite minituarised workmanship and design. Production ceased in November 1970 although sales continued through 1973. At least 150,000 of ~~the various calculator models were made. [^//An Interview~~ with Curt Herzstark//^] For more on the Curta see the marvellous collection of documents and simulations at //The Curta Caclulator Page//.[^//The CURTA Calculator Page//, [[http://www.vcalc.net/cu.htm]], viewed 25 July 2013.^] The three Curta calculators in this collection are shown ~~below~~.

to:

The first model (the Model 1) began production in 1947. Top left is a (rare) example of the Model I Curta ( with pin sliders which were soon improved upon) in mint condition coming from the first 5500 made in ~July 1948, the year after production began and in the first 5,500 made. As can be seen the sliders are pins which were used by Curta before he introduced bakelite handles on them. Centre is a later Curta from 1967 complete with the original box in which it was sold and its instructions, all in mint condition. On the right is a Curta Model II from 1962. The Model II was a larger machine capable of a number input to 11 significant figures, compared with the more compact Model I which could accept a number accurate to 8 significant figures. Note the very 'modern' anodised aluminium sliders on the Model II which comes also with an optional leather carry case (not shown).

Deleted lines 254-255:

Top left is a very early Curta Model 1 from 1948, the year after production began and in the first 5,500 made. As can be seen the sliders are pins which were used by Curta before he introduced bakelite handles on them. Centre is a later Curta from 1967 complete with the original box in which it was sold and its instructions, all in mint condition. On the right is a Curta Model II from 1962. The Model II was a larger machine capable of a number input to 11 significant figures, compared with the more compact Model I which could accept a number accurate to 8 significant figures. Note the very 'modern' anodised aluminium sliders on the Model II which comes also with an optional leather carry case (not shown).

Added lines 256-259:

These machines thus constitute the pinacle reached in the development of the personal hand-operated mechanical digital calculator - able to carry out all four functions by means of a crank operated machine of exquisite minituarised workmanship and design. Production ceased in November 1970 although sales continued through 1973. At least 150,000 of the various calculator models were made. [^//An Interview with Curt Herzstark//^] For more on the Curta see the marvellous collection of documents and simulations at //The Curta Caclulator Page//.[^//The CURTA Calculator Page//, [[http://www.vcalc.net/cu.htm]], viewed 25 July 2013.^]

26 July 2013 by 58.6.237.118 -

Changed line 257 from:

On the top left machine we see the clearing ring protruding. Bringing all numbers to zero is achieved by lifting the top section and turning the clearing ring. Adding is achieved by setting successive numbers and turning the crank through a full turn. Ingeniously, pulling the crank up sets it for subtraction. Multiplication is done in the usual manner of multiplying by each successive integer of the multiplier with the upper register being advanced for each one by lifting the top section and rotating it one notch. Division is by the usual method of long division by repeated subtractions. Once more, for each partial product the operator must either correctly judge the correct number of times to turn the crank, or if an overflow is forced, reverse the operation by pushing in the crank and turning it one full turn. In short it is an excellent machine for addition and subtraction, but involves the normal ~~tedium for multiplication~~ and ~~division of any of the mechanical calculators which have not been~~ equipped to do it automatically.

to:

On the top left machine we see the clearing ring protruding. Bringing all numbers to zero is achieved by lifting the top section and turning the clearing ring. Adding is achieved by setting successive numbers and turning the crank through a full turn. Ingeniously, pulling the crank up sets it for subtraction. Multiplication is done in the usual manner of multiplying by each successive integer of the multiplier with the upper register being advanced for each one by lifting the top section and rotating it one notch. Division is by the usual method of long division by repeated subtractions. Once more, for each partial product the operator must either correctly judge the correct number of times to turn the crank, or if an overflow is forced, reverse the operation by pushing in the crank and turning it one full turn. In short it is an excellent machine for addition and subtraction, but involves the normal acquired skill, and tedium, required by multiplication and division in any of the mechanical calculators not equipped to do it automatically.

26 July 2013 by 58.6.237.118 -

Changed lines 255-257 from:

Top left is a very early Curta Model 1 from 1948, the year after production began and in the first 5,500 made. As can be seen the sliders are pins which were used by Curta before he introduced bakelite handles on them. Centre is a later Curta from 1967 complete with the original box in which it was sold and its instructions, all in mint condition. On the right is a Curta Model II from 1962. The Model II was a larger machine capable of a number input to 11 significant figures, compared with the more compact Model I which could accept a number accurate to 8 significant figures. Note the very 'modern' anodised aluminium sliders on the Model II ~~and its optional leather carry case.~~

to:

Top left is a very early Curta Model 1 from 1948, the year after production began and in the first 5,500 made. As can be seen the sliders are pins which were used by Curta before he introduced bakelite handles on them. Centre is a later Curta from 1967 complete with the original box in which it was sold and its instructions, all in mint condition. On the right is a Curta Model II from 1962. The Model II was a larger machine capable of a number input to 11 significant figures, compared with the more compact Model I which could accept a number accurate to 8 significant figures. Note the very 'modern' anodised aluminium sliders on the Model II which comes also with an optional leather carry case (not shown).

On the top left machine we see the clearing ring protruding. Bringing all numbers to zero is achieved by lifting the top section and turning the clearing ring. Adding is achieved by setting successive numbers and turning the crank through a full turn. Ingeniously, pulling the crank up sets it for subtraction. Multiplication is done in the usual manner of multiplying by each successive integer of the multiplier with the upper register being advanced for each one by lifting the top section and rotating it one notch. Division is by the usual method of long division by repeated subtractions. Once more, for each partial product the operator must either correctly judge the correct number of times to turn the crank, or if an overflow is forced, reverse the operation by pushing in the crank and turning it one full turn. In short it is an excellent machine for addition and subtraction, but involves the normal tedium for multiplication and division of any of the mechanical calculators which have not been equipped to do it automatically.

26 July 2013 by 58.6.237.118 -

Changed lines 248-250 from:

The first model (the Model 1) began production in 1947. A (rare) example of the Model I Curta ( with pin sliders which were soon improved upon) in mint condition coming from the first 5500 made in ~July 1948, is in this collection along with another Model I (complete with its packing box and instructions) from 1967, and a Model II Curta from 1962 (with an ‘extra’ leather carrying case). These machines constitute the pinacle reached in the development of the personal hand-operated mechanical digital calculator - able to carry out all four functions by means of a crank operated machine of exquisite minituarised workmanship and design. Production ceased in November 1970 although sales continued through 1973. At least 150,000 of the various calculator models were made. [^//An Interview with Curt Herzstark//^]

to:

The first model (the Model 1) began production in 1947. A (rare) example of the Model I Curta ( with pin sliders which were soon improved upon) in mint condition coming from the first 5500 made in ~July 1948, is in this collection along with another Model I (complete with its packing box and instructions) from 1967, and a Model II Curta from 1962 (with an ‘extra’ leather carrying case). These machines constitute the pinacle reached in the development of the personal hand-operated mechanical digital calculator - able to carry out all four functions by means of a crank operated machine of exquisite minituarised workmanship and design. Production ceased in November 1970 although sales continued through 1973. At least 150,000 of the various calculator models were made. [^//An Interview with Curt Herzstark//^] For more on the Curta see the marvellous collection of documents and simulations at //The Curta Caclulator Page//.[^//The CURTA Calculator Page//, [[http://www.vcalc.net/cu.htm]], viewed 25 July 2013.^] The three Curta calculators in this collection are shown below.

Changed line 255 from:

to:

Top left is a very early Curta Model 1 from 1948, the year after production began and in the first 5,500 made. As can be seen the sliders are pins which were used by Curta before he introduced bakelite handles on them. Centre is a later Curta from 1967 complete with the original box in which it was sold and its instructions, all in mint condition. On the right is a Curta Model II from 1962. The Model II was a larger machine capable of a number input to 11 significant figures, compared with the more compact Model I which could accept a number accurate to 8 significant figures. Note the very 'modern' anodised aluminium sliders on the Model II and its optional leather carry case.

26 July 2013 by 58.6.237.118 -

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->Mr. Munich said: See, Herzstark, I understand you've been working on a new thing, a small calculating machine. Do you know, I can give you a tip. We will allow you to make and draw everything. If it is really worth something, then we will give it to the Fuhrer as a present after we win the war. Then, surely, you will be made an Aryan." For me, that was the first time I thought to myself, my God, if you do this, you can extend your life. And then and there I started to draw the CURTA, the way I had imagined it.[^//An Interview with Curt Herzstark//, OH 140, conducted by Erwin Tomash on 10-11 September 1987, Nendeln, Liechtenstein, (English Translation).^]

Curta's role gave him a relatively protected status and he survived to 1944 when the camp was liberated by US troops. His calculator plans drawn up in pencil, complete with all dimensions and tolerances were completed just as the war ended. He developed the prototypes with the Rheinmettalwerk typewriter and calculator factory which was still operating near Weimar where he was named a Director. However for a range of reasons after much exploration agreed to a proposal by the Prince of Liechtenstein to produce the calculators there at a company established for the purpose which was named Contina AG.

to:

->Mr. Munich said: "See, Herzstark, I understand you've been working on a new thing, a small calculating machine. Do you know, I can give you a tip. We will allow you to make and draw everything. If it is really worth something, then we will give it to the Fuhrer as a present after we win the war. Then, surely, you will be made an Aryan." For me, that was the first time I thought to myself, my God, if you do this, you can extend your life. And then and there I started to draw the CURTA, the way I had imagined it.[^//An Interview with Curt Herzstark//, OH 140, conducted by Erwin Tomash on 10-11 September 1987, Nendeln, Liechtenstein, (English Translation).^]

Curta's role gave him a relatively protected status and he survived to 1944 when the camp was liberated by US troops. His calculator plans drawn up in pencil, complete with all dimensions and tolerances were completed just as the war ended. He developed the prototypes with the Rheinmettalwerk typewriter and calculator factory which was still operating near Weimar where he was named a Director. However for a range of reasons after much exploration he agreed to a proposal by the Prince of Liechtenstein to produce the calculators there at a company established for the purpose which was named Contina AG. The financial arrangements did not live up to their promise, but because he owned the patents he was able to negotiate what was in the end a satisfactory outcome.

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Finally there is the last and most beautifully mintuarised of the four function manual mechanical calculators designed by Curt Hertzstark. Curt was born in 1902 as the son of Samuel Hertzstark who had established a calculator manufacturing company in Vienna in 1905-6. He

which he developed when a prisoner in Buchenwald concentration camp. The first model (the Model 1) began production in 1947. A (rare) example of the Model I Curta ( with pin sliders which were soon improved upon) in mint condition coming from the first 5500 made in ~July 1948, is in this collection along with another Model I (complete with its packing box and instructions) from 1967, and a Model II Curta from 1962 (with an ‘extra’ leather carrying case). These machines constitute the pinacle reached in the development of the personal hand-operated mechanical digital calculator - able to carry out all four functions by means of a crank operated machine of exquisite minituarised workmanship and design. Production ceased in November 1970 although sales continued through 1973.

[^//An Interview with Curt Herzstark//, OH 140, conducted by Erwin Tomash on 10-11 September 1987, Nendeln, Liechtenstein, (English Translation).^]

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Finally there is the last and most beautifully mintuarised of the four function manual mechanical calculators designed by Curt Hertzstark. Curt was born in 1902 as the son of Samuel Hertzstark who had established a calculator manufacturing company in Vienna in 1905-6. Curt's father died in 1937 but by then Curt was both Director of the company and a highly competent designer in his own right. He began to design his ideal calculator, which would utilise the modern new light weight alloys of aluminium, magnesium, etc. By the end of 1937 he had the form of what he wished to accomplish firmly in his mind. It would be compact, lightweight, and in order to solve a series of problems it would use complementary arithmetic for subtraction. Then came Hitler. Herzstark found himself in 1943 arrested and imprisoned in Buchenwald concentration camp where he was placed in a small technical camp to manufacture instruments to assist the Nazi war effort.

While Curta had been imprisoned at Buchenwald he had told the supervisor his idea for a minature calculating machine. Curta recounts the conversation as:

->Mr. Munich said: See, Herzstark, I understand you've been working on a new thing, a small calculating machine. Do you know, I can give you a tip. We will allow you to make and draw everything. If it is really worth something, then we will give it to the Fuhrer as a present after we win the war. Then, surely, you will be made an Aryan." For me, that was the first time I thought to myself, my God, if you do this, you can extend your life. And then and there I started to draw the CURTA, the way I had imagined it.[^//An Interview with Curt Herzstark//, OH 140, conducted by Erwin Tomash on 10-11 September 1987, Nendeln, Liechtenstein, (English Translation).^]

Curta's role gave him a relatively protected status and he survived to 1944 when the camp was liberated by US troops. His calculator plans drawn up in pencil, complete with all dimensions and tolerances were completed just as the war ended. He developed the prototypes with the Rheinmettalwerk typewriter and calculator factory which was still operating near Weimar where he was named a Director. However for a range of reasons after much exploration agreed to a proposal by the Prince of Liechtenstein to produce the calculators there at a company established for the purpose which was named Contina AG.

The first model (the Model 1) began production in 1947. A (rare) example of the Model I Curta ( with pin sliders which were soon improved upon) in mint condition coming from the first 5500 made in ~July 1948, is in this collection along with another Model I (complete with its packing box and instructions) from 1967, and a Model II Curta from 1962 (with an ‘extra’ leather carrying case). These machines constitute the pinacle reached in the development of the personal hand-operated mechanical digital calculator - able to carry out all four functions by means of a crank operated machine of exquisite minituarised workmanship and design. Production ceased in November 1970 although sales continued through 1973. At least 150,000 of the various calculator models were made. [^//An Interview with Curt Herzstark//^]

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Samuel Herzstark, the father of Curt Herzstark who built the Curta, also was a pioneer in calculator construction and together with Gustav Perger established the Austria Calculator Machines Manufacturing Company in Vienna in 1905-6. In an interview in 1987 Curt Herzstark reports that in 1907 Samuel became the first to attach an electric motor to an arithmometer, which he equipped also with a keyboard. Curt also notes that this machine was equipped with automatic division.[^//An Interview with Curt Herzstark//, OH 140, conducted by Erwin Tomash on 10-11 September 1987, Nendeln, Liechtenstein, (English Translation).^] Below is an arithmometer in this collection branded by Samuel Herzstark from 1929, although by then he was not making machines. It is actually a Badenia (manufactured by the German Company Math. Bauerle in the ~~Black Forest) which Herzstark was by then re-badging (not long before he died)~~.

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Samuel Herzstark (1867-1937), the father of Curt Herzstark who built the Curta, also was a pioneer in calculator construction and together with Gustav Perger established the Austria Calculator Machines Manufacturing Company in Vienna in 1905-6. In an interview in 1987 Curt Herzstark reports that in 1907 Samuel became the first to attach an electric motor to an arithmometer, which he equipped also with a keyboard. Curt also notes that this machine was equipped with automatic division.[^//An Interview with Curt Herzstark//, OH 140, conducted by Erwin Tomash on 10-11 September 1987, Nendeln, Liechtenstein, (English Translation).^] However after the 1914-18 War Herzstark returned to a demolished business. He restarted with a combination of importing and selling calculators from other manufacturers, assembling old stock of his own design, and then as the business built up designing new machines. Below is an arithmometer in this collection branded by Samuel Herzstark from 1929. It is actually a Badenia (manufactured by the German Company Math. Bauerle in the Black Forest) which Herzstark was at that time re-badging and selling.

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Finally there is the last and most beautifully mintuarised of the four function manual mechanical calculators ~~buit~~ by Curt Hertzstark, the son of Samuel Hertzstark (mentioned earlier) which he developed when a prisoner in Buchenwald concentration camp. The first model (the Model 1) began production in 1947. A (rare) example of the Model I Curta ( with pin sliders which were soon improved upon) in ~~mint condition coming from~~ the ~~first 5500 made in ~July 1948, is in this collection along with another Model I (complete with its packing box and instructions) from 1967~~, and a Model II Curta from 1962 (with an ‘extra’ leather carrying case). These machines constitute the pinacle reached in the development of the personal hand-operated mechanical digital calculator - able to carry out all four functions by means of ~~a crank~~ operated ~~machine of exquisite minituarised workmanship and design. Production ceased in November 1970 although sales continued through 1973~~.

to:

Finally there is the last and most beautifully mintuarised of the four function manual mechanical calculators designed by Curt Hertzstark. Curt was born in 1902 as the son of Samuel Hertzstark who had established a calculator manufacturing company in Vienna in 1905-6. He

which he developed when a prisoner in Buchenwald concentration camp. The first model (the Model 1) began production in 1947. A (rare) example of the Model I Curta ( with pin sliders which were soon improved upon) in mint condition coming from the first 5500 made in ~July 1948, is in this collection along with another Model I (complete with its packing box and instructions) from 1967, and a Model II Curta from 1962 (with an ‘extra’ leather carrying case). These machines constitute the pinacle reached in the development of the personal hand-operated mechanical digital calculator - able to carry out all four functions by means of a crank operated machine of exquisite minituarised workmanship and design. Production ceased in November 1970 although sales continued through 1973.

[^//An Interview with Curt Herzstark//, OH 140, conducted by Erwin Tomash on 10-11 September 1987, Nendeln, Liechtenstein, (English Translation).^]

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Samuel Herzstark, the father of Curt Herzstark who built the Curta, also was a pioneer in calculator construction and together with Gustav Perger established the Austria Calculator Machines Manufacturing Company in Vienna in 1905-6. In an interview in 1987 Curt Herzstark reports that in 1907 Samuel became the first to attach an electric motor to an arithmometer, which he equipped also with a keyboard.[^//An Interview with Curt Herzstark//, OH 140, conducted by Erwin Tomash on 10-11 September 1987, Nendeln, Liechtenstein, (English Translation).^] Below is an arithmometer in this collection branded by Samuel Herzstark from 1929, although by then he was not making machines. It is actually a Badenia (manufactured by the German Company Math. Bauerle in the Black Forest) which Herzstark was by then re-badging (not long before he died).

to:

Samuel Herzstark, the father of Curt Herzstark who built the Curta, also was a pioneer in calculator construction and together with Gustav Perger established the Austria Calculator Machines Manufacturing Company in Vienna in 1905-6. In an interview in 1987 Curt Herzstark reports that in 1907 Samuel became the first to attach an electric motor to an arithmometer, which he equipped also with a keyboard. Curt also notes that this machine was equipped with automatic division.[^//An Interview with Curt Herzstark//, OH 140, conducted by Erwin Tomash on 10-11 September 1987, Nendeln, Liechtenstein, (English Translation).^] Below is an arithmometer in this collection branded by Samuel Herzstark from 1929, although by then he was not making machines. It is actually a Badenia (manufactured by the German Company Math. Bauerle in the Black Forest) which Herzstark was by then re-badging (not long before he died).

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~~Below is an arithmometer in this collection branded by Samuel Hertzstark from 1929, although by then he was not making machines. It is actually a Badenia (manufactured by the German~~ Company ~~Math. Bauerle~~ in ~~the Black Forest) which Hertzstark~~ was by then re-badging (not long before he died).

to:

Samuel Herzstark, the father of Curt Herzstark who built the Curta, also was a pioneer in calculator construction and together with Gustav Perger established the Austria Calculator Machines Manufacturing Company in Vienna in 1905-6. In an interview in 1987 Curt Herzstark reports that in 1907 Samuel became the first to attach an electric motor to an arithmometer, which he equipped also with a keyboard.[^//An Interview with Curt Herzstark//, OH 140, conducted by Erwin Tomash on 10-11 September 1987, Nendeln, Liechtenstein, (English Translation).^] Below is an arithmometer in this collection branded by Samuel Herzstark from 1929, although by then he was not making machines. It is actually a Badenia (manufactured by the German Company Math. Bauerle in the Black Forest) which Herzstark was by then re-badging (not long before he died).

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This is ~~happening at~~ a ~~time at a time when we are challenged to make the enormous changes~~ to ~~the way we live over~~ the next few decades required by the transition to a low carbon economy. This is increasingly widely understood to be necessary if humans are to have some hope of maintaining an acceptable physical environment for this and future generations. The story of innovation in ~~calculators tells us that whilst the time may be ripe for us to accept a great deal of change, it will require re-learning~~ to ~~be comfortable with the many innovations that will be needed~~ to ~~achieve it~~. ~~Getting there will require require people to reshape~~ attitudes, hidden assumptions and habitual ways of living. In seeking to make those changes, we might reflect on the many challenges overcome in the simpler long history of how humans have learned to calculate, and what that means for the learning and innovation that will now be required.

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This is of course a history of one area of innovation. So it may have some relevance to other areas of innovation in the world in which we now live. It is perhaps appropriate to remember that humans have reached the point where there innovation is actually destabilising the physical world in which they live - a situation unimaginable for most of the time in which the developments discussed here have taken place. But it is the case that humans are now challenged with the requirement to achieve an unprecedented level of innovation if the planet is to remain stable. The story of innovation in calculators tells us that whilst the time may be ripe for us to accept a great deal of change, it will require re-learning to be comfortable with the many innovations that will be needed to achieve it. Getting there will require people to re-learn and reshape many attitudes, hidden assumptions and habitual ways of living. In seeking to make those changes, we might reflect on the many challenges overcome in the simpler long history of how humans have learned to calculate, and what that means for the learning and innovation that will now be required.

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~~The~~ reason for collecting is ~~the~~ banal one ~~of consumerism - the desire to collect and own things of~~ rarity, and of course the thrill of the chase in finding, identifying and acquiring them. But beyond that it is possible for the objects to convey insight. ~~There are~~ stories of innovation ~~embodied in them raising~~ multiple questions. ~~These include not just why at some~~ particular ~~moment these were~~ invented~~, but also what was it that at a particular time~~ allowed some, but far from all~~, to be taken up in use.~~ ~~In particular why did some get established in actual and widespread use, and what limited much more sharply the success of others? Whilst it could not be claimed that~~ all the answers can be found here, some useful observations may be suggested.

First there is the more detailed story of mechanical evolution. This has been gestured at here but perhaps enough has been said to indicate that many good ideas have waited around for their moment to be realised rather than simply the whole being driven by discovery. Much could have happened after Schickard and Pascal, but it took centuries for the various devices to become widely useful. Of course, as discussed, the device of Schickard had a potential audience in the ~~restricted group of natural philosophers (in particular astronomers) with whom he communicated.~~ Pascal ~~found his machine more used as a curiosity amongst the aristocracy adding prestige, than in~~ the ~~operation~~ of adding money which was its inspiration.

In relation to this, there is an important consideration in relation to innovations. ~~An encounter with these devices suggests that that it is not possible~~ to ~~fully understand them~~, ~~including their limitations and potential, without actually using them.~~ ~~A trip to, say, one of the great technology museums (for example, CNAM in Paris) will tell you how limited the experience~~ is ~~of, for example, seeing a Pascaline~~, ~~or reading an essay about it. It is a very different experience~~ to try to calculate with one. This leads to a rather interesting connection between understanding these technologies retrospectively, and the reasons that led to their development in the first place. For the success of that development depended on whether people learned to ~~use them. In short this is~~ a history not only of mechanism but of learning how it can be used.

In short, the use of a calculating technology is not just intellectual. It is what Jean-François Gauvin[^Jean-François Gauvin , Habits of Knowledge: Artisans, Savants and Mechanical Devices in Seventeenth-Century French Natural Philosophy, The Department of ~~the History of Science, in partial fulfillment of~~ the ~~requirements for the degree of Doctor of Philosophy in the subject of History of Science, Harvard University~~, ~~Cambridge, Mass., USA~~, ~~November 2008, pp. 113. ^] refers to as "gestural". Gestural knowledge is~~ the ~~embodied knowledge that artisans rely on when they execute work of~~ the ~~highest~~ craft skill. The first time someone looks at a Thomas de Colmar arithmometer learning how to add and subtract takes some time. Doing division and multiplication is much more challenging, especially if attempted without a good knowledge of how it can be done on paper. The first time is slow and subject to mistakes. It is only after repeated practice that the gestures required become so practiced that they are quick, instinctive and reliable. It is only then that the potential for calculation with such a device can be can be judged. And it would only have been after this sort of practice that one could credit the Gentleman's Magazine of 1857 claim that:

to:

One reason for collecting is a banal one - the desire to collect and own things of rarity, and of course the thrill of the chase in finding, identifying and acquiring them. But beyond that it is possible for the objects to convey insight. The objects embody stories of innovation which can raise multiple questions. For example, why at some particular moment were these particular objects invented? And at a particular time what was it that allowed some, but far from all of the objects, once invented, to be taken up in use? In particular why did some get established in actual and widespread use? What limited so much more sharply the success of others? Certainly not all the answers to these sorts can be found here. But it is possible to make some potentially useful observations.

Of course, we have not considered even all the available information. There is the story of the detail of the evolution of the mechanism of the bewilderingly wide array of calculators that were built, which at best has been broadly gestured at here. Even so, perhaps enough has been said to indicate that many good ideas have waited around for their moment to be realised rather than simply the whole being driven by discovery. Much could have happened after Schickard and Pascal, but it took centuries for the various devices to become widely useful. Of course, as discussed, the device of Schickard had a potential audience in the restricted group of natural philosophers (in particular astronomers) with whom he communicated. Pascal found his machine more used as a curiosity amongst the aristocracy to add prestige, than used to add up money which was its inspiration.

There is another important consideration in relation to these sorts of innovations. An encounter with these devices suggests that that it is not possible to fully understand them, including their limitations and potential, without actually using them. A trip to, say, one of the great technology museums (for example, CNAM in Paris) will tell you how limited the experience is of, for example, seeing a Pascaline, or reading an essay about it. It is a very different experience to try to calculate with one. This leads to a rather interesting connection between understanding these technologies retrospectively, and the reasons that led to their development in the first place. For the success of that development depended on whether people learned to use them. In short this is a history not only of mechanism but of learning how it can be used.

In short, the use of a calculating technology is not just intellectual. It is what Jean-François Gauvin[^Jean-François Gauvin , Habits of Knowledge: Artisans, Savants and Mechanical Devices in Seventeenth-Century French Natural Philosophy, The Department of the History of Science, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of History of Science, Harvard University, Cambridge, Mass., USA, November 2008, pp. 113. ^] refers to as "gestural". Gestural knowledge is the embodied knowledge that artisans rely on when they execute work of high craft skill. The first time someone looks at a Thomas de Colmar arithmometer learning how to add and subtract takes some time. Doing division and multiplication is much more challenging, especially if attempted without a good knowledge of how it can be done on paper. The first time is slow and subject to mistakes. It is only after repeated practice that the gestures required become so practiced that they are quick, instinctive and reliable. It is only then that the potential for calculation with such a device can be can be judged. And it would only have been after this sort of practice that one could credit the Gentleman's Magazine of 1857 claim that:

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A much sought after goal for calculator designers was to develop a method which would completely automatically carry out division. All the previous arithmometers required a process of "long division" where the divisor was subtracted until no more subtractions were possible. However, this required the operator to either guess when this point had been reached, or subtract one time too many (creating an "overflow") and then reversing the subtraction to get the correct outcome. A race had been on to try to solve this particular problem, and in 1901 Alexander Rechnitzer filed a patent in the US Patent Office with a solution. In essence it involved a mechanism that could determine that an overflow had occurred (indicated by the most extreme left hand dial going from 0 to 9). When this occurred the mechanism advanced the carriage one place and added the subtracted number back one time, thus setting the machine up for the next partial division to take place.[^US Patent 809075, Filed by Alexander Rechnitzer of Viennea, US Patent Office, 29 June 1901, granted 2 January 1906, page 9, clauses 80-110.^]

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A much sought after goal for calculator designers was to develop a method which would completely automatically carry out division. All the previous arithmometers required a process of "long division" where the divisor was subtracted until no more subtractions were possible. However, this required the operator to either guess when this point had been reached, or subtract one time too many (creating an "overflow") and then reversing the subtraction to get the correct outcome. A race had been on to try to solve this particular problem, and in 1901 Alexander Rechnitzer filed a patent in the US Patent Office with a solution. In essence it involved a mechanism that could determine that an overflow had occurred (indicated by the most extreme left hand dial going from 0 to 9). When this occurred the mechanism advanced the carriage one place and added the subtracted number back one time, thus setting the machine up for the next partial division to take place.[^US Patent 809075, Filed by Alexander Rechnitzer of Viennea, US Patent Office, 29 June 1901, granted 2 January 1906, page 9, clauses 80-110. For a more comprehensive set of his patents see [[http://www.rechnerlexikon.de/en/wiki.phtml?srch=rechnitzer&title=Spezial%3APatentpage]] viewed 25 July 2013.^]

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%center% %height=200px%[[Site.~~DemonstrationPinwheel~~|http://meta-studies.net/pmwiki/uploads/Misc/RackMech.jpg]]

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%center% %height=200px%[[Site.RackMech|http://meta-studies.net/pmwiki/uploads/Misc/RackMech.jpg]]

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The late MADAS 20BTG calculator, seen above, which is part of this collection represents a classic exemplar of the late stages of this evolutionary development. Now fully utilising an electric motor it could fluently perform all the operations of arithmetic, complete with automatic clearing and moving the carriage entirely automatically as necessary. It and could also be further ~~automated~~ to extract square roots. Its mechanism was also adopted in its essentials, then with many innovations (but with less of the Swiss robust construction of the Madas), in the US Frieden calculators. As it turned out, this final class of machines represented the pinacle of achievement in motorised mechanical calculation.

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The late MADAS 20BTG calculator, seen above, which is part of this collection represents a classic exemplar of the late stages of this evolutionary development. Now fully utilising an electric motor it could fluently perform all the operations of arithmetic, complete with automatic clearing and moving the carriage entirely automatically as necessary. It and could also be further extended to automatically extract square roots. Its mechanism was also adopted in its essentials, then with many innovations (but with less of the Swiss robust construction of the Madas), in the US Frieden calculators. As it turned out, this final class of machines represented the pinacle of achievement in motorised mechanical calculation.

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A much sought after goal for calculator designers was to develop a method which would completely automatically carry out division. All the previous arithmometers required a process of "long division" where the divisor was subtracted until no more subtractions were possible. However, this required the operator to either guess when this point had been reached, or subtract one time too many (creating an "overflow") and then reversing the subtraction to get the correct outcome. A race had been on to try to solve this particular problem, and in 1901 Alexander Rechnitzer filed a patent in the US Patent Office with a solution. In essence it involved a mechanism that could determine that an overflow had occurred (indicated by the most extreme left hand dial going from 0 to 9). When this occurred the mechanism advanced the carriage one place and added the subtracted number back one time, thus setting the machine up for the next partial division to take place. [^US Patent 809075, Filed by Alexander Rechnitzer of Viennea, US Patent Office, 29 June 1901, granted 2 January 1906, page 9, clauses 80-110.^]

to:

A much sought after goal for calculator designers was to develop a method which would completely automatically carry out division. All the previous arithmometers required a process of "long division" where the divisor was subtracted until no more subtractions were possible. However, this required the operator to either guess when this point had been reached, or subtract one time too many (creating an "overflow") and then reversing the subtraction to get the correct outcome. A race had been on to try to solve this particular problem, and in 1901 Alexander Rechnitzer filed a patent in the US Patent Office with a solution. In essence it involved a mechanism that could determine that an overflow had occurred (indicated by the most extreme left hand dial going from 0 to 9). When this occurred the mechanism advanced the carriage one place and added the subtracted number back one time, thus setting the machine up for the next partial division to take place.[^US Patent 809075, Filed by Alexander Rechnitzer of Viennea, US Patent Office, 29 June 1901, granted 2 January 1906, page 9, clauses 80-110.^]

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In 1906 Christel Haman founded the Mercedes-Euklid company who adopted the rack mechanism. In 1910 he incorporated the mechanism patented by Alexander Rechnitzer, referred to earlier, which enabled his machine to automatically perform the process of division, thus becoming the first mass produced machine with this capacity. The fully working Mercedes-Euklid 29 ~~(below, left) and a demonstration Mercedes-Euklid (model 29 from 1934, below right)~~ can be seen below.

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In 1906 Christel Haman founded the Mercedes-Euklid company who adopted the rack mechanism. In 1910 he incorporated the mechanism patented by Alexander Rechnitzer, referred to earlier, which enabled his machine to automatically perform the process of division, thus becoming the first mass produced machine with this capacity. The fully working Mercedes-Euklid 29 can be seen below (left) and a demonstration Mercedes-Euklid (model 29 from 1934) can be seen below (right).

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A much sought after goal for calculator designers was to develop a method which would completely automatically carry out division. All the previous arithmometers required a process of "long division" where the divisor was subtracted until no more subtractions were possible. However, this required the operator to either guess when this point had been reached, or subtract one time too many (creating an "overflow") and then reversing the subtraction to get the correct outcome. In the third machine above, a method was developed which allowed the machine to anticipate when this point had been reached, and advance the carriage. The a MADAS arithmometer was developed by Erwin Janz and manufactured by Egli in Zurich, starting in 1913. ~~The acronym MADAS was short for “Multiplication, Addition, Division - Automatically, Substraction”~~). ~~As already noted this machine achieved~~ an entirely automatic division process - the first ever for an arithmometer style calculator. In this collection there is a MADAS IX Maxima calculator (produced in 1917), an ambitious machine also in that it could accept 9 digits, up to one thousand million, as input and could display 16 digits (representing numbers up to ten thousand trillion) in its results register. Two MADAS models were produced and by 1920 about 1,000 were being produced with some 7,000 having been sold from countries as wide apart as Europe and Australia.[^Martin Reese, Hamburg, //55 erfolgreiche Jahre: MADAS-Rechenautomaten aus der Schweiz 1913 - 1968//, http://www.rechnerlexikon.de/files/MADAS—8-2010.pdf, viewed 18 February 2012.^]

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A much sought after goal for calculator designers was to develop a method which would completely automatically carry out division. All the previous arithmometers required a process of "long division" where the divisor was subtracted until no more subtractions were possible. However, this required the operator to either guess when this point had been reached, or subtract one time too many (creating an "overflow") and then reversing the subtraction to get the correct outcome. A race had been on to try to solve this particular problem, and in 1901 Alexander Rechnitzer filed a patent in the US Patent Office with a solution. In essence it involved a mechanism that could determine that an overflow had occurred (indicated by the most extreme left hand dial going from 0 to 9). When this occurred the mechanism advanced the carriage one place and added the subtracted number back one time, thus setting the machine up for the next partial division to take place. [^US Patent 809075, Filed by Alexander Rechnitzer of Viennea, US Patent Office, 29 June 1901, granted 2 January 1906, page 9, clauses 80-110.^]

The above principle was incorporated into a MADAS arithmometer, developed by Erwin Janz and manufactured by Egli in Zurich, starting in 1913. The acronym MADAS was short for “Multiplication, Addition, Division - Automatically, Substraction”). The achievement of an entirely automatic division process - the first ever for an arithmometer style calculator. In this collection there is a MADAS IX Maxima calculator (produced in 1917), an ambitious machine also in that it could accept 9 digits, up to one thousand million, as input and could display 16 digits (representing numbers up to ten thousand trillion) in its results register. Two MADAS models were produced and by 1920 about 1,000 were being produced with some 7,000 having been sold from countries as wide apart as Europe and Australia.[^Martin Reese, Hamburg, //55 erfolgreiche Jahre: MADAS-Rechenautomaten aus der Schweiz 1913 - 1968//, http://www.rechnerlexikon.de/files/MADAS—8-2010.pdf, viewed 18 February 2012.^]

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In 1906 Christel Haman founded the Mercedes-Euklid company who adopted the rack mechanism. ~~With it, after considerable development, he was able to create a machine that could automatically perform the process of division.~~ The fully working Mercedes-Euklid 29 (below, left) and a demonstration Mercedes-Euklid (model 29 from 1934, below right) can be seen below.

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In 1906 Christel Haman founded the Mercedes-Euklid company who adopted the rack mechanism. In 1910 he incorporated the mechanism patented by Alexander Rechnitzer, referred to earlier, which enabled his machine to automatically perform the process of division, thus becoming the first mass produced machine with this capacity. The fully working Mercedes-Euklid 29 (below, left) and a demonstration Mercedes-Euklid (model 29 from 1934, below right) can be seen below.

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~~This required a process of guessing each partial product and then trying it out,~~ the ~~result being subtracted from the dividend~~ to give a remainder, exactly as is done in pen and paper long division. a race had been on to try to solve this particular problem, and as mentioned earlier, in both the MADAS arithmometer and Mercedes-Euklid rack calculator, a solution had been found so that once an overflow occurred (indicated by the most extreme left hand dial going from 0 to 9) the mechanism advanced the carriage one place and turned the extreme dial back from 9 to 0 thus setting the machine up for the next partial division to take place. This approach had been patented by Alexander Rechnitzer in 1902[^See also US Patent 809075, Filed by Alexander Rechnitzer of Viennea, US Patent Office, 29 June 1901, granted 2 January 1906, page 9, clauses 80-110.^] and had made its appearance first in the Mercedes-Euklid in 1910.[^//Origins of Cyberspace//, p. 242.^]

Thus the MADAS calculator, first produced in manual form, could first sense overflow and advance the carriage automatically one place at a time as division and multiplication were carried out. With progressive further modifications, including the insertion of an electric motor, the MADAS became the highly effective electric mechanical calculating machine whose use continued right into the 1960s.

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As already mentioned, both the MADAS arithmometer (and Mercedes-Euklid rack calculator) had utilised the invention by Rechnitzer to allow an overflow to be sensed and addressed by the mechanism so that division could be carried out fully automatically. With progressive further modifications, including the insertion of an electric motor, the MADAS became the highly effective electric mechanical calculating machine whose use continued right into the 1960s.

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This required a process of guessing each partial product and then trying it out, the result being subtracted from the dividend to give a remainder, exactly as is done in pen and paper long division. a race had been on to try to solve this particular problem, and as mentioned earlier, in both the MADAS arithmometer and Mercedes-Euklid rack calculator, a solution had been found so that ~~the mechanism could indicate that~~ the ~~next subtraction would produce an overflow, alerting the operator~~ to ~~cease turning~~ the ~~crank, and advancing~~ the carriage one place ~~for~~ the ~~next partial division to take place. The mechanism that they used~~ for ~~this had been patented by Alexander Rechnitzer in 1902~~ and had made its appearance first in the Mercedes-Euklid in 1910.[^//Origins of Cyberspace//, p. 242.^]

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This required a process of guessing each partial product and then trying it out, the result being subtracted from the dividend to give a remainder, exactly as is done in pen and paper long division. a race had been on to try to solve this particular problem, and as mentioned earlier, in both the MADAS arithmometer and Mercedes-Euklid rack calculator, a solution had been found so that once an overflow occurred (indicated by the most extreme left hand dial going from 0 to 9) the mechanism advanced the carriage one place and turned the extreme dial back from 9 to 0 thus setting the machine up for the next partial division to take place. This approach had been patented by Alexander Rechnitzer in 1902[^See also US Patent 809075, Filed by Alexander Rechnitzer of Viennea, US Patent Office, 29 June 1901, granted 2 January 1906, page 9, clauses 80-110.^] and had made its appearance first in the Mercedes-Euklid in 1910.[^//Origins of Cyberspace//, p. 242.^]

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Felt first demonstrated this famously with a model constructed in a wooden macaroni box in 1885. He patented his design in 1887 and began selling it from his manufacturing company in Chicago. In 1890 he gave it the name "the Comptometer" and energetically promoted it. Below is the Comptometer in this collections - an example from 1896 of the first model, cased in wood, and one of the 40 oldest known to still be in existence. Remarkably with a drop of oil on the springs it still works perfectly.

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Felt first demonstrated this famously with a model constructed in a wooden macaroni box in 1885. He patented his design in 1887 and began selling it from his manufacturing company in Chicago. In 1890 he gave it the name "the Comptometer" and energetically promoted it.[^//Origins of Cyberspace, p. 244.^] Below is the Comptometer in this collections - an example from 1896 of the first model, cased in wood, and one of the 40 oldest known to still be in existence. Remarkably with a drop of oil on the springs it still works perfectly.

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*something else that can be moved (for example, although it was barely used,[^An exception is the ingenious MONIAC hydraulic computer used to demonstrate macroeconomic theory. See for example, Anna Corkhill ‘A superb explanatory device’ //University of Melbourne Collections//, issue 10, June 2012^] the height of columns of water).

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*something else that can be moved (for example, although it was barely used,[^An exception is the ingenious MONIAC hydraulic computer used to demonstrate macroeconomic theory. See for example, Anna Corkhill ‘A superb explanatory device’ //University of Melbourne Collections//, issue 10, June 2012^] the height of columns of water).

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A further approach to the problem of the four functions is found in the American invention by Felt, of a device that he called the comptometer and patented in 1887. It performs the task of addition by a system of keys and levers. ~~Notably no crank handle needs to be turned in order~~ to ~~perform the addition. And the process of multiplication is done by multiple presses of the number. As already mentioned, in this collections one of the first models of the comptomoter - from 1896,~~ cased in wood, and one of the 40 oldest known to still be in existence. Remarkably with a drop of oil on the springs it still works perfectly.

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A further approach to the problem of the four functions is found in the American invention by Felt, of a device that he called the comptometer and patented in 1887. It performs the task of addition by a system of keys and levers. The keys press down rods which from key 1 to key 9 increase incrementally in length for each successive key. This difference in displacement, magnified by a lever turns an accumulating gear through 1 to 9 teeth as appropriate.

Notably no crank handle is needed. The small force required for the addition comes simply from the key press. The process of multiplication is done by multiple presses of the appropriate key. This is fast, not the least because with two hands up to ten keys can be pressed at once. But subtraction must be carried out by addition of complementary numbers. Carrying of “tens” is implemented between the accumulating read-out wheels.

Felt first demonstrated this famously with a model constructed in a wooden macaroni box in 1885. He patented his design in 1887 and began selling it from his manufacturing company in Chicago. In 1890 he gave it the name "the Comptometer" and energetically promoted it. Below is the Comptometer in this collections - an example from 1896 of the first model, cased in wood, and one of the 40 oldest known to still be in existence. Remarkably with a drop of oil on the springs it still works perfectly.

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Addition of a number automatically occurs whenever a corresponding key is pressed. This is fast. But subtraction must be carried out by addition of complementary numbers. Carrying of “tens” must be done by addition. The comptometer was a highly successful innovation and was sufficiently cheap and useful to reach a broad market. Characterised by extremely effective marketing and capable of being mass produced the device continued to be marketed for some 80 years unusually for such innovations leaving its inventor extremely wealthy. By then its essential mechanism was being utilised by more than one company. Shown below is the remaining comptometer in this collection, this time made of plastic in the 1950s by the British Bell Punch company. Also shown is a demonstration model showing the keys and lever system used in the Bell Punch machine.

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The comptometer was a highly successful innovation and was sufficiently cheap and useful to reach a broad market. Characterised by extremely effective marketing and capable of being mass produced the device continued to be marketed for some 80 years unusually for such innovations leaving its inventor extremely wealthy. By then its essential mechanism was being utilised by more than one company. Shown below is the remaining comptometer in this collection, this time made of plastic in the 1950s by the British Bell Punch company. Also shown is a demonstration model showing the keys and lever system used in the Bell Punch machine.

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The Pascaline and Moreland's inventions may have served their inventors in range of ways, but it was not in finding a broad market. The learning required to use it was to great, and the benefit to little in relation to existing technique. As noted earlier, even the arithmometer remained on the edge of this balance. Adding and subtracting could be quickly achieved, but then it was very expensive and not necessarily any faster than doing the job on paper. The appeal thus remained quitelimited, not only because of the economic price to be paid (which was high), but also the cost of acquiring the necessary embodied skill to render them genuinely superior to existing customary practice.

What goes for the Thomas arithmometer, in this sense, goes ~~also~~ for ~~every calculational technology~~, ~~from counting on one's fingers, to the use of calculi~~ on ~~a counting board~~, ~~or calculating with the abacus, the Pascaline, the Millionaire~~, ~~logarithms, the MADAS most sophisticated mechanical calculator. Indeed even~~ the HP-35 and HP-45 required a facility to do arithmetic backwards from the usual by its reliance on a method known as Reverse Polish. Thus for each technological development, whether Troncet or Omega, for it to find successful users each needed to be understood, and not only intellectually, but equally importantly, the potential users needed to be able to incorporate it into their embodied capacity, with each required gesture becoming so automatic as to require no or little thought.

In the above sense the history of calculation technology can be characterised not so much as the progress of mechanical invention, as it is sometimes presented, but as a more subtle evolving relationship between mind, body and material artefacts or put another way as interaction of of evolving technology, history, culture, mental skills, social capacities and aspirations. The search for a successful innovation was a strange mix of finding a place where these aspects converged to make the innovation seem useful, and at the same time not only economically but also culturally accessible. The requirement to change was not just set in the machine, but also in the humans who made up the society. And the final conquest of the ~~electronic calculator occurred when literacy, design, familiarity, cost and perceived need coincided to sweep all else before it~~.

~~One might ask if there is any lesson in this for the future. Clearly the technology of calculation is now passing not only the first~~ but ~~even the second vanishing point where it converges~~ and ~~merges with other electronic devices which themselves have become so much part of the habitude of daily life~~, ~~especially in the developed world, that their presence is sinking into the invisibility of the routine environment. But in doing so much of habit had~~ to ~~be relearned, and in the consequence human thinking, as well as collective culture has transformed. At a time when we are challenged to make enormous changes to~~ the ~~way we live over~~ the ~~next few decades, in order to have some hope~~ of ~~maintaining an acceptable physical environment for this and future generations, we~~ need to ~~recognise the extent to which that will require reshaping our attitudes, hidden assumptions and habitual ways~~ of living. In seeking to make those changes, we might reflect on the simpler long history of how humans have learned to calculate, and what that means for the learning and innovation that is now demanded of us.

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The Pascaline and Moreland's inventions may have served their inventors in range of ways, but it was not in finding a broad market. The learning required to use it was to great, and the benefit to little in relation to existing technique. As noted earlier, even Thomas de Colmar's arithmometer and its early successors remained on the edge of this balance. Adding and subtracting could be quickly achieved, but then it was very expensive and not necessarily any faster than doing the job on paper. The appeal thus remained quite limited, not only because of the economic price to be paid (which was high), but also the cost of acquiring the necessary embodied skill to render them genuinely superior to existing customary practice.

What goes for the Thomas arithmometer, in this sense, goes also for every calculational technology, from counting on one's fingers, to the use of calculi on a counting board, or calculating with the abacus, the Pascaline, the Millionaire, logarithms, the MADAS most sophisticated mechanical calculator. Indeed even the HP-35 and HP-45 required a facility to do arithmetic backwards from the usual by its reliance on a method known as Reverse Polish. Thus for each technological development, whether Troncet or Omega, for it to find successful users each needed to be understood, and not only intellectually, but equally importantly, the potential users needed to be able to incorporate it into their embodied capacity, with each required gesture becoming so automatic as to require no or little thought.

The achievement of the late mechanical calculators (such as the MADAS and the Euklid-Mercedes) was that they did greatly simplify what what needed to be learned by their operators to achieve efficiently all four arithmetic operations but they did so still at considerable economic cost. The Comptometer was really best for addition and (with practice) subtraction. With its key input it was fast, and its simple design was amenable to cheaper construction and mass-production. So it found a different and expanded market in the rapidly expanding commercial and government organisations of the C20. It has been said and is probably true that its inventors and promoters, Felt and Tarrant, were probably the first people in the world to become truly wealthy from the invention, production and sale of calculators.

In the above sense the history of calculation technology can be characterised not so much as the progress of mechanical invention, as it is sometimes presented, but as a more subtle evolving relationship between mind, body and material artefacts or put another way as interaction of of evolving technology, history, culture, mental skills, social capacities and aspirations. The search for a successful innovation was a strange mix of finding a place where these aspects converged to make the innovation seem useful, and at the same time not only economically but also culturally accessible. The requirement to change was not just set in the machine, but also in the humans who made up the society.

The final conquest of the electronic calculator occurred when literacy, design, familiarity, cost and perceived need coincided to sweep all else before it. Never had the market been more prevalent in the negotiation of daily life. Science and technology now dominated every corner of the developed world and was making rapid inroads elsewhere. Literacy was at its highest in the developed world with arithmetic education now a requirement for every child in the extended period of compulsory schooling. Money promised to free time and technology was now widely accepted as being the answer to drudgery. Further still, there was a social acceptance of life-long change, and an emerging concept of the desirability of 'life-long learning'. The new consumer calculators were increasingly cheap, required little knowledge to use, displaced the mental effort of recall of multiplication tables and mental and written arithmetic. Printers attached to them produced now permanent records. And the whole increasingly seamlessly fitted a world which would soon be interconnected through computers and telecommunications into an ever more pervasive communications web. Calculators had not only reached a desired end. They also had found their moment when that end was widely required.

One might ask if there is any lesson in this for the future. Clearly the technology of calculation is now passing not only the first but perhaps even towards the second vanishing point where it converges and merges with other electronic devices which themselves have become so much part of the habitude of daily life, especially in the developed world, that their presence is sinking into the invisibility of the routine environment. But in doing so much of habit had to be relearned, and in the consequence human thinking, as well as collective culture has transformed.

This is happening at a time at a time when we are challenged to make the enormous changes to the way we live over the next few decades required by the transition to a low carbon economy. This is increasingly widely understood to be necessary if humans are to have some hope of maintaining an acceptable physical environment for this and future generations. The story of innovation in calculators tells us that whilst the time may be ripe for us to accept a great deal of change, it will require re-learning to be comfortable with the many innovations that will be needed to achieve it. Getting there will require require people to reshape attitudes, hidden assumptions and habitual ways of living. In seeking to make those changes, we might reflect on the many challenges overcome in the simpler long history of how humans have learned to calculate, and what that means for the learning and innovation that will now be required.

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It was in July 1972, that the old ways for scientists and citizen alike were definitively undermined. In that month, to some astonishment, the Hewlett Packard company produced the HP-35 electronic 'pocket' calculator. It was an extraordinary leap forward, equipped not only with a red lit showing smooth performance of the arithmetic functions but also reciprocals, powers, square roots, logarithms and anti-logarithms (base e and 10), the trigonometric functions, pi, and a system of registers which enabled chain operations without having to write down intermediate results. For those of a technical orientation who could afford it, all else was now as obsolete as gaslight. Hewlett Packard followed quickly with the HP-45 appearing in the following year with a configurable display, more functions and registers, a variety of constants, and a more compact shape, more suited for the male shirt top pocket. A year later in 1974 the HP-65 was launched with all that could be done by the HP-45 but with the added feature of being user-programmable through a small built in magnetic strip reader. With that the diminutive HP calculator had taken a huge step towards the first mass-marketed personal computers (the TRS-80 ~~launched by Tandy and the Apple-II launched by Apple both~~ in 1977).

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It was in July 1972, that the old ways for scientists and citizen alike were definitively undermined. In that month, to some astonishment, the Hewlett Packard company produced the HP-35 electronic 'pocket' calculator. It was an extraordinary leap forward, equipped not only with a red lit showing smooth performance of the arithmetic functions but also reciprocals, powers, square roots, logarithms and anti-logarithms (base e and 10), the trigonometric functions, pi, and a system of registers which enabled chain operations without having to write down intermediate results. For those of a technical orientation who could afford it, all else was now as obsolete as gaslight. Hewlett Packard followed quickly with the HP-45 appearing in the following year with a configurable display, more functions and registers, a variety of constants, and a more compact shape, more suited for the male shirt top pocket. A year later in 1974 the HP-65 was launched with all that could be done by the HP-45 but with the added feature of being user-programmable through a small built in magnetic strip reader. With that the diminutive HP calculator had taken a huge step towards the first mass-marketed personal computers (the TRS-80 - the author wrote his second book on one of these in 1981 - launched by Tandy, and the Apple-II by Apple, both launched in 1977).

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The ~~obvious~~ reason for collecting is the banal one of consumerism - the desire to collect and own things of rarity, and of course the thrill of the chase in finding, identifying and acquiring them. ~~No-one who collects can credibly claim~~ to be immune to this somewhat base motivation. However, it is additionally possible for the objects to convey insight. There is a story of innovation told in them. It raises multiple questions, not just why at some ~~particular moment these were invented~~, ~~but also what was it that at a~~ particular ~~time allowed~~ some, but far from all to become a success in terms of being taken up in use. In particular why did some get established in actual and widespread use, and what limited much more sharply the success of others? Whilst it could not be claimed that all the answers can be found here, some useful observations may be suggested.

In relation to this, there is an important consideration in relation to ~~innovations. An encounter with these devices suggests that that it is not possible to fully understand them~~ without actually using them. A trip to, say, one of the great technology museums (for example, CNAM in Paris) will tell you how limited the experience is of, for example, seeing a Pascaline, or reading an essay about it. It is a very different experience to try to calculate with one. This leads to a rather interesting connection between understanding these technologies retrospectively, and the reasons that led to their development in the first place. For the success of that development depended on whether people learned to use them. In short this is a history not only of mechanism but of learning how it can be used.

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The reason for collecting is the banal one of consumerism - the desire to collect and own things of rarity, and of course the thrill of the chase in finding, identifying and acquiring them. But beyond that it is possible for the objects to convey insight. There are stories of innovation embodied in them raising multiple questions. These include not just why at some particular moment these were invented, but also what was it that at a particular time allowed some, but far from all, to be taken up in use. In particular why did some get established in actual and widespread use, and what limited much more sharply the success of others? Whilst it could not be claimed that all the answers can be found here, some useful observations may be suggested.

First there is the more detailed story of mechanical evolution. This has been gestured at here but perhaps enough has been said to indicate that many good ideas have waited around for their moment to be realised rather than simply the whole being driven by discovery. Much could have happened after Schickard and Pascal, but it took centuries for the various devices to become widely useful. Of course, as discussed, the device of Schickard had a potential audience in the restricted group of natural philosophers (in particular astronomers) with whom he communicated. Pascal found his machine more used as a curiosity amongst the aristocracy adding prestige, than in the operation of adding money which was its inspiration.

In relation to this, there is an important consideration in relation to innovations. An encounter with these devices suggests that that it is not possible to fully understand them, including their limitations and potential, without actually using them. A trip to, say, one of the great technology museums (for example, CNAM in Paris) will tell you how limited the experience is of, for example, seeing a Pascaline, or reading an essay about it. It is a very different experience to try to calculate with one. This leads to a rather interesting connection between understanding these technologies retrospectively, and the reasons that led to their development in the first place. For the success of that development depended on whether people learned to use them. In short this is a history not only of mechanism but of learning how it can be used.

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~~It is reasonable to wonder what if anything can be drawn from all this.~~ ~~The first thing of course is that this account is built around a collection of historical objects. So it is reasonable to ask why collect them? What does that achieve?~~ ~~After all there~~ are ~~plenty of photographs of these objects in books, journal articles and on the web.~~ The technologies are well described elsewhere in much more mechanically detailed websites. So why the collection?

There are of ~~course more than one reasons why one might collect. The obvious ones are to do with consumerism~~ - the desire to collect and own things of rarity. There is of course a broader attraction. This is after all a story of innovation - that is what allowed some inventions to have significant success in becoming established in actual and widespread use, and what limited much more sharply the success of others? Whilst it could not be claimed that all ~~the answers can be found here, perhaps~~ some useful observations may be suggested.

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One feature of this account is it is built around a collection of historical objects. It is reasonable to ask why collect them? Why not just build it based on the great diversity of photographs of these objects in books, journal articles and on the web. The technologies are well described elsewhere in much more mechanically detailed websites. So why bring in the collection?

The obvious reason for collecting is the banal one of consumerism - the desire to collect and own things of rarity, and of course the thrill of the chase in finding, identifying and acquiring them. No-one who collects can credibly claim to be immune to this somewhat base motivation. However, it is additionally possible for the objects to convey insight. There is a story of innovation told in them. It raises multiple questions, not just why at some particular moment these were invented, but also what was it that at a particular time allowed some, but far from all to become a success in terms of being taken up in use. In particular why did some get established in actual and widespread use, and what limited much more sharply the success of others? Whilst it could not be claimed that all the answers can be found here, some useful observations may be suggested.

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~~Above we can see to~~ the ~~left the motor, now coupled to~~ the ~~characteristic step drums of an arithmometer,~~ with the carry mechanism above. This puts paid to any simple story of the linear development of innovation in the calculator. Here the most modern device of the motor is being coupled to the longest serving commercial system of an arithmometer.

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In the left lower corner of the above can be seen the motor, now coupled to the characteristic step drums of an arithmometer (bottom center and right), with the carry mechanism above. This puts paid to any simple story of the linear development of innovation in the calculator. Here the most modern device of the motor is being coupled to the longest serving commercial system of an arithmometer.

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It was in July 1972, that the old ways for scientists and citizen alike were definitively undermined. In that month, to some astonishment, the Hewlett Packard company produced the HP-35 electronic 'pocket' calculator. It was an extraordinary leap forward, equipped not only with a red lit showing smooth performance of the arithmetic functions but also reciprocals, powers, square roots, logarithms and anti-logarithms (base e and 10), the trigonometric functions, pi, and a system of registers which enabled chain operations without having to write down intermediate results. For those of a technical orientation who could afford it, all else was now as obsolete as gaslight. ~~Other models by Hewlett Packard followed quickly with~~ the ~~HP-45 appearing in the following year with~~ more functions and registers, a variety of constants, and a more compact shape, more suited for the male shirt top pocket.

to:

It was in July 1972, that the old ways for scientists and citizen alike were definitively undermined. In that month, to some astonishment, the Hewlett Packard company produced the HP-35 electronic 'pocket' calculator. It was an extraordinary leap forward, equipped not only with a red lit showing smooth performance of the arithmetic functions but also reciprocals, powers, square roots, logarithms and anti-logarithms (base e and 10), the trigonometric functions, pi, and a system of registers which enabled chain operations without having to write down intermediate results. For those of a technical orientation who could afford it, all else was now as obsolete as gaslight. Hewlett Packard followed quickly with the HP-45 appearing in the following year with a configurable display, more functions and registers, a variety of constants, and a more compact shape, more suited for the male shirt top pocket. A year later in 1974 the HP-65 was launched with all that could be done by the HP-45 but with the added feature of being user-programmable through a small built in magnetic strip reader. With that the diminutive HP calculator had taken a huge step towards the first mass-marketed personal computers (the TRS-80 launched by Tandy and the Apple-II launched by Apple both in 1977).

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~~This was what might be called the "First Vanishing Point" -~~ the ~~point at which all~~ the ~~arithmetic operations and common scientific functions required for calculation became available in a single small electronic calculator, capable of being carried on a belt or in~~ a ~~shirt pocket (albeit~~ in ~~serious peril of it falling out when one bent over to pick something up). Electronic calculators now proliferated throughout the developed and developing world displacing~~ the ~~rigours of mental arithmetic and caught in an 'arms race' to make them smaller, more powerful, easier~~ to ~~use, and find a niche in a highly competitive~~ and ~~very cluttered market. What might be labelled the "Second Vanishing Point" - the point at which these~~ electronic ~~calculators began to disappear, displaced now by "virtual calculators" encoded in~~ the ~~software of desk and lap-top computers, tablets, smart phones, and much else was perhaps in sight but not yet arrived. But from that vantage point,~~ ~~even the stand-alone electronic calculators, might begin to follow their mechanical predecessors of two decades before as they fade~~ into the misty light of receding memory.

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The launch of the HP-35 marks what might be called the "First Vanishing Point" - the point at which all the arithmetic operations and common scientific functions required for calculation became available in a single small electronic calculator, capable of being carried on a belt or in a shirt pocket (albeit in serious peril of it falling out when one bent over to pick something up). Electronic calculators now proliferated throughout the developed and developing world displacing the rigours of mental arithmetic and caught in an 'arms race' to make them smaller, more powerful, easier to use, and find a niche in a highly competitive and very cluttered market.

Forty years later, in 2012, electronic solid state calculators could be found in their billions across the world. By then what might be labelled the "Second Vanishing Point" - the point at which these electronic calculators began to disappear, displaced now by "virtual calculators" encoded in the software of desk and lap-top computers, tablets, smart phones, and much else was perhaps in sight but not yet arrived. But from that vantage point, even the stand-alone electronic calculators, might begin to follow their mechanical predecessors of two decades before as they faded into the misty light of receding memory.

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It was in July 1972, that the old ways for scientists and citizen alike were definitively undermined. In that month, to some astonishment, the Hewlett Packard company produced the HP-35 electronic 'pocket' calculator. It was an extraordinary leap forward, equipped not only with a red lit showing smooth performance of the arithmetic functions but also reciprocals, powers, square roots, logarithms and anti-logarithms (base e and 10), the trigonometric functions, pi, and a system of registers which enabled chain operations without having to write down intermediate results. For those of a technical orientation who could afford it, all else was now as obsolete as gaslight. Other models by Hewlett Packard followed quickly with the HP-45 appearing in

to:

It was in July 1972, that the old ways for scientists and citizen alike were definitively undermined. In that month, to some astonishment, the Hewlett Packard company produced the HP-35 electronic 'pocket' calculator. It was an extraordinary leap forward, equipped not only with a red lit showing smooth performance of the arithmetic functions but also reciprocals, powers, square roots, logarithms and anti-logarithms (base e and 10), the trigonometric functions, pi, and a system of registers which enabled chain operations without having to write down intermediate results. For those of a technical orientation who could afford it, all else was now as obsolete as gaslight. Other models by Hewlett Packard followed quickly with the HP-45 appearing in the following year with more functions and registers, a variety of constants, and a more compact shape, more suited for the male shirt top pocket.

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This was what might be called the "First Vanishing Point" - the point at which all the arithmetic operations and common scientific functions required for calculation became available in a single small electronic calculator, capable of being carried on a belt or in a shirt pocket (albeit in serious peril of it falling out when one bent over to pick something up). Electronic calculators now proliferated throughout the developed and developing world displacing the rigours of mental arithmetic and caught in an 'arms race' to make them smaller, more powerful, easier to use, and find a niche in a highly competitive and very cluttered market. ~~It would~~ be ~~another two decades before what might be labelled the "Second Vanishing Point" - the point at which these electronic~~ calculators ~~began to disappear, displaced now by "virtual calculators" encoded in the software of desk and lap-top computers, tablets, smart phones, and much else~~. ~~From~~ that vantage point, ~~not only~~ the ~~mechanical~~ calculators ~~of only 20 years before, but even the stand-alone electronic calculator, were already fading~~ into the misty light of receding memory.

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This was what might be called the "First Vanishing Point" - the point at which all the arithmetic operations and common scientific functions required for calculation became available in a single small electronic calculator, capable of being carried on a belt or in a shirt pocket (albeit in serious peril of it falling out when one bent over to pick something up). Electronic calculators now proliferated throughout the developed and developing world displacing the rigours of mental arithmetic and caught in an 'arms race' to make them smaller, more powerful, easier to use, and find a niche in a highly competitive and very cluttered market. What might be labelled the "Second Vanishing Point" - the point at which these electronic calculators began to disappear, displaced now by "virtual calculators" encoded in the software of desk and lap-top computers, tablets, smart phones, and much else was perhaps in sight but not yet arrived. But from that vantage point, even the stand-alone electronic calculators, might begin to follow their mechanical predecessors of two decades before as they fade into the misty light of receding memory.

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!!!The Vanishing point: electronics and the arrival of the HP35

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!!!The Vanishing point: solid state electronics and the arrival of the HP35

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Electricity could be utilised in appliances once it was available through an electricity grid. In the US, the first electrical supply was in 1882 for lighting, with 85 customers. Electrification spread over subsequent decades, primarily in the big cities through private power companies in the first two decades of the C20. In 1926 in the UK separate electricity grids began to be connected into a national grid. It was not surprising therefore that this period of the early C20 was conducive to the introduction of electric motors to many purposes, including adding machines.

to:

Electricity could be utilised in appliances once it was available through an electricity grid. In the US, the first electrical supply was in 1882 for lighting, with 85 customers. Electrification spread over subsequent decades, primarily in the big cities through private power companies in the first two decades of the C20. In 1926 in the UK separate electricity grids began to be connected into a national grid. It was not surprising therefore that this period of the early C20 was conducive to the introduction of electric motors to many purposes, including adding machines.

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~~Variety~~ of ~~electronic desk calculators from the ANITA on. But these could not replace~~ the portable slide rules and other mathematical aids that were still in use in parallel with the large mechanical desktop calculators that these electronic machines began to replace. It was in July 1972 however, that the old ways for scientists and citizen alike were definitively undermined. In that month, to some astonishment, the Hewlett Packard company produced the HP-35 electronic 'pocket' calculator. It was an extraordinary leap forward, equipped not only with a red lit showing smooth performance of the arithmetic functions but also reciprocals, powers, square roots, logarithms and anti-logarithms (base e and 10), the trigonometric functions, pi, and a system of registers which enabled chain operations without having to write down intermediate results. ~~For those of a technical orientation who could afford it, all else was gaslight.~~

to:

Another means of performing arithmetic had largely been neglected for calculators although it had already been employed in the enormous computers that had developed from earlier work by Babbage and Scheutz (who devised remarkably complex special purpose "difference engines" for calculating logarithms), and then later work by Turing and others giving rise to the electronic computing machines developed in the second world war for decoding. The electronic version initially used valves to control on/off electric circuits each representing a single binary digit (or bit). 1 was represented by 1, two by 10, three by 11 and so on. It has been recognised since Leibniz that arithmetic could be done with these (since they represented numbers). Indeed - the method is in retrospect obvious. 10 + 01 = 11. 11+01 = 100, etc.

Utilising switches it was therefore possible to build a very efficient calculating machine. Valves were too bulky, energy consuming, and unreliable for a consumer device but prior sales of mechanical calculators had by now established a massive potential market. The invention of the transistor in 1947 at Bell Telephone labs, based on the quantum properties of crystals, laid the way for "solid state" electric switches at tiny scale, able to be turned on and off by one another. Light emitting diodes (LEDs) - another solid state device which emitted light when electrons forced into a higher energy ("excited") state fell back to their stable energy - began to appear as practical output devices in 1962.

The first calculators to use solid-state electronics in desktop form were the ANITA VII and VIII calculators launched simultaneously in 1961, too early to use LEDs, and using instead vacuum tube displays. A variety of desktop four function calculators followed. But these could not replace the portable slide rules and other mathematical aids that were still in use in parallel with the large mechanical desktop calculators that these electronic machines began to replace.

It was in July 1972, that the old ways for scientists and citizen alike were definitively undermined. In that month, to some astonishment, the Hewlett Packard company produced the HP-35 electronic 'pocket' calculator. It was an extraordinary leap forward, equipped not only with a red lit showing smooth performance of the arithmetic functions but also reciprocals, powers, square roots, logarithms and anti-logarithms (base e and 10), the trigonometric functions, pi, and a system of registers which enabled chain operations without having to write down intermediate results. For those of a technical orientation who could afford it, all else was now as obsolete as gaslight. Other models by Hewlett Packard followed quickly with the HP-45 appearing in

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This required a process of guessing each partial product and then trying it out, the result being subtracted from the dividend to give a remainder, exactly as is done in pen and paper long division. a race had been on to try to solve this particular problem, and as mentioned earlier, in both the MADAS arithmometer and Mercedes-Euklid rack calculator, a solution had been found so that the mechanism could indicate that the next subtraction would produce an overflow, alerting the operator to cease turning the crank, and advancing the carriage one place for the next partial division to take place.

to:

This required a process of guessing each partial product and then trying it out, the result being subtracted from the dividend to give a remainder, exactly as is done in pen and paper long division. a race had been on to try to solve this particular problem, and as mentioned earlier, in both the MADAS arithmometer and Mercedes-Euklid rack calculator, a solution had been found so that the mechanism could indicate that the next subtraction would produce an overflow, alerting the operator to cease turning the crank, and advancing the carriage one place for the next partial division to take place. The mechanism that they used for this had been patented by Alexander Rechnitzer in 1902 and had made its appearance first in the Mercedes-Euklid in 1910.[^//Origins of Cyberspace//, p. 242.^]

Thus the MADAS calculator, first produced in manual form, could first sense overflow and advance the carriage automatically one place at a time as division and multiplication were carried out. With progressive further modifications, including the insertion of an electric motor, the MADAS became the highly effective electric mechanical calculating machine whose use continued right into the 1960s.

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~~Thus the~~ MADAS calculator, first produced in manual form, could first sense overflow and advance the carriage automatically one place at a time as division and multiplication were carried out. With progressive further modifications, including the ~~insertion~~ of ~~an electric motor, the MADAS became~~ the highly effective electric mechanical calculating machine whose use continued right into the 1960s. The late MADAS 20BTG calculator which is part of this collection represents a classic exemplar of the late stages of this evolutionary development. Its mechanism was also adopted in its essentials, then with many innovations (but with less of the Swiss robust construction of the Madas), in the US Frieden calculators. As it turned out, this final class of machines represented the pinacle of achievement in motorised mechanical calculation.

to:

The late MADAS 20BTG calculator, seen above, which is part of this collection represents a classic exemplar of the late stages of this evolutionary development. Now fully utilising an electric motor it could fluently perform all the operations of arithmetic, complete with automatic clearing and moving the carriage entirely automatically as necessary. It and could also be further automated to extract square roots. Its mechanism was also adopted in its essentials, then with many innovations (but with less of the Swiss robust construction of the Madas), in the US Frieden calculators. As it turned out, this final class of machines represented the pinacle of achievement in motorised mechanical calculation.

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This required a process of guessing each partial product and then trying it out, the result being subtracted from the dividend to give a remainder, exactly as is done in pen and paper long division.

to:

This required a process of guessing each partial product and then trying it out, the result being subtracted from the dividend to give a remainder, exactly as is done in pen and paper long division. a race had been on to try to solve this particular problem, and as mentioned earlier, in both the MADAS arithmometer and Mercedes-Euklid rack calculator, a solution had been found so that the mechanism could indicate that the next subtraction would produce an overflow, alerting the operator to cease turning the crank, and advancing the carriage one place for the next partial division to take place.

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H.W. Egli now approached the chain of innovation to mechanise this process, but only by abandonning the sophistication of the Millionaire and like Haman returning to the principles of the arithmometer. The result was the MADAS calculator, first produced in manual form, which could advance the carriage automatically one place at a time as division and multiplication were carried out. With progressive further modifications, including the insertion of an electric motor, the MADAS became the highly effective electric mechanical calculating machine whose use continued right into the 1960s. The late MADAS 20BTG calculator which is part of this collection represents a classic exemplar of the late stages of this evolutionary development. Its mechanism was also adopted in its essentials, then with many innovations (but with less of the Swiss robust construction of the Madas), in the US Frieden calculators. As it turned out, this final class of machines represented the pinacle of achievement in motorised mechanical calculation.

to:

Thus the MADAS calculator, first produced in manual form, could first sense overflow and advance the carriage automatically one place at a time as division and multiplication were carried out. With progressive further modifications, including the insertion of an electric motor, the MADAS became the highly effective electric mechanical calculating machine whose use continued right into the 1960s. The late MADAS 20BTG calculator which is part of this collection represents a classic exemplar of the late stages of this evolutionary development. Its mechanism was also adopted in its essentials, then with many innovations (but with less of the Swiss robust construction of the Madas), in the US Frieden calculators. As it turned out, this final class of machines represented the pinacle of achievement in motorised mechanical calculation.

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~~In this collection there is an arithmometer~~ branded by Samuel Hertzstark from 1929, although by then he was not making machines. It is actually a Badenia (manufactured by the German Company Math. Bauerle in the Black Forest) which Hertzstark was by then re-badging (not long before he died).

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Below is an arithmometer in this collection branded by Samuel Hertzstark from 1929, although by then he was not making machines. It is actually a Badenia (manufactured by the German Company Math. Bauerle in the Black Forest) which Hertzstark was by then re-badging (not long before he died).

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This calculator features its original electric motor, still in good working order, and with a keyboard instead of sliders for input. The features of it were not only that it had a keyboard for input, but also a control mechanism consisting of a column of keys which enabled a number to be entered and then added through 0 to 8 repeats representing multiplication by one to nine.

to:

This calculator features its original electric motor, still in good working order, and with a keyboard instead of sliders for input. The features of it were not only that it had a keyboard for input, but also a control mechanism consisting of a column of keys which enabled a number to be entered and then added through 0 to 8 repeats representing multiplication by one to nine. A view of the mechanism of this machine is shown below.

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~~Whilst the above was an obvious innovation,~~ the ~~clumsiest approach in all~~ the ~~calculating devices - from the first~~ arithmometer ~~through to~~ the ~~Millionaire was division, which could only be done by a process along~~ the ~~lines~~ of ~~that done~~ in ~~long division~~. ~~That is,~~ the ~~number to be divided (~~the ~~dividend)~~ is ~~considered sequentially from~~ the ~~highest power of ten, and thus decomposed into a series of partial products of~~ the ~~successive parts of~~ the ~~dividend with the divisor. This required a process of guessing each partial product and then trying it out, the result being subtracted from~~ the ~~dividend to give a remainder, exactly as~~ is ~~done in pen and paper long division~~.

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Above we can see to the left the motor, now coupled to the characteristic step drums of an arithmometer, with the carry mechanism above. This puts paid to any simple story of the linear development of innovation in the calculator. Here the most modern device of the motor is being coupled to the longest serving commercial system of an arithmometer.

Whilst the above was an obvious innovation, the clumsiest approach in all the calculating devices - from the first arithmometer through to the Millionaire was division, which could only be done by a process along the lines of that done in long division. That is, the number to be divided (the dividend) is considered sequentially from the highest power of ten, and thus decomposed into a series of partial products of the successive parts of the dividend with the divisor.

In the Millionaire the outcome for each partial product could be achieved by setting the correct number in the divisor with the selector. In the Herzstark arithmometer a key column to the far right (black keys, barely visible) allowed the operator to set an addition or subtraction to repeat up to 9 times giving the same effect as with the Millionaire. Thus, although Egli and Co. did fit a motor to their Millionaire, once a motor was available with this rudimentary control mechanism, the advantage posed by the complex and heavy mechanism of the Millionaire was largely lost.

This required a process of guessing each partial product and then trying it out, the result being subtracted from the dividend to give a remainder, exactly as is done in pen and paper long division.

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%center% ~1929 “Herzstark” electric Calculating Machine serial 6549\\badged by Herzstark, Vienna\\(essentially a Badenia Model TE 13 Duplex)\\

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%center% ~1929: “Herzstark” electric Calculating Machine serial 6549\\badged by Herzstark, Vienna\\(essentially a Badenia Model TE 13 Duplex)\\

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%center% %height=250px% [[Site.Herzstark Electric Mechanism|http://meta-studies.net/pmwiki/uploads/HerzstarkMech.jpg]]
%center% 1950s-1960s: Underneath view of the Herzstark mechanism\\- note the stepped drums
%center% (collection Calculant)

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The Millionaire calculating machine combines the idea of the physical embodiment of multiplication tables with that of the proportional rack. It is able to interrogate a multiplication table represented by metal rods, and in a single crank of the handle multiplies the multiplicand by a number set between 1 and 9 then advancing its internal carriage one place ready for the next multiplier to be set and applied. Thus, for example, to multiply 4689 x 2568 an arithmometer or pinwheel would take 21 cranks of the handle (8+6+5+2) whereas the Millionaire could achieve the same outcome with only four cranks of the handle.

~~Manufactured by H.W. Egli, some 4,655~~ of these were sold between 1895 and 1935[^//Origins of Cyberspace// p. 242.^] at a 1912 price of about US$480[^Price list in Edmonds Collins, //The Millionaire Calculating Machine//, pamphlet, Edmond Collins, ~~35 Dearborn St, Central Chicago, ~1912. See also price of US$500 at 1914 prices given by Luc de Brabandere cited in B~~.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, published in //Slide Rule and Calculation monographs//, Slide Rule Circle, UK, 2002, pp. 59-98.^] (about $11,700 in 2013 US dollars[^Calculated using the [[http://www.measuringworth.com]] calculator on 24 July 2013^]). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,[^Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant).^] and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

to:

The Millionaire calculating machine combines the idea of the physical embodiment of multiplication tables with that of the proportional rack. It is able to interrogate a multiplication table represented by metal rods, and in a single crank of the handle multiplies the multiplicand by a number set between 1 and 9 then advancing its internal carriage one place ready for the next multiplier to be set and applied. Thus, for example, to multiply 4689 x 2568 an arithmometer or pinwheel would take 21 cranks of the handle (8+6+5+2) whereas the Millionaire could achieve the same outcome with only four cranks of the handle. In the lid was a set of tables of factors to assist division, a brush to keep the machine clean, and a special bolt so when being transported the carriage was held clamped in place, since if the machine were dropped the carriage was heavy enough to punch through the end of the case.

Added lines 271-273:

Manufactured by H.W. Egli, some 4,655 Millionaires were sold between 1895 and 1935[^//Origins of Cyberspace// p. 242.^] at a 1912 price of about US$480[^Price list in Edmonds Collins, //The Millionaire Calculating Machine//, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. See also price of US$500 at 1914 prices given by Luc de Brabandere cited in B.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, published in //Slide Rule and Calculation monographs//, Slide Rule Circle, UK, 2002, pp. 59-98.^] (about $11,700 in 2013 US dollars[^Calculated using the [[http://www.measuringworth.com]] calculator on 24 July 2013^]). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,[^Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant).^] and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones. The machine still operates reliably after more than 100 years.

The Millionaire was reliable, but heavy (37 kg or 81 pounds) and expensive. It could produce an answer to 20 significant figures (100 billion billion). It came in various configurations, including with a keyboard mounted on top to drive the sliders. Its value to the user depended on whether long multiplications and divisions were central to the work to be done. Styled in a rugged 'no nonsense' industrial design it was adopted by scientists who swore by it, railway and telegraph companies, government treasuries, and other technically oriented companies and agencies.

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One helpful development in design was the development of a proportional rack which moved cogs through a series of increments depending on the length of a toothed rack with which they engaged. Shown below is the rack mechanism of such a calculator. Note how successive racks have moved increasing distances as the crank handle is turned (creating the diagonal pattern). ~~Different numbered keys could engage their accumulating gear with the corresponding rack to turn the gear the necessary number~~ of ~~times~~. ~~Keys in different columns of~~ a ~~keyboard could all engage with~~ the ~~racks at the same time adding~~ to ~~the respective accumulating disks.~~

to:

One helpful development in design was the development of a proportional rack which moved cogs through a series of increments depending on the length of a toothed rack with which they engaged. Shown below is the rack mechanism of such a calculator. Note how successive racks have moved increasing distances as the crank handle is turned (creating the diagonal pattern). The loose cogs seen on the square section axle are an example of the nine such cogs under each column of keys. Normally lying between the racks when a key is depressed it moves the corresponding cog sideways on the axle to engage with the appropriate rack for the number of the key depressed.

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Variety of electronic desk calculators from the ANITA on. But these could not replace the portable slide rules and other mathematical aids that were still in use in parallel with the large mechanical desktop calculators that these electronic machines began to replace. It was in July 1972 however, that the old ways for scientists and citizen alike were definitively undermined. In that month

to:

Variety of electronic desk calculators from the ANITA on. But these could not replace the portable slide rules and other mathematical aids that were still in use in parallel with the large mechanical desktop calculators that these electronic machines began to replace. It was in July 1972 however, that the old ways for scientists and citizen alike were definitively undermined. In that month, to some astonishment, the Hewlett Packard company produced the HP-35 electronic 'pocket' calculator. It was an extraordinary leap forward, equipped not only with a red lit showing smooth performance of the arithmetic functions but also reciprocals, powers, square roots, logarithms and anti-logarithms (base e and 10), the trigonometric functions, pi, and a system of registers which enabled chain operations without having to write down intermediate results. For those of a technical orientation who could afford it, all else was gaslight.

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Electricity could be utilised ~~once there was a national~~ grid....

to:

Electricity could be utilised in appliances once it was available through an electricity grid. In the US, the first electrical supply was in 1882 for lighting, with 85 customers. Electrification spread over subsequent decades, primarily in the big cities through private power companies in the first two decades of the C20. In 1926 in the UK separate electricity grids began to be connected into a national grid. It was not surprising therefore that this period of the early C20 was conducive to the introduction of electric motors to many purposes, including adding machines.

24 July 2013 by 58.6.237.118 -

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Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480[^Price list in Edmonds Collins, //The Millionaire Calculating Machine//, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. See also price of US$500 at 1914 prices given by Luc de Brabandere cited in B.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, published in //Slide Rule and Calculation monographs//, Slide Rule Circle, UK, 2002, pp. 59-98.^] (about $11,700 in 2013 US dollars[^Calculated using the [[http://www.measuringworth.com]] calculator on 24 July 2013^]). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,[^Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant).^] and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

to:

Manufactured by H.W. Egli, some 4,655 of these were sold between 1895 and 1935[^//Origins of Cyberspace// p. 242.^] at a 1912 price of about US$480[^Price list in Edmonds Collins, //The Millionaire Calculating Machine//, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. See also price of US$500 at 1914 prices given by Luc de Brabandere cited in B.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, published in //Slide Rule and Calculation monographs//, Slide Rule Circle, UK, 2002, pp. 59-98.^] (about $11,700 in 2013 US dollars[^Calculated using the [[http://www.measuringworth.com]] calculator on 24 July 2013^]). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,[^Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant).^] and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

24 July 2013 by 58.6.237.118 -

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Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480[^~~Letter from H.W. Egli Ltd~~, Zurich, dated 20 November 1967 (collection Calculant). See also price of US$500 at 1914 prices given by Luc de Brabandere cited in B.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, ~~published in //Slide Rule and Calculation monographs//~~, ~~Slide Rule Circle, UK, 2002, pp. 59-98.^] (about $11~~,~~700 in 2013 US dollars[~~^~~Calculated using the~~ [[http://www.measuringworth.com]] calculator on 24 July 2013^]).~~[^Price list in Edmonds Collins, //The Millionaire Calculating Machine//, pamphlet, Edmond Collins, 35 Dearborn St~~, ~~Central Chicago, ~1912~~.~~^] The Millionaire calculating machine in this collection was manufactured on 16 October 1912,~~ and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

to:

Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480[^Price list in Edmonds Collins, //The Millionaire Calculating Machine//, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. See also price of US$500 at 1914 prices given by Luc de Brabandere cited in B.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, published in //Slide Rule and Calculation monographs//, Slide Rule Circle, UK, 2002, pp. 59-98.^] (about $11,700 in 2013 US dollars[^Calculated using the [[http://www.measuringworth.com]] calculator on 24 July 2013^]). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,[^Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant).^] and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

24 July 2013 by 58.6.237.118 -

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Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480[^Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant)~~^][^see~~ also price of US$500 at 1914 prices given by Luc de Brabandere cited in B.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, published in //Slide Rule and Calculation monographs//, Slide Rule Circle, UK, 2002, pp. 59-98.^] (about $11,700 in 2013 US dollars[^Calculated using the [[http://www.measuringworth.com]] calculator on 24 July 2013^]).[^Price list in Edmonds Collins, //The Millionaire Calculating Machine//, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912.^] The Millionaire calculating machine in this collection was manufactured on 16 October 1912, and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

to:

Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480[^Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant). See also price of US$500 at 1914 prices given by Luc de Brabandere cited in B.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, published in //Slide Rule and Calculation monographs//, Slide Rule Circle, UK, 2002, pp. 59-98.^] (about $11,700 in 2013 US dollars[^Calculated using the [[http://www.measuringworth.com]] calculator on 24 July 2013^]).[^Price list in Edmonds Collins, //The Millionaire Calculating Machine//, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912.^] The Millionaire calculating machine in this collection was manufactured on 16 October 1912, and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

24 July 2013 by 58.6.237.118 -

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Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480 ~~(about $11,700 in 2013 US$ [^Calculated using the~~ [~~[http://www.measuringworth.com]] calculator on 24 July 2013^]).[^Price list in Edmonds Collins, //The Millionaire Calculating Machine//, pamphlet, Edmond Collins~~, ~~35 Dearborn St, Central Chicago, ~1912.^] The Millionaire calculating machine in this collection was manufactured on 16 October 1912~~,~~[^Letter from H~~.~~W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant)^][^see also price of US$500 at 1914 prices given by Luc de Brabandere cited in B.O.B. Williams~~,~~" Check Figures—A Once Ubiquitous Tool for Book-keepers, published in //Slide Rule and Calculation monographs//, Slide Rule Circle, UK, 2002, pp. 59-98.^]~~ and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

to:

Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480[^Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant)^][^see also price of US$500 at 1914 prices given by Luc de Brabandere cited in B.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, published in //Slide Rule and Calculation monographs//, Slide Rule Circle, UK, 2002, pp. 59-98.^] (about $11,700 in 2013 US dollars[^Calculated using the [[http://www.measuringworth.com]] calculator on 24 July 2013^]).[^Price list in Edmonds Collins, //The Millionaire Calculating Machine//, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912.^] The Millionaire calculating machine in this collection was manufactured on 16 October 1912, and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

24 July 2013 by 58.6.237.118 -

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Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480 (about $11,700 in 2013 US$[^Calculated using the [[http://www.measuringworth.com]] calculator on 24 July 2013^]).[^Price list in Edmonds Collins, //The Millionaire Calculating Machine//, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912.^] The Millionaire calculating machine in this collection was manufactured on 16 October 1912,[^Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant)^][^see also price of US$500 at 1914 prices given by Luc de Brabandere cited in B.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, published in //Slide Rule and Calculation monographs//, Slide Rule Circle, UK, 2002, pp. 59-98.^] and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

to:

Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480 (about $11,700 in 2013 US$ [^Calculated using the [[http://www.measuringworth.com]] calculator on 24 July 2013^]).[^Price list in Edmonds Collins, //The Millionaire Calculating Machine//, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912.^] The Millionaire calculating machine in this collection was manufactured on 16 October 1912,[^Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant)^][^see also price of US$500 at 1914 prices given by Luc de Brabandere cited in B.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, published in //Slide Rule and Calculation monographs//, Slide Rule Circle, UK, 2002, pp. 59-98.^] and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

24 July 2013 by 58.6.237.118 -

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Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480~~.[^Edmonds Collins, //The Millionaire Calculating Machine//, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912.~~^] ~~The Millionaire calculating machine in this collection was manufactured on 16 October 1912~~,~~[^Letter from H~~.~~W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant)^][^see also price of US$500 at 1914 prices (about $11~~,~~700 in 2013 US$[Calculated using the~~ [~~[http://www.measuringworth.com]] calculator on 24 July 2013)~~ given by Luc de Brabandere cited in B.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, published in //Slide Rule and Calculation monographs//, Slide Rule Circle, UK, 2002, pp. 59-98.^] and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

to:

Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480 (about $11,700 in 2013 US$[^Calculated using the [[http://www.measuringworth.com]] calculator on 24 July 2013^]).[^Price list in Edmonds Collins, //The Millionaire Calculating Machine//, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912.^] The Millionaire calculating machine in this collection was manufactured on 16 October 1912,[^Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant)^][^see also price of US$500 at 1914 prices given by Luc de Brabandere cited in B.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, published in //Slide Rule and Calculation monographs//, Slide Rule Circle, UK, 2002, pp. 59-98.^] and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

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Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480.[^Edmonds Collins, //The Millionaire Calculating Machine//, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912.^] The Millionaire calculating machine in this collection was manufactured on 16 October 1912,[^Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant)^][^see also price of US$500 at 1914 prices given by Luc de Brabandere cited in B.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, published in //Slide Rule and Calculation monographs//, Slide Rule Circle, UK, 2002, pp. 59-98.^] and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

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Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480.[^Edmonds Collins, //The Millionaire Calculating Machine//, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912.^] The Millionaire calculating machine in this collection was manufactured on 16 October 1912,[^Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant)^][^see also price of US$500 at 1914 prices (about $11,700 in 2013 US$[Calculated using the [[http://www.measuringworth.com]] calculator on 24 July 2013) given by Luc de Brabandere cited in B.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, published in //Slide Rule and Calculation monographs//, Slide Rule Circle, UK, 2002, pp. 59-98.^] and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

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~~Scheutz and Babbage - difference engines~~

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A further approach to the problem of the four functions is found in the American invention by Felt, of a device that he called the comptometer and patented in 1887. It performs the task of addition by a system of keys and levers. Notably no crank handle needs to be turned in order to perform the addition. And the process of multiplication is done by multiple presses of the number. As already mentioned, in this ~~collection we have one of the first models of the comptomoter - one from 1896 cased in wood? and one of the 40 oldest known to still be in existence,~~

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A further approach to the problem of the four functions is found in the American invention by Felt, of a device that he called the comptometer and patented in 1887. It performs the task of addition by a system of keys and levers. Notably no crank handle needs to be turned in order to perform the addition. And the process of multiplication is done by multiple presses of the number. As already mentioned, in this collections one of the first models of the comptomoter - from 1896, cased in wood, and one of the 40 oldest known to still be in existence. Remarkably with a drop of oil on the springs it still works perfectly.

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Similar principles were however utilised by Otto Steiger ~~who~~ patented a rather more practical “Millionaire calculating machine” which had a simple enough mechanism to enable production on a commercial scale.

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Similar principles were however utilised by Otto Steiger in Switzerland who in 1895 patented a rather more practical “Millionaire calculating machine” which had a simple enough mechanism to enable production on a commercial scale.

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The Millionaire calculating machine combines the idea of the physical embodiment of multiplication tables with that of the proportional rack. It is able to interrogate a multiplication table represented by metal rods, and in a single crank of the handle multiplies the multiplicand by a number set between 1 and 9 then advancing its internal carriage one place ready for the next multiplier to be set and applied. ~~Manufactured by H.W. Egli~~, ~~some 4,655 of these were sold. The Millionaire calculating machine in this collection is from 1912, and~~ is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

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The Millionaire calculating machine combines the idea of the physical embodiment of multiplication tables with that of the proportional rack. It is able to interrogate a multiplication table represented by metal rods, and in a single crank of the handle multiplies the multiplicand by a number set between 1 and 9 then advancing its internal carriage one place ready for the next multiplier to be set and applied. Thus, for example, to multiply 4689 x 2568 an arithmometer or pinwheel would take 21 cranks of the handle (8+6+5+2) whereas the Millionaire could achieve the same outcome with only four cranks of the handle.

Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480.[^Edmonds Collins, //The Millionaire Calculating Machine//, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912.^] The Millionaire calculating machine in this collection was manufactured on 16 October 1912,[^Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant)^][^see also price of US$500 at 1914 prices given by Luc de Brabandere cited in B.O.B. Williams," Check Figures—A Once Ubiquitous Tool for Book-keepers, published in //Slide Rule and Calculation monographs//, Slide Rule Circle, UK, 2002, pp. 59-98.^] and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

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The deck of the Millionaire in this collection is shown below with the selector on the right which picks the multiplying factor, and the selector on the right which sets it for addition, subtraction, multiplication and division. The ten sliders are obvious, as are the result windows, and on the far right, the crank handle.

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The deck of the Millionaire in this collection is shown below with the selector on the right which picks the multiplying factor, and the selector on the right which sets it for addition, subtraction, multiplication and division (AMDS). The ten sliders for setting the number to be operated on are obvious, as are the result windows, and on the far right, the crank handle.

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%center% %height=~~200px~~% [[Site.Millionaire1912|http://meta-studies.net/pmwiki/uploads/MillionaireDeck.jpg]]

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%center% %height=230px% [[Site.Millionaire1912|http://meta-studies.net/pmwiki/uploads/MillionaireDeck.jpg]]

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%center% %height=200px% [[Site.~~MillionaireDeck~~|http://meta-studies.net/pmwiki/uploads/MillionaireDeck.jpg]]

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%center% %height=200px% [[Site.Millionaire1912|http://meta-studies.net/pmwiki/uploads/MillionaireDeck.jpg]]

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The deck of the Millionaire in this collection is shown below with the selector on the right which picks the multiplying factor, and the selector on the right which sets it for addition, subtraction, multiplication and division. The ten sliders are obvious, as are the result windows.

%center% %height=300px% [[Site.MillionaireDeck|http://meta-studies.net/pmwiki/uploads/MillionaireDeck.jpg]]

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The deck of the Millionaire in this collection is shown below with the selector on the right which picks the multiplying factor, and the selector on the right which sets it for addition, subtraction, multiplication and division. The ten sliders are obvious, as are the result windows, and on the far right, the crank handle.

%center% %height=200px% [[Site.MillionaireDeck|http://meta-studies.net/pmwiki/uploads/MillionaireDeck.jpg]]

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~~%center% %height=300px% [[Site~~.~~MillionaireDeck|http://meta-studies~~.~~net/pmwiki/uploads/MillionaireDeck~~.~~png~~]]

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The Millionaire calculating machine combines the idea of the physical embodiment of multiplication tables with that of the proportional rack. It is able to interrogate a multiplication table represented by metal rods, and in a single crank of the handle multiplies the multiplicand by a number set between 1 and 9 then advancing its internal carriage one place ready for the next multiplier to be set and applied. Manufactured by H.W. Egli, some 4,655 of these were sold. The Millionaire calculating machine in this collection is from 1912, and is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

The deck of the Millionaire in this collection is shown below with the selector on the right which picks the multiplying factor, and the selector on the right which sets it for addition, subtraction, multiplication and division. The ten sliders are obvious, as are the result windows.

%center% %height=300px% [[Site.MillionaireDeck|http://meta-studies.net/pmwiki/uploads/MillionaireDeck.jpg]]

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The Millionaire calculating machine combines the idea of the physical embodiment of multiplication tables with that of the proportional rack. It is able to interrogate a multiplication table represented by metal rods, and in a single crank of the handle multiplies the multiplicand by a number set between 1 and 9 then advancing its internal carriage one place ready for the next multiplier to be set and applied. Manufactured by H.W. Egli, some 4,655 of these were sold. The Millionaire calculating machine in this collection is from 1912, and is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

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%center% %height=300px% [[Site.MillionaireDeck|http://meta-studies.net/pmwiki/uploads/~~Millionair~~.png]]

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%center% %height=300px% [[Site.MillionaireDeck|http://meta-studies.net/pmwiki/uploads/MillionaireDeck.png]]

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%center% %height=300px% [[Site.MillionaireDeck|http://meta-studies.net/pmwiki/uploads/Millionair.png]]
%center% Deck of the Millionaire Calculating Machine\\
%center% (collection Calculant)

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!To be continued
**This essay is under construction - especially what follows. If it is ever finished (:-) it is intended to utilise this collection to shape a continuing if idiosyncratic story of the development of embodied calculation up to the introduction of personal electronic calculation. So do visit again if you have got this far, and there may (should) be more.**

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There were of course many variations on this theme. These included the "Frieden Wheel" which managed to achieve the same effect as the ~~pin wheel~~ but through simply a nicely timed use of a cam. More of that sort of mechanical detail for all the machines referred to here can be found in the classic book by Martin,[^Martin, //The Calculating Machines//^] and the marvellous websites of Rechnerlexikon[^[[http://www.rechnerlexikon.de/en/artikel/Spezial:Allpages]]^] and John Wolff[^[[http://home.vicnet.net.au/~wolff/calculators/]]^].

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There were of course many variations on this theme. These included the "Frieden Wheel" which managed to achieve the same effect as the pinwheel but through simply a nicely timed use of a cam. More of that sort of mechanical detail for all the machines referred to here can be found in the classic book by Martin,[^Martin, //The Calculating Machines//^] and the marvellous websites of Rechnerlexikon[^[[http://www.rechnerlexikon.de/en/artikel/Spezial:Allpages]]^] and John Wolff[^[[http://home.vicnet.net.au/~wolff/calculators/]]^].

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There were of course many variations on this theme. These included the "Frieden Wheel" which managed to achieve the same effect as the pin wheel but through simply a nicely timed use of a cam. More of that sort of detail for all the machines referred to here can be found in the classic book by Martin,[^Martin, //The Calculating Machines//^] and the marvellous websites of Rechnerlexikon[^[[http://www.rechnerlexikon.de/en/artikel/Spezial:Allpages]]^] and John Wolff[^[[http://home.vicnet.net.au/~wolff/calculators/]]^].

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There were of course many variations on this theme. These included the "Frieden Wheel" which managed to achieve the same effect as the pin wheel but through simply a nicely timed use of a cam. More of that sort of mechanical detail for all the machines referred to here can be found in the classic book by Martin,[^Martin, //The Calculating Machines//^] and the marvellous websites of Rechnerlexikon[^[[http://www.rechnerlexikon.de/en/artikel/Spezial:Allpages]]^] and John Wolff[^[[http://home.vicnet.net.au/~wolff/calculators/]]^].

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this is a broad brush description of the various mechanisms. Many variations. Eg Frieden's cam timed "Frieden wheel". Described very well elsewhere - eg Martin, Rechnerlexicon and Wolff.

See http://ieeexplore.ieee.org.ezp.lib.unimelb.edu.au/stamp/stamp.jsp?tp=&arnumber=4637514

Kidwell - 'Yours for Improvement" IEEE

Martin

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There were of course many variations on this theme. These included the "Frieden Wheel" which managed to achieve the same effect as the pin wheel but through simply a nicely timed use of a cam. More of that sort of detail for all the machines referred to here can be found in the classic book by Martin,[^Martin, //The Calculating Machines//^] and the marvellous websites of Rechnerlexikon[^[[http://www.rechnerlexikon.de/en/artikel/Spezial:Allpages]]^] and John Wolff[^[[http://home.vicnet.net.au/~wolff/calculators/]]^].

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One helpful development in design was the development of a proportional rack which moved cogs through a series of increments depending on the length of a toothed rack with which they engaged. ~~Different lengths thus represented different numbers to be added~~.

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One helpful development in design was the development of a proportional rack which moved cogs through a series of increments depending on the length of a toothed rack with which they engaged. Shown below is the rack mechanism of such a calculator. Note how successive racks have moved increasing distances as the crank handle is turned (creating the diagonal pattern). Different numbered keys could engage their accumulating gear with the corresponding rack to turn the gear the necessary number of times. Keys in different columns of a keyboard could all engage with the racks at the same time adding to the respective accumulating disks.

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~~In 1906 Christel Haman founded the~~ Mercedes-Euklid ~~company who adopted this principle to create a machine that after a process of development eventually could automate the process of division. There is both~~ a ~~demonstration Mercedes-Euklid (model 29 from 1934) and then a~~ fully working Mercedes-Euklid 29 ~~in this collection~~.

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%center% Rack mechanism of a Mercedes-Euklid 29 calculator.\\(collection Calculant)

In 1906 Christel Haman founded the Mercedes-Euklid company who adopted the rack mechanism. With it, after considerable development, he was able to create a machine that could automatically perform the process of division. The fully working Mercedes-Euklid 29 (below, left) and a demonstration Mercedes-Euklid (model 29 from 1934, below right) can be seen below.

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One helpful development in design was the development of a proportional rack which moved cogs through a series of increments depending on the length of a toothed rack with which they engaged. Different lengths thus represented different numbers to be added. In 1906 Christel Haman founded the Mercedes-Euklid company who adopted this principle to create a machine that after a process of development eventually could automate the process of division. There is both a demonstration Mercedes-Euklid (model 29 from 1934) and then a fully working Mercedes-Euklid 29 in this collection.

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One helpful development in design was the development of a proportional rack which moved cogs through a series of increments depending on the length of a toothed rack with which they engaged. Different lengths thus represented different numbers to be added.

%center% %height=200px%[[Site.DemonstrationPinwheel|http://meta-studies.net/pmwiki/uploads/Misc/RackMech.jpg]]

In 1906 Christel Haman founded the Mercedes-Euklid company who adopted this principle to create a machine that after a process of development eventually could automate the process of division. There is both a demonstration Mercedes-Euklid (model 29 from 1934) and then a fully working Mercedes-Euklid 29 in this collection.

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In the above sense the history of calculation technology is not the steady progress of mechanical invention, as it is not infrequently presented, but a more subtle evolving relationship between mind, body and material artefacts in the context of evolving history, culture, and mental capacities and aspirations. The search for a successful innovation was a strange mix of finding a place where these aspects converged to make the innovation seem useful, and at the same time not only economically but also culturally accessible. The requirement to change was not just set in the machine, but also in the humans who made up the society. And the final conquest of the electronic calculator occurred when literacy, design, familiarity, cost and perceived need coincided to sweep all else before it.

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In the above sense the history of calculation technology can be characterised not so much as the progress of mechanical invention, as it is sometimes presented, but as a more subtle evolving relationship between mind, body and material artefacts or put another way as interaction of of evolving technology, history, culture, mental skills, social capacities and aspirations. The search for a successful innovation was a strange mix of finding a place where these aspects converged to make the innovation seem useful, and at the same time not only economically but also culturally accessible. The requirement to change was not just set in the machine, but also in the humans who made up the society. And the final conquest of the electronic calculator occurred when literacy, design, familiarity, cost and perceived need coincided to sweep all else before it.

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There are of course more than one reasons why one might collect. The obvious ones are to do with consumerism - the desire to collect and own things of rarity. ~~But there~~ is~~, in this case,~~ a ~~further consideration~~. ~~That~~ is that it is not possible to fully understand these objects without actually using them. A trip to, say, one of the great technology museums (for example, CNAM in Paris) will tell you how limited the experience is of, for example, seeing a Pascaline, or reading an essay about it. It is a very different experience to ~~calculate with one. There is here a rather interesting connection between understanding~~ these ~~technologies retrospectively, and the reasons that led~~ to ~~their development in the first place. In short this is a history not only~~ of mechanism but of learning how to use it.

The point here is that the use of a calculating technology is not just intellectual. It is what Jean-François Gauvin[^Jean-François Gauvin , Habits of Knowledge: Artisans, Savants and Mechanical Devices in Seventeenth-Century French Natural Philosophy, The Department of the History of Science, in partial fulfillment of the requirements for the ~~degree of Doctor of Philosophy~~ in the subject of History of Science, Harvard University, Cambridge, Mass., USA, November 2008, pp. 113. ^] refers to as "gestural". Gestural knowledge is the embodied knowledge that artisans rely on when they execute work of the highest craft skill. The first time someone looks at a Thomas de Colmar arithmometer learning how to add and subtract takes some time, whilst doing division and multiplication on is more challenging. The first time is slow and subject to mistakes. It is only after repeated practice that the ~~gestures required become so practiced that they are quick~~, ~~instinctive and reliable~~. It is only then that the calculation can be seen at what it can be, at its most efficient, and thus it is only with this skill that the technology, in one sense, can be judged. Clearly it was with this sort of practice that the Gentleman's Magazine of 1857 could claim:

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There are of course more than one reasons why one might collect. The obvious ones are to do with consumerism - the desire to collect and own things of rarity. There is of course a broader attraction. This is after all a story of innovation - that is what allowed some inventions to have significant success in becoming established in actual and widespread use, and what limited much more sharply the success of others? Whilst it could not be claimed that all the answers can be found here, perhaps some useful observations may be suggested.

In relation to this, there is an important consideration in relation to innovations. An encounter with these devices suggests that that it is not possible to fully understand them without actually using them. A trip to, say, one of the great technology museums (for example, CNAM in Paris) will tell you how limited the experience is of, for example, seeing a Pascaline, or reading an essay about it. It is a very different experience to try to calculate with one. This leads to a rather interesting connection between understanding these technologies retrospectively, and the reasons that led to their development in the first place. For the success of that development depended on whether people learned to use them. In short this is a history not only of mechanism but of learning how it can be used.

In short, the use of a calculating technology is not just intellectual. It is what Jean-François Gauvin[^Jean-François Gauvin , Habits of Knowledge: Artisans, Savants and Mechanical Devices in Seventeenth-Century French Natural Philosophy, The Department of the History of Science, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of History of Science, Harvard University, Cambridge, Mass., USA, November 2008, pp. 113. ^] refers to as "gestural". Gestural knowledge is the embodied knowledge that artisans rely on when they execute work of the highest craft skill. The first time someone looks at a Thomas de Colmar arithmometer learning how to add and subtract takes some time. Doing division and multiplication is much more challenging, especially if attempted without a good knowledge of how it can be done on paper. The first time is slow and subject to mistakes. It is only after repeated practice that the gestures required become so practiced that they are quick, instinctive and reliable. It is only then that the potential for calculation with such a device can be can be judged. And it would only have been after this sort of practice that one could credit the Gentleman's Magazine of 1857 claim that:

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As mentioned earlier (in [[Site.Part1BeforeTheModernEpoch|Part 1]]), gesture and mind are interconnected. When we 'learn' a gesture, recent neurological research demonstrates that our brains are growing new connections, in a sense rewiring, to accomodate that as what becomes a 'habit'. Therefore, the use of the technology changes our minds. ~~It is not just~~ a ~~question of our~~ minds of building a technology that meets our current capacities.

However, there is a limit to how much we can learn, or would want to learn, in any particular cultural circumstances and that depends in part what we have been able to ~~learn before, what we are prepared~~ to ~~give up in order to get some benefit. The claim in the //Gentleman's Magazine// was~~ that:

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As mentioned earlier (in [[Site.Part1BeforeTheModernEpoch|Part 1]]), gesture and mind are interconnected. When we 'learn' a gesture, recent neurological research demonstrates that our brains are growing new connections, in a sense rewiring, to accomodate that as what becomes a 'habit'. Therefore, the use of the technology changes our minds. So there is a co-evolution between minds and the combination of the technology and what is required to use it successfully (sometimes referred to as 'technique').

The history of the technology has been one of a competition between old habits, preparedness to learn new technique, and perceived need to do so. It is not easy to throw off old successful technique and replace it with the hard acquired new approaches. Part of the success of a technological innovation is thus likely to depend on the extent to which social forces may encourage through benefit, or require through necessity, the new learning required to use it. Most new inventions are of course promoted with claims that the benefits for user or employer will outstrip the costs of change. Not infrequently these benefits might be initially overstated. Thus for the arithmometer the //Gentleman's Magazine// claimed:

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These overblown claims are reminiscent of similar claims for their inventions by Pascal (with this machine the user can do with ease, "without effort of memory" and "without even thinking of it", every possible arithmetic operation[^Pascal, ligé de retenir ou d’emprunter les nombres nécessaires, et combien d’erreurs se glissent dans ces rétentions et emprunts, à mois d’une très longue habitude et, en outre, d’une attention profonde et qui fatigue l’esprit en peu de temps. Cette machine délivre celui qui opère par elle de cette vexation; il suffit qu’il ait le jugement, elle le relève du défaut de la mémoire; et, sans rien retenir ni emprunter, elle fait d’elle-même ce qu’il désire, sans même qu’il y pense.” p. 337^] and Moreland (allowing addition and subtraction "without charging the memory or disturbing the mind[^S. Moreland, //A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence// 1672, title page.^]). They show the hope, that the mental activity could be replaced by the machine. But in reality, for all of these machines it was not just a question of the high cost of obtaining it, but the learning and practice required to use it. ~~As for the Pascaline, the arithmometer remained on the edge~~ of the balance between existing habit based on pen and paper, or jeton and counting board. The appeal of both was quite limited, not only because of the economic price to be paid (which was high), but also the ~~cost~~ of ~~acquiring the necessary embodied skill (which was also not inconsiderable)~~.

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These overblown claims are reminiscent of similar claims for their inventions by Pascal (with this machine the user can do with ease, "without effort of memory" and "without even thinking of it", every possible arithmetic operation[^Pascal, ligé de retenir ou d’emprunter les nombres nécessaires, et combien d’erreurs se glissent dans ces rétentions et emprunts, à mois d’une très longue habitude et, en outre, d’une attention profonde et qui fatigue l’esprit en peu de temps. Cette machine délivre celui qui opère par elle de cette vexation; il suffit qu’il ait le jugement, elle le relève du défaut de la mémoire; et, sans rien retenir ni emprunter, elle fait d’elle-même ce qu’il désire, sans même qu’il y pense.” p. 337^] and Moreland (allowing addition and subtraction "without charging the memory or disturbing the mind[^S. Moreland, //A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence// 1672, title page.^]). They show the hope, that the mental activity could be replaced by the machine. But in reality, for all of these machines it was not just a question of the high cost of obtaining it, but the learning and practice required to use it.

The Pascaline and Moreland's inventions may have served their inventors in range of ways, but it was not in finding a broad market. The learning required to use it was to great, and the benefit to little in relation to existing technique. As noted earlier, even the arithmometer remained on the edge of this balance. Adding and subtracting could be quickly achieved, but then it was very expensive and not necessarily any faster than doing the job on paper. The appeal thus remained quitelimited, not only because of the economic price to be paid (which was high), but also the cost of acquiring the necessary embodied skill to render them genuinely superior to existing customary practice.

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These overblown claims are reminiscent of similar claims for their inventions by Pascal (with this machine the user can do with ease, without ~~even thinking~~ of it, every possible arithmetic operation[^Pascal, ligé de retenir ou d’emprunter les nombres nécessaires, et combien d’erreurs se glissent dans ces rétentions et emprunts, à mois d’une très longue habitude et, ~~en outre,~~ d’une ~~attention profonde~~ et qui fatigue l’esprit en peu de temps. Cette machine délivre celui qui opère par elle de cette vexation; il suffit qu’il ait le jugement, elle le relève du défaut de la mémoire; et, sans rien retenir ni emprunter, ~~elle fait d’elle-même ce qu’il désire~~, sans même qu’il y pense.” p. 337^] and Moreland (allowing addition and subtraction "without charging the memory or disturbing the mind[^S. Moreland, //A New and Most Useful Instrument for Addition and ~~Subtraction of Pounds, Shillings~~ and ~~Pence// 1672, title page.^]) for their calculators.~~ They show the hope, that the mental activity could be replaced by the machine. But in reality, for all of these machines it was not just a question of the high cost of obtaining it, but the learning and practice required to use it. As for the Pascaline, the arithmometer remained on the edge of the balance between existing habit based on pen and paper, or jeton and counting board. The appeal of both was quite limited, not only because of the economic price to be paid (which was high), but also the cost of acquiring the necessary embodied skill (which was also not inconsiderable).

to:

These overblown claims are reminiscent of similar claims for their inventions by Pascal (with this machine the user can do with ease, "without effort of memory" and "without even thinking of it", every possible arithmetic operation[^Pascal, ligé de retenir ou d’emprunter les nombres nécessaires, et combien d’erreurs se glissent dans ces rétentions et emprunts, à mois d’une très longue habitude et, en outre, d’une attention profonde et qui fatigue l’esprit en peu de temps. Cette machine délivre celui qui opère par elle de cette vexation; il suffit qu’il ait le jugement, elle le relève du défaut de la mémoire; et, sans rien retenir ni emprunter, elle fait d’elle-même ce qu’il désire, sans même qu’il y pense.” p. 337^] and Moreland (allowing addition and subtraction "without charging the memory or disturbing the mind[^S. Moreland, //A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence// 1672, title page.^]). They show the hope, that the mental activity could be replaced by the machine. But in reality, for all of these machines it was not just a question of the high cost of obtaining it, but the learning and practice required to use it. As for the Pascaline, the arithmometer remained on the edge of the balance between existing habit based on pen and paper, or jeton and counting board. The appeal of both was quite limited, not only because of the economic price to be paid (which was high), but also the cost of acquiring the necessary embodied skill (which was also not inconsiderable).

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~~The history of calculation technology is thus~~

to:

In the above sense the history of calculation technology is not the steady progress of mechanical invention, as it is not infrequently presented, but a more subtle evolving relationship between mind, body and material artefacts in the context of evolving history, culture, and mental capacities and aspirations. The search for a successful innovation was a strange mix of finding a place where these aspects converged to make the innovation seem useful, and at the same time not only economically but also culturally accessible. The requirement to change was not just set in the machine, but also in the humans who made up the society. And the final conquest of the electronic calculator occurred when literacy, design, familiarity, cost and perceived need coincided to sweep all else before it.

One might ask if there is any lesson in this for the future. Clearly the technology of calculation is now passing not only the first but even the second vanishing point where it converges and merges with other electronic devices which themselves have become so much part of the habitude of daily life, especially in the developed world, that their presence is sinking into the invisibility of the routine environment. But in doing so much of habit had to be relearned, and in the consequence human thinking, as well as collective culture has transformed. At a time when we are challenged to make enormous changes to the way we live over the next few decades, in order to have some hope of maintaining an acceptable physical environment for this and future generations, we need to recognise the extent to which that will require reshaping our attitudes, hidden assumptions and habitual ways of living. In seeking to make those changes, we might reflect on the simpler long history of how humans have learned to calculate, and what that means for the learning and innovation that is now demanded of us.

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What goes for the Thomas arithmometer, in this sense, goes also for every calculational technology, from counting on one's fingers, to the use of calculi on a counting board, or calculating with the abacus, the Pascaline, the Millionaire, logarithms, the MADAS most sophisticated mechanical calculator, the HP-45 electronic calculator, or indeed a spread sheet. Each needs to be understood, and not only intellectually, but equally importantly, it needs to become part of one's embodied capacity, where each required gesture becomes so automatic as to require no or little thought.

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These overblown claims are reminiscent of similar claims for their inventions by Pascal (with this machine the user can do with ease, without even thinking of it, every possible arithmetic operation[^~~^] and Moreland (allowing addition and subtraction "without charging the memory or disturbing the mind[^S. Moreland, //A New and Most Useful Instrument for Addition and Subtraction of Pounds~~, Shillings and Pence// 1672, title page.^]) for their calculators. They show the hope, that the mental activity could be replaced by the machine. But in reality, for all of these machines it was not just a question of the high cost of obtaining it, but the learning and practice required to use it. ~~As for the Pascaline, the arithmometer remained on the edge of~~ the ~~balance between existing habit based on pen~~ and ~~paper, or jeton and counting board. The appeal~~ of ~~both was quite limited~~, ~~not only because of the economic price to be paid (which was high), but also the cost of acquiring~~ the ~~necessary embodied skill (which was also not inconsiderable)~~.

to:

These overblown claims are reminiscent of similar claims for their inventions by Pascal (with this machine the user can do with ease, without even thinking of it, every possible arithmetic operation[^Pascal, ligé de retenir ou d’emprunter les nombres nécessaires, et combien d’erreurs se glissent dans ces rétentions et emprunts, à mois d’une très longue habitude et, en outre, d’une attention profonde et qui fatigue l’esprit en peu de temps. Cette machine délivre celui qui opère par elle de cette vexation; il suffit qu’il ait le jugement, elle le relève du défaut de la mémoire; et, sans rien retenir ni emprunter, elle fait d’elle-même ce qu’il désire, sans même qu’il y pense.” p. 337^] and Moreland (allowing addition and subtraction "without charging the memory or disturbing the mind[^S. Moreland, //A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence// 1672, title page.^]) for their calculators. They show the hope, that the mental activity could be replaced by the machine. But in reality, for all of these machines it was not just a question of the high cost of obtaining it, but the learning and practice required to use it. As for the Pascaline, the arithmometer remained on the edge of the balance between existing habit based on pen and paper, or jeton and counting board. The appeal of both was quite limited, not only because of the economic price to be paid (which was high), but also the cost of acquiring the necessary embodied skill (which was also not inconsiderable).

What goes for the Thomas arithmometer, in this sense, goes also for every calculational technology, from counting on one's fingers, to the use of calculi on a counting board, or calculating with the abacus, the Pascaline, the Millionaire, logarithms, the MADAS most sophisticated mechanical calculator. Indeed even the HP-35 and HP-45 required a facility to do arithmetic backwards from the usual by its reliance on a method known as Reverse Polish. Thus for each technological development, whether Troncet or Omega, for it to find successful users each needed to be understood, and not only intellectually, but equally importantly, the potential users needed to be able to incorporate it into their embodied capacity, with each required gesture becoming so automatic as to require no or little thought.

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These overblown claims are reminiscent of similar claims ~~by Pascal and Moreland~~ for their calculators. They show the hope, that the mental activity could be replaced by the machine. But in reality, for all of these machines it was not just a question of the high cost of obtaining it, but the learning and practice required to use it. As for the Pascaline, the arithmometer remained on the edge of the balance between existing habit based on pen and paper, or jeton and counting board. The appeal of both was quite limited, not only because of the economic price to be paid (which was high), but also the cost of acquiring the necessary embodied skill (which was also not inconsiderable).

to:

These overblown claims are reminiscent of similar claims for their inventions by Pascal (with this machine the user can do with ease, without even thinking of it, every possible arithmetic operation[^^] and Moreland (allowing addition and subtraction "without charging the memory or disturbing the mind[^S. Moreland, //A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence// 1672, title page.^]) for their calculators. They show the hope, that the mental activity could be replaced by the machine. But in reality, for all of these machines it was not just a question of the high cost of obtaining it, but the learning and practice required to use it. As for the Pascaline, the arithmometer remained on the edge of the balance between existing habit based on pen and paper, or jeton and counting board. The appeal of both was quite limited, not only because of the economic price to be paid (which was high), but also the cost of acquiring the necessary embodied skill (which was also not inconsiderable).

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Ohdner began manufacture of his machines in 1886 under the name "Original Ohdner" but sold his rights also to Grimme, Natalis and Co., Braunsweig, who began marketing the machines under the name Brunsviga.[^ibid^] In turn they also licenced agents such as Schuster to sell them. Reflecting a later start these machines were made from a wider range of materials than the arithmometers, including iron and nickel alloys as well as brass and steel. Below is the very early Brunsviga-Schuster pinwheel calculator from 1896 in this collection.

to:

Ohdner began manufacture of his machines in 1886 under the name "Original Ohdner" but sold his rights also to Grimme, Natalis and Co., Braunsweig, who began marketing the machines under the name Brunsviga.[^ibid^] In turn they also licenced agents such as Schuster to sell them. Reflecting a later start these machines were made from a wider range of materials than the arithmometers, including iron and nickel alloys as well as brass and steel. The Brunsviga was a quick success selling 20,000 units between 1892 and 1912.[[^Hook and Norman, //Origins of Cyberspace//, p. 255.^] Below is the very early Brunsviga-Schuster pinwheel calculator from 1896 in this collection.

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->M. Thomas's arithmometer may be used without the least trouble or possibility of error, not only for addition, subtraction, multiplication, and division, but also for much more complex operations, such as the extraction of the square root, involution, the resolution of triangles, etc...A multiplication of eight figures by eight others is made in eighteen seconds; a division of sixteen figures by eight figures, in twenty four seconds; and in one minute and a quarter one can extract the square root of sixteen figures, and also prove the accuracy of the calculation...[^//The Gentleman's Magazine//, Volume 202, "The monthly intelligencer", January 1857 [[http://books.google.fr/books?id=Rf0IAAAAIAAJ&pg=PA100&dq=arithmometer&as_brr=1#v=onepage&q=arithmometer&f=false]], viewed 23 July 2013.^]

to:

->M. Thomas's arithmometer may be used without the least trouble or possibility of error, not only for addition, subtraction, multiplication, and division, but also for much more complex operations, such as the extraction of the square root, involution, the resolution of triangles, etc...A multiplication of eight figures by eight others is made in eighteen seconds; a division of sixteen figures by eight figures, in twenty four seconds; and in one minute and a quarter one can extract the square root of sixteen figures, and also prove the accuracy of the calculation...[^//The Gentleman's Magazine//, Volume 202, "The monthly intelligencer", January 1857, p. 100, [[http://books.google.fr/books?id=Rf0IAAAAIAAJ&pg=PA100&dq=arithmometer&as_brr=1#v=onepage&q=arithmometer&f=false]], viewed 23 July 2013.^]

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However, there is a limit to how much we can learn, or would want to learn, in any particular cultural circumstances~~. The question therefore arises not only as to the~~

to:

However, there is a limit to how much we can learn, or would want to learn, in any particular cultural circumstances and that depends in part what we have been able to learn before, what we are prepared to give up in order to get some benefit. The claim in the //Gentleman's Magazine// was that:

->Instead of simply reproducing man's intelligence the arithmometer relieves that intelligence from the necessity of making the operations. Instead of repeating responses dictated to it, this instrument instantaneously dictates the proper answer to the man who asks it a question. It is not matter producing material effects, but matter which thinks, reflects, reasons, calculates, and executes all the most difficult and complicated arithmetical operations with a rapidity and infallibility which defies all the calculators in the world..... It will soon be considered as indispensable and be as generally used as a clock....[^ibid^]

These overblown claims are reminiscent of similar claims by Pascal and Moreland for their calculators. They show the hope, that the mental activity could be replaced by the machine. But in reality, for all of these machines it was not just a question of the high cost of obtaining it, but the learning and practice required to use it. As for the Pascaline, the arithmometer remained on the edge of the balance between existing habit based on pen and paper, or jeton and counting board. The appeal of both was quite limited, not only because of the economic price to be paid (which was high), but also the cost of acquiring the necessary embodied skill (which was also not inconsiderable).

The history of calculation technology is thus

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->M. Thomas's arithmometer may be used without the least trouble or possibility of error, not only for addition, subtraction, multiplication, and division, but also for much more complex operations, such as the extraction of the square root, involution, the resolution of triangles, etc...A multiplication of eight figures by eight others is made in eighteen seconds; a division of sixteen figures by eight figures, in twenty four seconds; and in one minute and a quarter one can extract the square root of sixteen figures, and also prove the accuracy of the calculation...[^//The Gentleman's Magazine//, 1857.^]

to:

->M. Thomas's arithmometer may be used without the least trouble or possibility of error, not only for addition, subtraction, multiplication, and division, but also for much more complex operations, such as the extraction of the square root, involution, the resolution of triangles, etc...A multiplication of eight figures by eight others is made in eighteen seconds; a division of sixteen figures by eight figures, in twenty four seconds; and in one minute and a quarter one can extract the square root of sixteen figures, and also prove the accuracy of the calculation...[^//The Gentleman's Magazine//, Volume 202, "The monthly intelligencer", January 1857 [[http://books.google.fr/books?id=Rf0IAAAAIAAJ&pg=PA100&dq=arithmometer&as_brr=1#v=onepage&q=arithmometer&f=false]], viewed 23 July 2013.^]

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As mentioned earlier (in [[Site.Part1BeforeTheModernEpoch|Part 1]], gesture and mind are interconnected. When we 'learn' a gesture, recent neurological research demonstrates that our brains are growing new connections, in a sense rewiring, to accomodate that as what becomes a 'habit'. Therefore, the use of the technology changes our minds. It is not just a question of our minds of building a technology that meets our current capacities.

to:

As mentioned earlier (in [[Site.Part1BeforeTheModernEpoch|Part 1]]), gesture and mind are interconnected. When we 'learn' a gesture, recent neurological research demonstrates that our brains are growing new connections, in a sense rewiring, to accomodate that as what becomes a 'habit'. Therefore, the use of the technology changes our minds. It is not just a question of our minds of building a technology that meets our current capacities.

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As mentioned earlier, gesture and mind are interconnected. When we 'learn' a gesture, recent neurological research demonstrates that our brains are growing new connections, in a sense rewiring, to accomodate that as what becomes a 'habit'. Therefore, the use of the technology changes our minds. It is not just a question of our minds of building a technology that meets our current capacities.

to:

As mentioned earlier (in [[Site.Part1BeforeTheModernEpoch|Part 1]], gesture and mind are interconnected. When we 'learn' a gesture, recent neurological research demonstrates that our brains are growing new connections, in a sense rewiring, to accomodate that as what becomes a 'habit'. Therefore, the use of the technology changes our minds. It is not just a question of our minds of building a technology that meets our current capacities.

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What goes for the Thomas arithmometer, in this sense, goes also for every calculational technology, from counting on one's fingers, to the use of calculi on a counting board, or calculating with the abacus, the Pascaline, the Millionaire, logarithms, the MADAS most sophisticated mechanical calculator, the HP-45 electronic calculator, or indeed a spread sheet. Each needs to be understood, and not only intellectually, but equally importantly, it needs to become part of one's embodied capacity, where each required gesture becomes so automatic as to require no or little thought. The question therefore arises not only as to the

to:

What goes for the Thomas arithmometer, in this sense, goes also for every calculational technology, from counting on one's fingers, to the use of calculi on a counting board, or calculating with the abacus, the Pascaline, the Millionaire, logarithms, the MADAS most sophisticated mechanical calculator, the HP-45 electronic calculator, or indeed a spread sheet. Each needs to be understood, and not only intellectually, but equally importantly, it needs to become part of one's embodied capacity, where each required gesture becomes so automatic as to require no or little thought.

As mentioned earlier, gesture and mind are interconnected. When we 'learn' a gesture, recent neurological research demonstrates that our brains are growing new connections, in a sense rewiring, to accomodate that as what becomes a 'habit'. Therefore, the use of the technology changes our minds. It is not just a question of our minds of building a technology that meets our current capacities.

However, there is a limit to how much we can learn, or would want to learn, in any particular cultural circumstances. The question therefore arises not only as to the

23 July 2013 by 58.6.237.118 -

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->M. Thomas's arithmometer may be used without the least trouble or possibility of error, not only for addition, subtraction, multiplication, and division, but also for much more complex operations, such as the extraction of the square root, involution, the resolution of triangles, etc...A multiplication of eight figures by eight others is made in eighteen seconds; a division of sixteen figures by eight figures, in twenty four seconds; and in one minute and a quarter one can extract the square root of sixteen figures, and also prove the accuracy of the calculation...

to:

->M. Thomas's arithmometer may be used without the least trouble or possibility of error, not only for addition, subtraction, multiplication, and division, but also for much more complex operations, such as the extraction of the square root, involution, the resolution of triangles, etc...A multiplication of eight figures by eight others is made in eighteen seconds; a division of sixteen figures by eight figures, in twenty four seconds; and in one minute and a quarter one can extract the square root of sixteen figures, and also prove the accuracy of the calculation...[^//The Gentleman's Magazine//, 1857.^]

What goes for the Thomas arithmometer, in this sense, goes also for every calculational technology, from counting on one's fingers, to the use of calculi on a counting board, or calculating with the abacus, the Pascaline, the Millionaire, logarithms, the MADAS most sophisticated mechanical calculator, the HP-45 electronic calculator, or indeed a spread sheet. Each needs to be understood, and not only intellectually, but equally importantly, it needs to become part of one's embodied capacity, where each required gesture becomes so automatic as to require no or little thought. The question therefore arises not only as to the

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The point here is that the use of a calculating technology is not just intellectual. It is what Jean-François Gauvin[^Jean-François Gauvin , Habits of Knowledge: Artisans, Savants and Mechanical Devices in Seventeenth-Century French Natural Philosophy, The Department of the History of Science, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of History of Science, Harvard University, Cambridge, Mass., USA, November 2008, pp. 113. ^] refers to as "gestural". Gestural knowledge is the embodied knowledge that artisans rely on when they execute work of the highest craft skill. The first time someone looks at a Thomas de Colmar arithmometer learning how to add and subtract takes some time, whilst doing division and multiplication on is more challenging. The first time is slow and subject to mistakes. It is only after repeated practice that the gestures required become so practiced that they are quick, instinctive and reliable. It is only then that the calculation can be seen at what it can be, at its most efficient, and thus it is only with this skill that the technology, in one sense, can be judged.

to:

The point here is that the use of a calculating technology is not just intellectual. It is what Jean-François Gauvin[^Jean-François Gauvin , Habits of Knowledge: Artisans, Savants and Mechanical Devices in Seventeenth-Century French Natural Philosophy, The Department of the History of Science, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of History of Science, Harvard University, Cambridge, Mass., USA, November 2008, pp. 113. ^] refers to as "gestural". Gestural knowledge is the embodied knowledge that artisans rely on when they execute work of the highest craft skill. The first time someone looks at a Thomas de Colmar arithmometer learning how to add and subtract takes some time, whilst doing division and multiplication on is more challenging. The first time is slow and subject to mistakes. It is only after repeated practice that the gestures required become so practiced that they are quick, instinctive and reliable. It is only then that the calculation can be seen at what it can be, at its most efficient, and thus it is only with this skill that the technology, in one sense, can be judged. Clearly it was with this sort of practice that the Gentleman's Magazine of 1857 could claim:

->M. Thomas's arithmometer may be used without the least trouble or possibility of error, not only for addition, subtraction, multiplication, and division, but also for much more complex operations, such as the extraction of the square root, involution, the resolution of triangles, etc...A multiplication of eight figures by eight others is made in eighteen seconds; a division of sixteen figures by eight figures, in twenty four seconds; and in one minute and a quarter one can extract the square root of sixteen figures, and also prove the accuracy of the calculation...

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It is reasonable to wonder what if anything can be drawn from all this. The first thing of course is that this account is built around a collection of historical objects. So it is reasonable to ask why collect them? What does that achieve? After all there are plenty of photographs of these objects in books, journal articles and on the web. The technologies are well described elsewhere in much more mechanically detailed websites. So why the collection?

There are of course more than one reasons why one might collect. The obvious ones are to do with consumerism - the desire to collect and own things of rarity. But there is, in this case, a further consideration. That is that it is not possible to fully understand these objects without actually using them. A trip to, say, one of the great technology museums (for example, CNAM in Paris) will tell you how limited the experience is of, for example, seeing a Pascaline, or reading an essay about it. It is a very different experience to calculate with one. There is here a rather interesting connection between understanding these technologies retrospectively, and the reasons that led to their development in the first place. In short this is a history not only of mechanism but of learning how to use it.

The point here is that the use of a calculating technology is not just intellectual. It is what Jean-François Gauvin[^Jean-François Gauvin , Habits of Knowledge: Artisans, Savants and Mechanical Devices in Seventeenth-Century French Natural Philosophy, The Department of the History of Science, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of History of Science, Harvard University, Cambridge, Mass., USA, November 2008, pp. 113. ^] refers to as "gestural". Gestural knowledge is the embodied knowledge that artisans rely on when they execute work of the highest craft skill. The first time someone looks at a Thomas de Colmar arithmometer learning how to add and subtract takes some time, whilst doing division and multiplication on is more challenging. The first time is slow and subject to mistakes. It is only after repeated practice that the gestures required become so practiced that they are quick, instinctive and reliable. It is only then that the calculation can be seen at what it can be, at its most efficient, and thus it is only with this skill that the technology, in one sense, can be judged.

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The main progress that had been made was thus not so much in functionality as in production methodology. This is epitomised by the Walther 160 and later Walther calculators. Karl Walther's ancestors made rifles and in 1858 he established his own hunting and shooting rifle company.[^"Walther Company History", [[http://www.carl-walther.de/cw.php?lang=en&content=history]], viewed 23 July 2013. He developed then into pistols including the famous Walther PP series military pistols production of which began in 1928 and were a worldwide success. However, the second world war in 1945 left his son Fritz with 80 patents and little else. He was able to rebuild the business both in relation to weapons, but also by diversifying into making office machinery, and in particular calculators. By the 1950s he had four large factories equipped with advanced machinery and technique.[^Ray Mackay, "The Walther Company: Historic Recollections", December 1997. [[http://www.xnumber.com/xnumber/walther.htm]], viewed 22 July 2013.^] The Walther 160 was by now a classic product of modern manufacturing technology, mass produced, comparatively lightly made, and accessibly cheap. As a result many thousands of them were sold. By 1970 the Walther Office Machines company (Walther Büromaschinen GmbH) employed 2000 staff and was producing almost 120,000 machines per year, with about 50% for export.[^John Wolff, "John Wolff's Web Museum: Walther Calculators Overview" [[http://home.vicnet.net.au/~wolff/calculators/Walther/Walther.htm]], viewed 23 July 2013.^]

to:

The main progress that had been made was thus not so much in functionality as in production methodology. This is epitomised by the Walther 160 and later Walther calculators. Karl Walther's ancestors made rifles and in 1858 he established his own hunting and shooting rifle company.[^"Walther Company History", [[http://www.carl-walther.de/cw.php?lang=en&content=history]], viewed 23 July 2013.^]. He developed then into pistols including the famous Walther PP series military pistols production of which began in 1928 and were a worldwide success. However, the second world war in 1945 left his son Fritz with 80 patents and little else. He was able to rebuild the business both in relation to weapons, but also by diversifying into making office machinery, and in particular calculators. By the 1950s he had four large factories equipped with advanced machinery and technique.[^Ray Mackay, "The Walther Company: Historic Recollections", December 1997. [[http://www.xnumber.com/xnumber/walther.htm]], viewed 22 July 2013.^] The Walther 160 was by now a classic product of modern manufacturing technology, mass produced, comparatively lightly made, and accessibly cheap. As a result many thousands of them were sold. By 1970 the Walther Office Machines company (Walther Büromaschinen GmbH) employed 2000 staff and was producing almost 120,000 machines per year, with about 50% for export.[^John Wolff, "John Wolff's Web Museum: Walther Calculators Overview" [[http://home.vicnet.net.au/~wolff/calculators/Walther/Walther.htm]], viewed 23 July 2013.^]

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The main progress that had been made was thus not so much in functionality as in production methodology. This is epitomised by the Walther 160. Karl Walther's ancestors made rifles and in 1858 he established his own hunting and shooting rifle company.[^"Walther Company History", [[http://www.carl-walther.de/cw.php?lang=en&content=history]], viewed 23 July 2013. He developed then into pistols including the famous Walther PP series military pistols production of which began in 1928 and were a worldwide success. However, the second world war in 1945 left his son Fritz with 80 patents and little else. He was able to rebuild the business both in relation to weapons, but also by diversifying into making office machinery, and in particular calculators. By the 1950s he had four large factories equipped with advanced machinery and technique.[^Ray Mackay, "The Walther Company: Historic Recollections", December 1997. [[http://www.xnumber.com/xnumber/walther.htm]], viewed 22 July 2013.^] The Walther 160 was by now a classic product of modern manufacturing technology, mass produced, comparatively lightly made, and accessibly cheap. As a result many thousands of them were sold. By 1970 the Walther Office Machines company (Walther Büromaschinen GmbH) employed 2000 staff and was producing almost 120,000 machines per year, with about 50% for export.[^John Wolff, "John Wolff's Web Museum: Walther Calculators Overview" [[http://home.vicnet.net.au/~wolff/calculators/Walther/Walther.htm]], viewed 23 July 2013.^]

to:

The main progress that had been made was thus not so much in functionality as in production methodology. This is epitomised by the Walther 160 and later Walther calculators. Karl Walther's ancestors made rifles and in 1858 he established his own hunting and shooting rifle company.[^"Walther Company History", [[http://www.carl-walther.de/cw.php?lang=en&content=history]], viewed 23 July 2013. He developed then into pistols including the famous Walther PP series military pistols production of which began in 1928 and were a worldwide success. However, the second world war in 1945 left his son Fritz with 80 patents and little else. He was able to rebuild the business both in relation to weapons, but also by diversifying into making office machinery, and in particular calculators. By the 1950s he had four large factories equipped with advanced machinery and technique.[^Ray Mackay, "The Walther Company: Historic Recollections", December 1997. [[http://www.xnumber.com/xnumber/walther.htm]], viewed 22 July 2013.^] The Walther 160 was by now a classic product of modern manufacturing technology, mass produced, comparatively lightly made, and accessibly cheap. As a result many thousands of them were sold. By 1970 the Walther Office Machines company (Walther Büromaschinen GmbH) employed 2000 staff and was producing almost 120,000 machines per year, with about 50% for export.[^John Wolff, "John Wolff's Web Museum: Walther Calculators Overview" [[http://home.vicnet.net.au/~wolff/calculators/Walther/Walther.htm]], viewed 23 July 2013.^]

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The main progress that had been made was thus not so much in functionality as in production methodology. ~~The Karl Walther Company itself, which had begun as a German sporting weapons company~~ in ~~1886 had turned to making calculators in 1926 following the exigencies of the First World War~~. ~~By the 1950s it had four large factories equipped with advanced machinery and technique.[^Ray Mackay, "The Walther Company: Historic Recollections", December 1997. [[http://www~~.xnumber.com/xnumber/walther.htm]], viewed 22 July 2013.^] The Walther 160 was by now a classic product of modern manufacturing technology, mass produced, comparatively lightly made, and accessibly cheap. As a result many thousands of them were sold.

to:

The main progress that had been made was thus not so much in functionality as in production methodology. This is epitomised by the Walther 160. Karl Walther's ancestors made rifles and in 1858 he established his own hunting and shooting rifle company.[^"Walther Company History", [[http://www.carl-walther.de/cw.php?lang=en&content=history]], viewed 23 July 2013. He developed then into pistols including the famous Walther PP series military pistols production of which began in 1928 and were a worldwide success. However, the second world war in 1945 left his son Fritz with 80 patents and little else. He was able to rebuild the business both in relation to weapons, but also by diversifying into making office machinery, and in particular calculators. By the 1950s he had four large factories equipped with advanced machinery and technique.[^Ray Mackay, "The Walther Company: Historic Recollections", December 1997. [[http://www.xnumber.com/xnumber/walther.htm]], viewed 22 July 2013.^] The Walther 160 was by now a classic product of modern manufacturing technology, mass produced, comparatively lightly made, and accessibly cheap. As a result many thousands of them were sold. By 1970 the Walther Office Machines company (Walther Büromaschinen GmbH) employed 2000 staff and was producing almost 120,000 machines per year, with about 50% for export.[^John Wolff, "John Wolff's Web Museum: Walther Calculators Overview" [[http://home.vicnet.net.au/~wolff/calculators/Walther/Walther.htm]], viewed 23 July 2013.^]

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||%center% %height=~~300px~~% 1623: Recreation of \\Wilhelm Schickard's machine\\(collection Calculant)||%center% 1904-1905: Bamberger’s Omega\\ Calculating Machine\\(collection Calculant)||

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||%center% %height=250px% 1623: Recreation of \\Wilhelm Schickard's machine\\(collection Calculant)||%center% 1904-1905: Bamberger’s Omega\\ Calculating Machine\\(collection Calculant)||

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||%center% %height=300px% 1623: Recreation of \\Wilhelm Schickard's machine\\(collection Calculant)||%center% 1904-1905: Bamberger’s Omega\\ Calculating Machine\\(collection Calculant)||

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||%center% 1623: Recreation of \\Wilhelm Schickard's machine\\(collection Calculant)||%center% 1904-1905: Bamberger’s Omega\\ Calculating Machine\\(collection Calculant)||

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||%center% %height=250px% 1623: Recreation of \\Wilhelm Schickard's machine\\(collection Calculant)||%center% 1904-1905: Bamberger’s Omega\\ Calculating Machine\\(collection Calculant)||

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!!!The quest for ~~true~~ multiplication and division

to:

!!!The quest for direct multiplication and division

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!!!~~Evolutionary cul-de-sac: the search~~ for true multiplication and division

to:

!!!The quest for true multiplication and division

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As will be recalled, the earliest of these machines, that of Schickard (below, left), utilised a set of rotatable Napier's rods in the upper part, and an adding machine in the bottom section. A late and unique expression of these in this collection (below, right) is Justin Bamberger’s Omega Calculating Machine (1903-6). It combines a stylus operated adding machine (complete with provision for automatic carry) ~~with a sophisticated Napier bones based machine for discovering~~ the ~~partial products of two multiplied numbers (a bit like that in Schickard’s much earlier device), which can then be added in~~ the ~~adding machine to find corresponding products and quotients~~.

to:

As will be recalled, the earliest of these machines, that of Schickard (below, left). In the upper part is a set of rotatable Napier's rods in the upper part, revealed by windows to give partial products. In the lower part is the world's first known stylus operated adding machine to add them up. A late and unique expression of these in this collection (below, right) is Justin Bamberger’s Omega Calculating Machine (1903-6). In the upper section is a set of Napier's bones revealed by moveable windows for discovering the partial products of two multiplied numbers. In the lower section is a Locke adding machine for adding them up.

Added line 253:

Bamberger's Omega uses linear strips rather than the rotatable mechanisms of both halves of the Schickard. It also has some additional provision for storing intermediate results to assist long division, including the register on the top right, and the notebook. Otherwise the two machines are very similar in operation and both, with some considerable effort, can be used to perform all four functions of arithmetic. The fact that neither took off in the market place may be in part a factor of their difficulty of use and part a lack of adequately determined marketing.

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As will be recalled, the earliest of these machines, that of Schickard (~~see~~ below), utilised a set of rotatable Napier's rods in the upper part, and an adding machine in the bottom section.

A late and unique expression of these in this collection ~~is Justin Bamberger’s Omega Calculating Machine~~ (1903-6). It combines a stylus operated adding machine (complete with provision for automatic carry) with a sophisticated Napier bones based machine for discovering the partial products of two multiplied numbers (a bit like that in Schickard’s much earlier device), which can then be added in the adding machine to find corresponding products and quotients.

to:

As will be recalled, the earliest of these machines, that of Schickard (below, left), utilised a set of rotatable Napier's rods in the upper part, and an adding machine in the bottom section. A late and unique expression of these in this collection (below, right) is Justin Bamberger’s Omega Calculating Machine (1903-6). It combines a stylus operated adding machine (complete with provision for automatic carry) with a sophisticated Napier bones based machine for discovering the partial products of two multiplied numbers (a bit like that in Schickard’s much earlier device), which can then be added in the adding machine to find corresponding products and quotients.

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||%center% 1623: Recreation of \\Wilhelm Schickard's machine\\(collection Calculant)||%center% 1904-1905: Bamberger’s Omega\\ Calculating Machine\\
~~%center%~~ (collection Calculant)||

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||%center% 1623: Recreation of \\Wilhelm Schickard's machine\\(collection Calculant)||%center% 1904-1905: Bamberger’s Omega\\ Calculating Machine\\(collection Calculant)||

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||%center% 1623: Recreation of Wilhelm Schickard's machine//(collection Calculant)||%center% 1904-1905: Bamberger’s Omega Calculating Machine\\

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||%center% 1623: Recreation of \\Wilhelm Schickard's machine\\(collection Calculant)||%center% 1904-1905: Bamberger’s Omega\\ Calculating Machine\\

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%center% %width=250px% http://meta-studies.net/pmwiki/uploads/Schickard1.jpg
%center% 1623: Recreation of Wilhelm Schickard's machine//(collection Calculant)

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%center% %~~height~~=250px% ~~[[Site.BambergerOmega1904|~~http://meta-studies.net/pmwiki/uploads/~~BambergerOmega~~.~~png]]~~
%center% 1904-1905: Bamberger’s Omega Calculating Machine\\
%center% (collection Calculant)

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||%center% %width=250px% http://meta-studies.net/pmwiki/uploads/Schickard1.jpg||%center% %height=250px% [[Site.BambergerOmega1904|http://meta-studies.net/pmwiki/uploads/BambergerOmega.png]]||
||%center% 1623: Recreation of Wilhelm Schickard's machine//(collection Calculant)||%center% 1904-1905: Bamberger’s Omega Calculating Machine\\
%center% (collection Calculant)||

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Added lines 248-249:

As will be recalled, the earliest of these machines, that of Schickard (see below), utilised a set of rotatable Napier's rods in the upper part, and an adding machine in the bottom section.

Changed line 253 from:

A late and unique expression of these in this collection is Justin Bamberger’s Omega Calculating Machine (1903-6). It combines a stylus operated adding machine (complete with provision for automatic carry) with a sophisticated Napier bones based machine for discovering the partial products of two multiplied numbers (a bit like that in Schickard’s much earlier device), which can then be added in the adding machine to find corresponding products and quotients.

to:

A late and unique expression of these in this collection is Justin Bamberger’s Omega Calculating Machine (1903-6). It combines a stylus operated adding machine (complete with provision for automatic carry) with a sophisticated Napier bones based machine for discovering the partial products of two multiplied numbers (a bit like that in Schickard’s much earlier device), which can then be added in the adding machine to find corresponding products and quotients.

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An entirely different evolutionary path which has already been mentioned was attempted to solving the problem of mechanising the four arithmetic operations (+, -, x, /), with emphasis on finding ways to directly perform the more difficult two operations of multiplication and division. This developed from the Napier’s rods - or “bones” (developed by John Napier (1550–1617) to which we have already referred. As already mentioned calculational approaches were designed around them by Wilhelm Schickard in 1623, Charles Cotterel in 1667, Gaspard Schott in 1668, and Samuel Morland between 1625 and 1695. A late and unique expression of these in this collection is Justin Bamberger’s Omega Calculating Machine (1903-6). It combines a stylus operated adding machine (complete with provision for automatic carry) with a sophisticated Napier bones based machine for discovering the partial products of two multiplied numbers (a bit like that in Schickard’s much earlier device), which can then be added in the adding machine to find corresponding products and quotients.

to:

An entirely different evolutionary path which has already been mentioned was attempted to solving the problem of mechanising the four arithmetic operations (+, -, x, /), with emphasis on finding ways to directly perform the more difficult two operations of multiplication and division. This developed from the Napier’s rods - or “bones” (developed by John Napier (1550–1617) to which we have already referred. As already mentioned calculational approaches were designed around them by Wilhelm Schickard in 1623, Charles Cotterel in 1667, Gaspard Schott in 1668, and Samuel Morland between 1625 and 1695.

%center% %width=250px% http://meta-studies.net/pmwiki/uploads/Schickard1.jpg
%center% 1623: Recreation of Wilhelm Schickard's machine//(collection Calculant)

A late and unique expression of these in this collection is Justin Bamberger’s Omega Calculating Machine (1903-6). It combines a stylus operated adding machine (complete with provision for automatic carry) with a sophisticated Napier bones based machine for discovering the partial products of two multiplied numbers (a bit like that in Schickard’s much earlier device), which can then be added in the adding machine to find corresponding products and quotients.

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Ohdner began manufacture of his machines in 1886 under the name "Original Ohdner" but sold his rights also to Grimme, Natalis and Co., Braunsweig, who began marketing the machines under the name Brunsviga.[^ibid^] In turn they also licenced agents such as Schuster to sell them. Below is the very early Brunsviga-Schuster pinwheel calculator from 1896 in this collection.

to:

Ohdner began manufacture of his machines in 1886 under the name "Original Ohdner" but sold his rights also to Grimme, Natalis and Co., Braunsweig, who began marketing the machines under the name Brunsviga.[^ibid^] In turn they also licenced agents such as Schuster to sell them. Reflecting a later start these machines were made from a wider range of materials than the arithmometers, including iron and nickel alloys as well as brass and steel. Below is the very early Brunsviga-Schuster pinwheel calculator from 1896 in this collection.

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As the range of dates for the set of pinwheel calculators in this collection suggests, the pinwheel design was highly successful and capable of being improved on for the better part of three quarters of a century. The second Ohdner in the collection is from 1938, and although possessing some improvements (such as the capacity to move the carriage back and forth with tab keys), was little different in concept. The same can be said for the Facit calculator from around 1945, and even from the 1950s, near the end of the production of such machines, despite its more modern finish and use of plastic fittings~~, the Walther 160 remains quite similar in operation to the Brunsviga of 1896, which, significantly, still works as smoothly as the~~ Walther.

to:

As the range of dates for the set of pinwheel calculators in this collection suggests, the pinwheel design was highly successful and capable of being improved on for the better part of three quarters of a century. The second Ohdner in the collection is from 1938, and although possessing some improvements (such as the capacity to move the carriage back and forth with tab keys), was little different in concept. The same can be said for the Facit calculator from around 1945, and even from the 1950s, near the end of the production of such machines, despite its more modern finish and use of plastic fittings (and some improvements such as clearing levers), the Walther 160 remains quite similar in operation to the Brunsviga of 1896, which, significantly, still works as smoothly as the Walther.

The main progress that had been made was thus not so much in functionality as in production methodology. The Karl Walther Company itself, which had begun as a German sporting weapons company in 1886 had turned to making calculators in 1926 following the exigencies of the First World War. By the 1950s it had four large factories equipped with advanced machinery and technique.[^Ray Mackay, "The Walther Company: Historic Recollections", December 1997. [[http://www.xnumber.com/xnumber/walther.htm]], viewed 22 July 2013.^] The Walther 160 was by now a classic product of modern manufacturing technology, mass produced, comparatively lightly made, and accessibly cheap. As a result many thousands of them were sold.

Deleted lines 205-210:

Like arithmometers, Brunsviga calculating machines were lever-set and operated by turning a crank (Figure 3). Instead of stepped drums, they had a pinwheel mechanism that carried out cal- culations. Smaller and lighter than arithmome- ters, they were made from a larger range of ma- terials, including iron and nickel alloys as well as brass and steel. Pinwheel machines had been patented by Frank S. Baldwin and W. T. Odhner. They were successfully marketed by Odhner in Russia and Sweden, and by Brunsviga in Ger- many. They were sold by Marchant in the United States.

See How Calculating Machines Worked

See nice diagrams and descriptions of the three mechanisms.

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The above three arithmometers demonstrate the sorts of improvements to the basic arithmometer design which now emerged. The first, a TIM (“Time is Money” ) arithmometer manufactured by Ludwig Spitz and Co. of Berlin-Tempelhof in 1909 was greatly strengthened from the Thomas design to create a much more robust and reliable machine. First produced in a wooden box it was later made much stronger by installing it in a cast iron frame which held all parts rigidly.[^See Ernst Martin, //The Calculating Machines (Die Rechenmaschinen): Their History and Development//, ed. and trs. by Peggy Aldridge Kidwell and Michael R. Williams, MIT Press, Mass., 1992, p. 191–4^] Beginning a change in style that would be emulated in many other machines the brass panels were now enamelled black consistent with the management, industrial and commercial settings where it was intended to find its market. The other two machines in this set would also originally have had a similar black finish. (Unfortunately, there ~~has been~~ a ~~historical~~ tendency in the late C20 to "take the machines back to brass" in the same way that in the 1960s there was a trend to remove plaster from brick walls in old houses.)

to:

The above three arithmometers demonstrate the sorts of improvements to the basic arithmometer design which now emerged. The first, a TIM (“Time is Money” ) arithmometer manufactured by Ludwig Spitz and Co. of Berlin-Tempelhof in 1909 was greatly strengthened from the Thomas design to create a much more robust and reliable machine. First produced in a wooden box it was later made much stronger by installing it in a cast iron frame which held all parts rigidly.[^See Ernst Martin, //The Calculating Machines (Die Rechenmaschinen): Their History and Development//, ed. and trs. by Peggy Aldridge Kidwell and Michael R. Williams, MIT Press, Mass., 1992, p. 191–4^] Beginning a change in style that would be emulated in many other machines the brass panels were now enamelled black consistent with the management, industrial and commercial settings where it was intended to find its market. The other two machines in this set would also originally have had a similar black finish. (Unfortunately, there was a tendency in the late C20 to "take the machines back to brass" in the same way that in the 1960s there was a trend to remove the original finish from wood on vintage furniture, and plaster from brick walls in old houses.)

Changed lines 198-201 from:

As the range of dates for the set of pinwheel calculators in this collection suggests, the pinwheel design was highly successful and capable of being improved on for the better part of ~~a century. The second Ohdner in the collection is from 1938, and although possessing some improvements (such as the capacity to move~~ the carriage back and forth with tab keys), was little different in concept.

In the pinwheels in this collection there is a later Ohdner from 1938 and a Facit calculator from ~~around 1945~~, ~~and then from near~~ the ~~end~~ of ~~production of such~~ machines, ~~from the 1950s a very nice demonstration Walther 160 calculator~~, ~~showing its mechanism, complemented by a complete and fully operational Walther~~ of ~~the same model~~.

to:

As the range of dates for the set of pinwheel calculators in this collection suggests, the pinwheel design was highly successful and capable of being improved on for the better part of three quarters of a century. The second Ohdner in the collection is from 1938, and although possessing some improvements (such as the capacity to move the carriage back and forth with tab keys), was little different in concept. The same can be said for the Facit calculator from around 1945, and even from the 1950s, near the end of the production of such machines, despite its more modern finish and use of plastic fittings, the Walther 160 remains quite similar in operation to the Brunsviga of 1896, which, significantly, still works as smoothly as the Walther.

22 July 2013 by 121.219.189.30 -

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The above three arithmometers demonstrate the sorts of improvements to the basic arithmometer design which now emerged. The first, a TIM (“Time is Money” ) arithmometer manufactured by Ludwig Spitz and Co. of Berlin-Tempelhof in 1909 was greatly strengthened from the Thomas design to create a much more robust and reliable machine. First produced in a wooden box it was later made much stronger by installing it in a cast iron frame which held all parts rigidly.[^See Ernst Martin, //The Calculating Machines (Die Rechenmaschinen): Their History and Development//, ed. and trs. by Peggy Aldridge Kidwell and Michael R. Williams, MIT Press, Mass., 1992, p. 191–4^] Beginning a change in style that would be emulated in many other machines the brass panels were now enamelled black consistent with the management, industrial and commercial settings where it was intended to find its market.

to:

The above three arithmometers demonstrate the sorts of improvements to the basic arithmometer design which now emerged. The first, a TIM (“Time is Money” ) arithmometer manufactured by Ludwig Spitz and Co. of Berlin-Tempelhof in 1909 was greatly strengthened from the Thomas design to create a much more robust and reliable machine. First produced in a wooden box it was later made much stronger by installing it in a cast iron frame which held all parts rigidly.[^See Ernst Martin, //The Calculating Machines (Die Rechenmaschinen): Their History and Development//, ed. and trs. by Peggy Aldridge Kidwell and Michael R. Williams, MIT Press, Mass., 1992, p. 191–4^] Beginning a change in style that would be emulated in many other machines the brass panels were now enamelled black consistent with the management, industrial and commercial settings where it was intended to find its market. The other two machines in this set would also originally have had a similar black finish. (Unfortunately, there has been a historical tendency in the late C20 to "take the machines back to brass" in the same way that in the 1960s there was a trend to remove plaster from brick walls in old houses.)

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||~1915||Golden Gem Automatic\\Adding Machine||H. & H. Goldmann||Chain||%height=~~125px~~%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg]]||

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||~1915||Golden Gem Automatic\\Adding Machine||H. & H. Goldmann||Chain||%height=100px%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg]]||

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||1903 ||Adix Adding Machine\\Original model||Manheim||Key input\\lever &\\gears||%height=~~125px~~%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/Adix.png]]||

to:

||1903 ||Adix Adding Machine\\Original model||Manheim||Key input\\lever &\\gears||%height=175px%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/Adix.png]]||

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%center% %height=~~250px~~% [[Site.Millionaire1912|http://meta-studies.net/pmwiki/uploads/Millionair.png]]

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%center% %height=300px% [[Site.Millionaire1912|http://meta-studies.net/pmwiki/uploads/Millionair.png]]

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||1950s ||Bell Sumlock Comptometer||Bell Sumlock||Model 909/S/117.878||%height=~~100px~~%[[Site.SumlockComptometer1950s| http://meta-studies.net/pmwiki/uploads/Sumlock.png]]||
||~1955||Bell Punch Sumlock ||Bell Punch||Demonstration\\Comptometer||%height=~~100px~~%[[Site.SumlockDemonstrator1955| http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png]]||

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||1950s ||Bell Sumlock Comptometer||Bell Sumlock||Model 909/S/117.878||%height=250px%[[Site.SumlockComptometer1950s| http://meta-studies.net/pmwiki/uploads/Sumlock.png]]||
||~1955||Bell Punch Sumlock ||Bell Punch||Demonstration\\Comptometer||%height=250px%[[Site.SumlockDemonstrator1955| http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png]]||

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||1909 ||TIM (Time is Money)\\ Arithmometer||Ludwig Spitz\\ & Co||Arithmometer||%height=~~100px~~%[[Site.TIM1909| http://meta-studies.net/pmwiki/uploads/TIM.JPG]]||
||~1913 ||Bunzel-Denton Arithmometer||Bunzel||Prototype\\Front Crank||%height=~~100px~~%[[Site.BunzelPrototype1913| http://meta-studies.net/pmwiki/uploads/Bunzel.JPG]]||
||~1917 ||Madas IX Maxima||Madas||Auto Division||%height=~~100px~~%[[Site.Madas-IX-Maxima| http://meta-studies.net/pmwiki/uploads/MADAS-1917.jpg]]||

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||1909 ||TIM (Time is Money)\\ Arithmometer||Ludwig Spitz\\ & Co||Arithmometer||%height=150px%[[Site.TIM1909| http://meta-studies.net/pmwiki/uploads/TIM.JPG]]||
||~1913 ||Bunzel-Denton Arithmometer||Bunzel||Prototype\\Front Crank||%height=150px%[[Site.BunzelPrototype1913| http://meta-studies.net/pmwiki/uploads/Bunzel.JPG]]||
||~1917 ||Madas IX Maxima||Madas||Auto Division||%height=125px%[[Site.Madas-IX-Maxima| http://meta-studies.net/pmwiki/uploads/MADAS-1917.jpg]]||

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||1945 ||Facit Model S Calculator\\serial 210652||Facit||Pinwheel||%height=~~100px~~%[[Site.Facit1945| http://meta-studies.net/pmwiki/uploads/Facit.png]]||

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||1945 ||Facit Model S Calculator\\serial 210652||Facit||Pinwheel||%height=150px%[[Site.Facit1945| http://meta-studies.net/pmwiki/uploads/Facit.png]]||

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||~1957 ||Walther WSR160\\Pinwheel Calculator||Walther||Pinwheel||%height=~~100px~~%[[Site.Walther1957| http://meta-studies.net/pmwiki/uploads/Walther.png]]||
||~1957 ||Walther WSR160\\Demonstration\\Pinwheel Calculator||Walther||Demonstration\\Pinwheel||%height=~~100px~~%[[Site.WaltherDemonstrator1957| http://meta-studies.net/pmwiki/uploads/WaltherDemo.png]]||

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||~1957 ||Walther WSR160\\Pinwheel Calculator||Walther||Pinwheel||%height=150px%[[Site.Walther1957| http://meta-studies.net/pmwiki/uploads/Walther.png]]||
||~1957 ||Walther WSR160\\Demonstration\\Pinwheel Calculator||Walther||Demonstration\\Pinwheel||%height=150px%[[Site.WaltherDemonstrator1957| http://meta-studies.net/pmwiki/uploads/WaltherDemo.png]]||

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||~1946 ||Lightning Portable\\Adding Machine||Lightning\\Adding Machine\\Co. L.A.||7 Wheels||%height=~~75px~~%[[Site.Lightning1946| http://meta-studies.net/pmwiki/uploads/Lightning.png]]||

to:

||~1946 ||Lightning Portable\\Adding Machine||Lightning\\Adding Machine\\Co. L.A.||7 Wheels||%height=125px%[[Site.Lightning1946| http://meta-studies.net/pmwiki/uploads/Lightning.png]]||

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||1890-1900 ||A. M. Stevenson Adder||Joliet, Ill.\\||2 Wheel||%height=~~100px~~%[[Stevenson1890| http://meta-studies.net/pmwiki/uploads/Stevenson.png]]||

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||1890-1900 ||A. M. Stevenson Adder||Joliet, Ill.\\||2 Wheel||%height=75px%[[Stevenson1890| http://meta-studies.net/pmwiki/uploads/Stevenson.png]]||

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||~1946 ||Lightning Portable\\Adding Machine||Lightning\\Adding Machine\\Co. L.A.||7 Wheels||%height=~~100px~~%[[Site.Lightning1946| http://meta-studies.net/pmwiki/uploads/Lightning.png]]||
||1968 ||SEE Demonstration\\Adding Machine||Selective Educational\\Equipment Corporation||4 Wheels||%height=~~100px~~%[[Site.SEE1968| http://meta-studies.net/pmwiki/uploads/SEE-1.jpg]]||

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||~1946 ||Lightning Portable\\Adding Machine||Lightning\\Adding Machine\\Co. L.A.||7 Wheels||%height=75px%[[Site.Lightning1946| http://meta-studies.net/pmwiki/uploads/Lightning.png]]||
||1968 ||SEE Demonstration\\Adding Machine||Selective Educational\\Equipment Corporation||4 Wheels||%height=75px%[[Site.SEE1968| http://meta-studies.net/pmwiki/uploads/SEE-1.jpg]]||

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||1910-20s||Comptator (9 col)||Schubert\\& Salzer||Chain||%height=~~150px~~%[[Site.Comptator1910|http://meta-studies.net/pmwiki/uploads/Comptator.png]]||
||~1915||Golden Gem Automatic\\Adding Machine||H. & H. Goldmann||Chain||%height=~~150px~~%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg]]||
||1920||Addiator Troncet adder||Ruthard & Co||Chain||%height=~~100px~~%[[Site.Addiator1920 |http://meta-studies.net/pmwiki/uploads/Addiator.png]]||

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||1910-20s||Comptator (9 col)||Schubert\\& Salzer||Chain||%height=125px%[[Site.Comptator1910|http://meta-studies.net/pmwiki/uploads/Comptator.png]]||
||~1915||Golden Gem Automatic\\Adding Machine||H. & H. Goldmann||Chain||%height=125px%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg]]||
||1920||Addiator Troncet adder||Ruthard & Co||Chain||%height=125px%[[Site.Addiator1920 |http://meta-studies.net/pmwiki/uploads/Addiator.png]]||

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||1937||Add-O-Matic\\Adding Machine||Allied MFG. Co.||Chain||%height=~~150px~~%[[Site.Add-O-Matic1937 |http://meta-studies.net/pmwiki/uploads/AddOMatic1.jpg]]||

to:

||1937||Add-O-Matic\\Adding Machine||Allied MFG. Co.||Chain||%height=125px%[[Site.Add-O-Matic1937 |http://meta-studies.net/pmwiki/uploads/AddOMatic1.jpg]]||

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||1890-1900 ||A. M. Stevenson Adder||Joliet, Ill.\\||2 Wheel||%height=~~150px~~%[[Stevenson1890| http://meta-studies.net/pmwiki/uploads/Stevenson.png]]||
||1903 ||Adix Adding Machine\\Original model||Manheim||Key input\\lever &\\gears||%height=~~150px~~%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/Adix.png]]||
||1910 ||Adall Adding Machine||Dreyfus\\and Levy ||Key input\\Concentric \\toothed disk\\and groove||%height=~~150px~~%[[Site.Adall1910| http://meta-studies.net/pmwiki/uploads/Adall.jpg]]||
||~1946 ||Lightning Portable\\Adding Machine||Lightning\\Adding Machine\\Co. L.A.||7 Wheels||%height=~~150px~~%[[Site.Lightning1946| http://meta-studies.net/pmwiki/uploads/Lightning.png]]||
||1968 ||SEE Demonstration\\Adding Machine||Selective Educational\\Equipment Corporation||4 Wheels||%height=~~150px~~%[[Site.SEE1968| http://meta-studies.net/pmwiki/uploads/SEE-1.jpg]]||

to:

||1890-1900 ||A. M. Stevenson Adder||Joliet, Ill.\\||2 Wheel||%height=100px%[[Stevenson1890| http://meta-studies.net/pmwiki/uploads/Stevenson.png]]||
||1903 ||Adix Adding Machine\\Original model||Manheim||Key input\\lever &\\gears||%height=125px%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/Adix.png]]||
||1910 ||Adall Adding Machine||Dreyfus\\and Levy ||Key input\\Concentric \\toothed disk\\and groove||%height=125px%[[Site.Adall1910| http://meta-studies.net/pmwiki/uploads/Adall.jpg]]||
||~1946 ||Lightning Portable\\Adding Machine||Lightning\\Adding Machine\\Co. L.A.||7 Wheels||%height=100px%[[Site.Lightning1946| http://meta-studies.net/pmwiki/uploads/Lightning.png]]||
||1968 ||SEE Demonstration\\Adding Machine||Selective Educational\\Equipment Corporation||4 Wheels||%height=100px%[[Site.SEE1968| http://meta-studies.net/pmwiki/uploads/SEE-1.jpg]]||

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||1890-1900 ||A. M. Stevenson Adder||Joliet, Ill.\\||2 Wheel||%height=~~100px~~%[[Stevenson1890| http://meta-studies.net/pmwiki/uploads/Stevenson.png]]||
||1903 ||Adix Adding Machine\\Original model||Manheim||Key input\\lever &\\gears||%height=~~100px~~%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/Adix.png]]||
||1910 ||Adall Adding Machine||Dreyfus\\and Levy ||Key input\\Concentric \\toothed disk\\and groove||%height=~~100px~~%[[Site.Adall1910| http://meta-studies.net/pmwiki/uploads/Adall.jpg]]||
||~1946 ||Lightning Portable\\Adding Machine||Lightning\\Adding Machine\\Co. L.A.||7 Wheels||%height=~~100px~~%[[Site.Lightning1946| http://meta-studies.net/pmwiki/uploads/Lightning.png]]||
||1968 ||SEE Demonstration\\Adding Machine||Selective Educational\\Equipment Corporation||4 Wheels||%height=~~100px~~%[[Site.SEE1968| http://meta-studies.net/pmwiki/uploads/SEE-1.jpg]]||

to:

||1890-1900 ||A. M. Stevenson Adder||Joliet, Ill.\\||2 Wheel||%height=150px%[[Stevenson1890| http://meta-studies.net/pmwiki/uploads/Stevenson.png]]||
||1903 ||Adix Adding Machine\\Original model||Manheim||Key input\\lever &\\gears||%height=150px%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/Adix.png]]||
||1910 ||Adall Adding Machine||Dreyfus\\and Levy ||Key input\\Concentric \\toothed disk\\and groove||%height=150px%[[Site.Adall1910| http://meta-studies.net/pmwiki/uploads/Adall.jpg]]||
||~1946 ||Lightning Portable\\Adding Machine||Lightning\\Adding Machine\\Co. L.A.||7 Wheels||%height=150px%[[Site.Lightning1946| http://meta-studies.net/pmwiki/uploads/Lightning.png]]||
||1968 ||SEE Demonstration\\Adding Machine||Selective Educational\\Equipment Corporation||4 Wheels||%height=150px%[[Site.SEE1968| http://meta-studies.net/pmwiki/uploads/SEE-1.jpg]]||

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||1910-20s||Comptator (9 col)||Schubert\\& Salzer||Chain||%height=~~100px~~%[[Site.Comptator1910|http://meta-studies.net/pmwiki/uploads/Comptator.png]]||
||~1915||Golden Gem Automatic\\Adding Machine||H. & H. Goldmann||Chain||%height=~~100px~~%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg]]||

to:

||1910-20s||Comptator (9 col)||Schubert\\& Salzer||Chain||%height=150px%[[Site.Comptator1910|http://meta-studies.net/pmwiki/uploads/Comptator.png]]||
||~1915||Golden Gem Automatic\\Adding Machine||H. & H. Goldmann||Chain||%height=150px%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg]]||

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||1922||Scribola 10 column\\printing\\Adding Machine||Addiator Gesellschaft||Rod||%height=~~100px~~%[[Site.Scribola1922 |http://meta-studies.net/pmwiki/uploads/Scribola.jpg]]||
||1937||Add-O-Matic\\Adding Machine||Allied MFG. Co.||Chain||%height=~~100px~~%[[Site.Add-O-Matic1937 |http://meta-studies.net/pmwiki/uploads/AddOMatic1.jpg]]||

to:

||1922||Scribola 10 column\\printing\\Adding Machine||Addiator Gesellschaft||Rod||%height=150px%[[Site.Scribola1922 |http://meta-studies.net/pmwiki/uploads/Scribola.jpg]]||
||1937||Add-O-Matic\\Adding Machine||Allied MFG. Co.||Chain||%height=150px%[[Site.Add-O-Matic1937 |http://meta-studies.net/pmwiki/uploads/AddOMatic1.jpg]]||

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These pinwheels thus replaced the much larger and more cumbersome step drums of the arithmometers. ~~Being thing and able to be nestled side by~~ side ~~in a compact manner (right, above) these calculators were much lighter and~~ more compact than the arithmometers. The crank handle was conveniently on the right end of the machine, and could be turned either forward or backwards (corresponding to addition or subtraction). The output wheels were set in the base, and as with the arithmometer, the input mechanism (including the pinwheels and sliders) could be moved parallel to it allowing long multiplication and division to be carried out.

to:

These pinwheels thus replaced the much larger and more cumbersome step drums of the arithmometers. Thin as these were, and able to be nestled side by side in a compact manner (right, above), these allowed the calculators to be lighter and much more compact than the arithmometers. The crank handle was conveniently on the right end of the machine, and could be turned either forward or backwards (corresponding to addition or subtraction). The output wheels were set in the base, and as with the arithmometer, the input mechanism (including the pinwheels and sliders) could be moved parallel to it allowing long multiplication and division to be carried out.

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~~Notes~~

to:

As the range of dates for the set of pinwheel calculators in this collection suggests, the pinwheel design was highly successful and capable of being improved on for the better part of a century. The second Ohdner in the collection is from 1938, and although possessing some improvements (such as the capacity to move the carriage back and forth with tab keys), was little different in concept.

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||%center% %height=~~150px~~%[[Site.DemonstrationPinwheel|http://meta-studies.net/pmwiki/uploads/PinWheelSingle.jpg]]||%center% %height=~~150px~~%[[Site.DemonstrationPinwheelMechanism|http://meta-studies.net/pmwiki/uploads/PinwheelDemo.jpg]]||

to:

||%center% %height=200px%[[Site.DemonstrationPinwheel|http://meta-studies.net/pmwiki/uploads/PinWheelSingle.jpg]]||%center% %height=200px%[[Site.DemonstrationPinwheelMechanism|http://meta-studies.net/pmwiki/uploads/PinwheelDemo.jpg]]||

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~~In this collection there is the already mentioned very early Brunsviga-Schuster pinwheel calculator from 1896 (an Ohdner Brunsviga which had been re-badged by Schuster~~ who ~~on-sold them)~~.

to:

Ohdner began manufacture of his machines in 1886 under the name "Original Ohdner" but sold his rights also to Grimme, Natalis and Co., Braunsweig, who began marketing the machines under the name Brunsviga.[^ibid^] In turn they also licenced agents such as Schuster to sell them. Below is the very early Brunsviga-Schuster pinwheel calculator from 1896 in this collection.

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||%center% 1923: Mercedes-Euklid Model 29 calculator||%center% 1923: Mercedes-Euklid Model 29\\Demonstration calculator||

to:

||%center% 1923: Mercedes-Euklid\\Model 29 calculator||%center% 1923: Mercedes-Euklid Model 29\\Demonstration calculator||

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||%center% 1923: Mercedes-Euklid Model 29 calculator~~\\(collection Calculant)~~||%center% 1923: Mercedes-Euklid Model 29\\Demonstration calculator||

to:

||%center% 1923: Mercedes-Euklid Model 29 calculator||%center% 1923: Mercedes-Euklid Model 29\\Demonstration calculator||
||(collection Calculant)||(collection Calculant)||

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||(collection Calculant)||(collection Calculant) ||

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||(collection Calculant)||(collection Calculant) ||(collection Calculant)||

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||(collection Calculant)|| ||

to:

||(collection Calculant)||(collection Calculant)||

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||(collection Calculant)|| || ||

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||(collection Calculant)||(collection Calculant) ||

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||%center%A single pinwheel||%center% Mechanism of the ~~Walther~~\\pinwheel calculator||

to:

||%center%A single pinwheel||%center% Mechanism of the\\Walther pinwheel calculator\\(parts removed for demonstration)||

22 July 2013 by 58.6.237.118 -

Changed lines 174-175 from:

The pinwheel calculator was developed as an improvement on the arithmometer~~, utilising~~ a clever ‘counting gear’ in which the number of teeth protruding could be adjusted by sliders (and later a push-down keyboard). A pinwheel and the internal mechanism (with some pinwheels removed) from a Walther pinwheel calculator in this collection is shown below.

to:

The pinwheel calculator was developed as an improvement on the arithmometer more or less simultaneously in Russia in 1878 by Swedish engineer Willgodt Theophil Odhner (1845-1905) and in the US in 1874, by Frank Stephen Baldwin (1838-1925). Although they worked independently of each there machines were so similar that the 'Ohdner' or 'Baldwin' machine became more or less interchangeable terms.[^Diana H. Hook and Jeremy M. Norman, //Origins of Cyberspace//, Novato, California, 2002, p. 255.^]. The designs utilised a clever ‘counting gear’ in which the number of teeth protruding could be adjusted by sliders (and later a push-down keyboard). A pinwheel and the internal mechanism (with some pinwheels removed) from a Walther pinwheel calculator in this collection is shown below.

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||%center%A single pinwheel||%center% Mechanism of the Walther pinwheel calculator||

to:

||%center%A single pinwheel||%center% Mechanism of the Walther\\pinwheel calculator||

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~~A step drum from~~ a ~~later arithmometer,~~ showing the slider, drum with its 'counting gear' positioned for the input of '5'. In this arithmometer the input number selected shows in the immediately adjacent window. Note the square section axle on which the counting gear moves.

to:

Immediately below is a picture of a step drum from a later arithmometer, but based on the Thomas mechanism, showing the slider, drum with its 'counting gear' positioned for the input of '5'. In this arithmometer the input number selected shows in the immediately adjacent window. Note the square section axle on which the counting gear moves.

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Added lines 128-129:

A step drum from a later arithmometer, showing the slider, drum with its 'counting gear' positioned for the input of '5'. In this arithmometer the input number selected shows in the immediately adjacent window. Note the square section axle on which the counting gear moves.

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[[Site.StepDrumTIM|http://meta-studies.net/pmwiki/uploads/TIMDrum.jpg]]

to:

%center% %height=200px% [[Site.StepDrumTIM|http://meta-studies.net/pmwiki/uploads/TIMDrum.jpg]]
%center%Step drum (in a later 'TIM' arithmometer)\\(collection Calculant)

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[[Site.StepDrumTIM]]

to:

[[Site.StepDrumTIM|http://meta-studies.net/pmwiki/uploads/TIMDrum.jpg]]

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Added lines 129-130:

[[Site.StepDrumTIM]]

Changed lines 176-178 from:

As can be seen above, the pinwheel (left, above) is a thin disk with the slider shown protruding in the top right corner. It is in the '3' position, with the cam slot rotated pushing 3 teeth out (seen between and behind the fixed teeth at the bottom). These then are the teeth that are added by the counting wheel. ~~The pinwheels thus replaced the much larger and more cumbersome step drum~~ of the arithmometers. Being thing and able to be nestled side by side in a compact manner (right, above) these calculators were much lighter and more compact than the arithmometers. The crank handle was conveniently on the right end of the machine, and could be turned either forward or backwards (corresponding to addition or subtraction). The output wheels were set in the base, and as with the arithmometer, the input mechanism (including the pinwheels and sliders) could be moved parallel to it allowing long multiplication and division to be carried out.

to:

As can be seen above, the pinwheel (left, above) is a thin disk with the slider shown protruding in the top right corner. It is in the '3' position, with the cam slot rotated pushing 3 teeth out (seen between and behind the fixed teeth at the bottom). These then are the teeth that are added by the counting wheel. (Click on the image to enlarge.)

These pinwheels thus replaced the much larger and more cumbersome step drums of the arithmometers. Being thing and able to be nestled side by side in a compact manner (right, above) these calculators were much lighter and more compact than the arithmometers. The crank handle was conveniently on the right end of the machine, and could be turned either forward or backwards (corresponding to addition or subtraction). The output wheels were set in the base, and as with the arithmometer, the input mechanism (including the pinwheels and sliders) could be moved parallel to it allowing long multiplication and division to be carried out.

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As can be seen above, the pinwheel (left, above) is a thin disk with the slider shown protruding in the top right corner. It is in the '~~zero~~' position, ~~and as it is~~ rotated ~~clockwise the cam wheel which is shown pushes additional~~ teeth ~~(currently retracted) forward~~. These then are the teeth that are added by the counting wheel. The pinwheels thus replaced the much larger and more cumbersome step drum of the arithmometers. Being thing and able to be nestled side by side in a compact manner (right, above) these calculators were much lighter and more compact than the arithmometers. The crank handle was conveniently on the right end of the machine, and could be turned either forward or backwards (corresponding to addition or subtraction). The output wheels were set in the base, and as with the arithmometer, the input mechanism (including the pinwheels and sliders) could be moved parallel to it allowing long multiplication and division to be carried out.

to:

As can be seen above, the pinwheel (left, above) is a thin disk with the slider shown protruding in the top right corner. It is in the '3' position, with the cam slot rotated pushing 3 teeth out (seen between and behind the fixed teeth at the bottom). These then are the teeth that are added by the counting wheel. The pinwheels thus replaced the much larger and more cumbersome step drum of the arithmometers. Being thing and able to be nestled side by side in a compact manner (right, above) these calculators were much lighter and more compact than the arithmometers. The crank handle was conveniently on the right end of the machine, and could be turned either forward or backwards (corresponding to addition or subtraction). The output wheels were set in the base, and as with the arithmometer, the input mechanism (including the pinwheels and sliders) could be moved parallel to it allowing long multiplication and division to be carried out.

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Changed lines 174-176 from:

As can be seen above, the pinwheel (left) is a thin disk with the slider shown protruding in the top right corner~~, and~~ in a position ~~to reveal~~

In this collection there is the already mentioned very early Brunsviga-Schuster pinwheel calculator from 1896 (an Ohdner Brunsviga which had been re-badged by Schuster who on-sold them).

to:

As can be seen above, the pinwheel (left, above) is a thin disk with the slider shown protruding in the top right corner. It is in the 'zero' position, and as it is rotated clockwise the cam wheel which is shown pushes additional teeth (currently retracted) forward. These then are the teeth that are added by the counting wheel. The pinwheels thus replaced the much larger and more cumbersome step drum of the arithmometers. Being thing and able to be nestled side by side in a compact manner (right, above) these calculators were much lighter and more compact than the arithmometers. The crank handle was conveniently on the right end of the machine, and could be turned either forward or backwards (corresponding to addition or subtraction). The output wheels were set in the base, and as with the arithmometer, the input mechanism (including the pinwheels and sliders) could be moved parallel to it allowing long multiplication and division to be carried out.

In this collection there is the already mentioned very early Brunsviga-Schuster pinwheel calculator from 1896 (an Ohdner Brunsviga which had been re-badged by Schuster who on-sold them).

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Changed lines 168-169 from:

The pinwheel calculator was developed as an improvement on the arithmometer, utilising a clever ‘counting gear’ in which the number of teeth could be adjusted by sliders (and later a push-down keyboard). ~~In this collection there is the already mentioned very early Brunsviga-Schuster pinwheel calculator from 1896 (an Ohdner Brunsviga which had been re-badged by Schuster who on-sold them)~~.

to:

The pinwheel calculator was developed as an improvement on the arithmometer, utilising a clever ‘counting gear’ in which the number of teeth protruding could be adjusted by sliders (and later a push-down keyboard). A pinwheel and the internal mechanism (with some pinwheels removed) from a Walther pinwheel calculator in this collection is shown below.

Changed lines 174-176 from:

to:

As can be seen above, the pinwheel (left) is a thin disk with the slider shown protruding in the top right corner, and in a position to reveal

In this collection there is the already mentioned very early Brunsviga-Schuster pinwheel calculator from 1896 (an Ohdner Brunsviga which had been re-badged by Schuster who on-sold them).

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||%center% %height=~~200px~~%[[Site.DemonstrationPinwheel|http://meta-studies.net/pmwiki/uploads/PinWheelSingle.jpg]]||%center% %height=~~200px~~%[[Site.DemonstrationPinwheelMechanism|http://meta-studies.net/pmwiki/uploads/PinwheelDemo.jpg]]||

to:

||%center% %height=150px%[[Site.DemonstrationPinwheel|http://meta-studies.net/pmwiki/uploads/PinWheelSingle.jpg]]||%center% %height=150px%[[Site.DemonstrationPinwheelMechanism|http://meta-studies.net/pmwiki/uploads/PinwheelDemo.jpg]]||

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[[Site.DemonstrationPinwheel]]
[[Site.DemonstrationPinwheelMechanism]]

|~~|%center% %height=250px%[[Site.DemonstrationPinwheel|~~http://meta-studies.net/pmwiki/uploads/PinWheelSingle.jpg]]||%center% %height=~~250px~~%[[Site.DemonstrationPinwheelMechanism|http://meta-studies.net/pmwiki/uploads/PinwheelDemo.jpg]]||

to:

||%center% %height=200px%[[Site.DemonstrationPinwheel|http://meta-studies.net/pmwiki/uploads/PinWheelSingle.jpg]]||%center% %height=200px%[[Site.DemonstrationPinwheelMechanism|http://meta-studies.net/pmwiki/uploads/PinwheelDemo.jpg]]||

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||%center% %height=250px%[[Site.~~HP-35-1972~~|http://meta-studies.net/pmwiki/uploads/~~HP35~~.jpg]]||%center% %height=250px%[[Site.~~HP-45-1973~~|http://meta-studies.net/pmwiki/uploads/~~HP-45~~.jpg]]||
||%center% ~~July1972\\Hewlett Packard\\HP 35 Calculator\\serial 1230A 79429, 1972||%center% December 1973\\Hewlett Packard\\HP 45 Calculator\\serial 1350A 36719, 1973~~||

to:

||%center% %height=250px%[[Site.DemonstrationPinwheel|http://meta-studies.net/pmwiki/uploads/PinWheelSingle.jpg]]||%center% %height=250px%[[Site.DemonstrationPinwheelMechanism|http://meta-studies.net/pmwiki/uploads/PinwheelDemo.jpg]]||
||%center%A single pinwheel||%center% Mechanism of the Walther pinwheel calculator||

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Changed lines 168-175 from:

The pinwheel calculator was developed as an improvement on the arithmometer, utilising a clever ‘counting gear’ in which the number of teeth could be adjusted by sliders (and later a push-down keyboard). In this collection there is the already mentioned very early Brunsviga-Schuster pinwheel calculator from 1896 (an Ohdner Brunsviga which had been re-badged by Schuster who on-sold them).

to:

The pinwheel calculator was developed as an improvement on the arithmometer, utilising a clever ‘counting gear’ in which the number of teeth could be adjusted by sliders (and later a push-down keyboard). In this collection there is the already mentioned very early Brunsviga-Schuster pinwheel calculator from 1896 (an Ohdner Brunsviga which had been re-badged by Schuster who on-sold them).

[[Site.DemonstrationPinwheel]]
[[Site.DemonstrationPinwheelMechanism]]

||%center% %height=250px%[[Site.HP-35-1972|http://meta-studies.net/pmwiki/uploads/HP35.jpg]]||%center% %height=250px%[[Site.HP-45-1973|http://meta-studies.net/pmwiki/uploads/HP-45.jpg]]||
||%center% July1972\\Hewlett Packard\\HP 35 Calculator\\serial 1230A 79429, 1972||%center% December 1973\\Hewlett Packard\\HP 45 Calculator\\serial 1350A 36719, 1973||
||(collection Calculant)|| ||

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Notes

Added lines 189-200:

See http://ieeexplore.ieee.org.ezp.lib.unimelb.edu.au/stamp/stamp.jsp?tp=&arnumber=4637514

Like arithmometers, Brunsviga calculating machines were lever-set and operated by turning a crank (Figure 3). Instead of stepped drums, they had a pinwheel mechanism that carried out cal- culations. Smaller and lighter than arithmome- ters, they were made from a larger range of ma- terials, including iron and nickel alloys as well as brass and steel. Pinwheel machines had been patented by Frank S. Baldwin and W. T. Odhner. They were successfully marketed by Odhner in Russia and Sweden, and by Brunsviga in Ger- many. They were sold by Marchant in the United States.

See How Calculating Machines Worked

See nice diagrams and descriptions of the three mechanisms.

Kidwell - 'Yours for Improvement" IEEE

Martin

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Thomas ~~himself was the director of an insurance~~ company. In the 1820s the insurance industry was rapidly expanding as a consequence of free trade and the transport revolution, and France had become international centres of the industry.[^Peter Borscheid, "Europe: Overview", in Peter Borscheid and Niels Vigo Haueter (eds), //World Insurance: The Evolution of a Global Risk Network//, Oxford University Press, Oxford, 2012, p. 39.^] ~~Whilst the~~ likely consequent intensification of work no doubt galvanised ~~his~~ interest in finding an efficient way of handling multiple calculations, It is unlikely then that Thomas de Colmar would have been able to spend all or even a great deal of his time on designing and building more arithmometers over the next several decades. Indeed it was not until 1844 that the arithmometer, very much re-designed, appeared at a French national exhibition where it was placed amongst precision instruments in a category of ‘diverse measures, counters and calculating machines’.[^ibid.^] Johnston thus argues that far from being a lone pioneer, the machines of Thomas were in competition (and regarded initially as a poor second) to others. However, over a half century, the machines of Thomas, as they evolved, prevailed.[^As cited by Johnston, Jean Marguin, //Histoire des instruments et machines à calculer//, Paris, 1994, p. 111: ‘Pendant un demi-siècle, la machine y régna seule.’^] Johnston notes that to achieve this "Thomas campaigned both through the press and in commissioned publications. He also engaged in the rituals of patronage, rituals that we might more readily associate with the decoratively elaborate calculating machines of the 18th century."[^Johnston, "Making the arithmometer count".^] However, the design of the Thomas machine was sufficiently beautifully executed to make it an appropriate gift to persons of high standing, a property essential to its successful promotion.

to:

Thomas de Colmar himself was the director of an insurance company. In the 1820s the insurance industry was rapidly expanding as a consequence of free trade and the transport revolution, and France had become international centres of the industry.[^Peter Borscheid, "Europe: Overview", in Peter Borscheid and Niels Vigo Haueter (eds), //World Insurance: The Evolution of a Global Risk Network//, Oxford University Press, Oxford, 2012, p. 39.^] The likely consequent intensification of work no doubt galvanised Thomas's interest in finding an efficient way of handling multiple calculations. But given his responsibilities in an intense commercial environment is unlikely that he would have been able to spend all or even a great deal of his time on designing and building more arithmometers over the next several decades. Indeed it was not until several decades later that, in 1844, the arithmometer, very much re-designed, appeared at a French national exhibition. There it could be found amongst precision instruments in a category of ‘diverse measures, counters and calculating machines’.[^ibid.^] Johnston thus argues that far from being a lone pioneer, the machines of Thomas were in competition (and regarded initially as a poor second) to others. However, over a half century, the machines of Thomas, as they evolved, prevailed.[^As cited by Johnston, Jean Marguin, //Histoire des instruments et machines à calculer//, Paris, 1994, p. 111: ‘Pendant un demi-siècle, la machine y régna seule.’^] Johnston notes that to achieve this "Thomas campaigned both through the press and in commissioned publications. He also engaged in the rituals of patronage, rituals that we might more readily associate with the decoratively elaborate calculating machines of the 18th century."[^Johnston, "Making the arithmometer count".^] However, the design of the Thomas machine was sufficiently beautifully executed to make it an appropriate gift to persons of high standing, a property essential to its successful promotion.

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Deleted lines 174-175:

There is also a later Ohdner from 1938 and a Facit calculator from around 1945, and then from near the end of production of such machines, from the 1950s a very nice demonstration Walther 160 calculator, showing its mechanism, complemented by a complete and fully operational Walther of the same model.

Changed lines 183-186 from:

~~Of course~~ this is a broad brush description of the various mechanisms. Many variations. Eg Frieden's cam timed "Frieden wheel". Described very well elsewhere - eg Martin, Rechnerlexicon and Wolff.

to:

In the pinwheels in this collection there is a later Ohdner from 1938 and a Facit calculator from around 1945, and then from near the end of production of such machines, from the 1950s a very nice demonstration Walther 160 calculator, showing its mechanism, complemented by a complete and fully operational Walther of the same model.

this is a broad brush description of the various mechanisms. Many variations. Eg Frieden's cam timed "Frieden wheel". Described very well elsewhere - eg Martin, Rechnerlexicon and Wolff.

Added line 284:

This was what might be called the "First Vanishing Point" - the point at which all the arithmetic operations and common scientific functions required for calculation became available in a single small electronic calculator, capable of being carried on a belt or in a shirt pocket (albeit in serious peril of it falling out when one bent over to pick something up). Electronic calculators now proliferated throughout the developed and developing world displacing the rigours of mental arithmetic and caught in an 'arms race' to make them smaller, more powerful, easier to use, and find a niche in a highly competitive and very cluttered market. It would be another two decades before what might be labelled the "Second Vanishing Point" - the point at which these electronic calculators began to disappear, displaced now by "virtual calculators" encoded in the software of desk and lap-top computers, tablets, smart phones, and much else. From that vantage point, not only the mechanical calculators of only 20 years before, but even the stand-alone electronic calculator, were already fading into the misty light of receding memory.

21 July 2013 by 58.6.237.118 -

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A much sought after goal for calculator designers was to develop a method which would completely automatically carry out division. All the previous ~~machines~~ required a process of "long division" where the divisor was subtracted until no more subtractions were possible. However, this required the operator to either guess when this point had been reached, or subtract one time too many (creating an "overflow") and then reversing the subtraction to get the correct outcome. In the third machine above, a method was developed which allowed the machine to anticipate when this point had been reached, and advance the carriage. The a MADAS arithmometer was developed by Erwin Janz and manufactured by Egli in Zurich, starting in 1913. The acronym MADAS was short for “Multiplication, Addition, Division - Automatically, Substraction”). As already noted this machine achieved an entirely automatic division process - the first ever for an arithmometer style calculator. In this collection there is a MADAS IX Maxima calculator (produced in 1917), an ambitious machine also in that it could accept 9 digits, up to one thousand million, as input and could display 16 digits (representing numbers up to ten thousand trillion) in its results register. Two MADAS models were produced and by 1920 about 1,000 were being produced with some 7,000 having been sold from countries as wide apart as Europe and Australia.[^Martin Reese, Hamburg, //55 erfolgreiche Jahre: MADAS-Rechenautomaten aus der Schweiz 1913 - 1968//, http://www.rechnerlexikon.de/files/MADAS—8-2010.pdf, viewed 18 February 2012.^]

to:

A much sought after goal for calculator designers was to develop a method which would completely automatically carry out division. All the previous arithmometers required a process of "long division" where the divisor was subtracted until no more subtractions were possible. However, this required the operator to either guess when this point had been reached, or subtract one time too many (creating an "overflow") and then reversing the subtraction to get the correct outcome. In the third machine above, a method was developed which allowed the machine to anticipate when this point had been reached, and advance the carriage. The a MADAS arithmometer was developed by Erwin Janz and manufactured by Egli in Zurich, starting in 1913. The acronym MADAS was short for “Multiplication, Addition, Division - Automatically, Substraction”). As already noted this machine achieved an entirely automatic division process - the first ever for an arithmometer style calculator. In this collection there is a MADAS IX Maxima calculator (produced in 1917), an ambitious machine also in that it could accept 9 digits, up to one thousand million, as input and could display 16 digits (representing numbers up to ten thousand trillion) in its results register. Two MADAS models were produced and by 1920 about 1,000 were being produced with some 7,000 having been sold from countries as wide apart as Europe and Australia.[^Martin Reese, Hamburg, //55 erfolgreiche Jahre: MADAS-Rechenautomaten aus der Schweiz 1913 - 1968//, http://www.rechnerlexikon.de/files/MADAS—8-2010.pdf, viewed 18 February 2012.^]

21 July 2013 by 58.6.237.118 -

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A much sought after goal for calculator designers was to develop a method which would completely automatically carry out division. All the previous machines required a process of "long division" where the divisor was subtracted until no more subtractions were possible. However, this required the operator to either guess when this point had been reached, or subtract one time too many (creating an "overflow") and then reversing the subtraction to get the correct outcome. In the third machine above, a method was developed which allowed the machine to anticipate when this point had been reached, and advance the carriage. The a MADAS arithmometer was developed by Erwin Janz and manufactured by Egli in Zurich, starting in 1913. The acronym MADAS was short for “Multiplication, Addition, Division - Automatically, Substraction”). As already noted this machine achieved an entirely automatic division process - the first ever for an arithmometer style calculator. In this collection there is a MADAS IX Maxima calculator (produced in 1917), an ambitious machine also in that it could accept 9 digits, up to one thousand million, as input and could display 16 digits (representing numbers up to ten thousand trillion) in its results register. Two MADAS models were produced and by 1920 about 1,000 were being produced with some 7,000 having been sold from countries as wide apart as ~~Germany~~ and Australia.[^Martin Reese, Hamburg, //55 erfolgreiche Jahre: MADAS-Rechenautomaten aus der Schweiz 1913 - 1968//, http://www.rechnerlexikon.de/files/MADAS—8-2010.pdf, viewed 18 February 2012.^]

to:

A much sought after goal for calculator designers was to develop a method which would completely automatically carry out division. All the previous machines required a process of "long division" where the divisor was subtracted until no more subtractions were possible. However, this required the operator to either guess when this point had been reached, or subtract one time too many (creating an "overflow") and then reversing the subtraction to get the correct outcome. In the third machine above, a method was developed which allowed the machine to anticipate when this point had been reached, and advance the carriage. The a MADAS arithmometer was developed by Erwin Janz and manufactured by Egli in Zurich, starting in 1913. The acronym MADAS was short for “Multiplication, Addition, Division - Automatically, Substraction”). As already noted this machine achieved an entirely automatic division process - the first ever for an arithmometer style calculator. In this collection there is a MADAS IX Maxima calculator (produced in 1917), an ambitious machine also in that it could accept 9 digits, up to one thousand million, as input and could display 16 digits (representing numbers up to ten thousand trillion) in its results register. Two MADAS models were produced and by 1920 about 1,000 were being produced with some 7,000 having been sold from countries as wide apart as Europe and Australia.[^Martin Reese, Hamburg, //55 erfolgreiche Jahre: MADAS-Rechenautomaten aus der Schweiz 1913 - 1968//, http://www.rechnerlexikon.de/files/MADAS—8-2010.pdf, viewed 18 February 2012.^]

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A much sought after goal for calculator designers was to develop a method which would completely automatically carry out division. All the previous machines required a process of "long division" where the divisor was subtracted until no more subtractions were possible. However, this required the operator to either guess when this point had been reached, or subtract one time too many (creating an "overflow") and then reversing the subtraction to get the correct outcome. In the third machine above, a method was developed which allowed the machine to anticipate when this point had been reached, and advance the carriage. The a MADAS arithmometer was developed by Erwin Janz and manufactured by Egli in Zurich, starting in 1913. The acronym MADAS was short for “Multiplication, Addition, Division - Automatically, Substraction”). As already noted this machine achieved an entirely automatic division process - the first ever for an arithmometer style calculator. In this collection there is a MADAS IX Maxima calculator (produced in 1917), an ambitious machine also in that it could accept 9 digits, up to one thousand million, as input and could display 16 digits (representing numbers up to ten thousand trillion) in its results register.

to:

A much sought after goal for calculator designers was to develop a method which would completely automatically carry out division. All the previous machines required a process of "long division" where the divisor was subtracted until no more subtractions were possible. However, this required the operator to either guess when this point had been reached, or subtract one time too many (creating an "overflow") and then reversing the subtraction to get the correct outcome. In the third machine above, a method was developed which allowed the machine to anticipate when this point had been reached, and advance the carriage. The a MADAS arithmometer was developed by Erwin Janz and manufactured by Egli in Zurich, starting in 1913. The acronym MADAS was short for “Multiplication, Addition, Division - Automatically, Substraction”). As already noted this machine achieved an entirely automatic division process - the first ever for an arithmometer style calculator. In this collection there is a MADAS IX Maxima calculator (produced in 1917), an ambitious machine also in that it could accept 9 digits, up to one thousand million, as input and could display 16 digits (representing numbers up to ten thousand trillion) in its results register. Two MADAS models were produced and by 1920 about 1,000 were being produced with some 7,000 having been sold from countries as wide apart as Germany and Australia.[^Martin Reese, Hamburg, //55 erfolgreiche Jahre: MADAS-Rechenautomaten aus der Schweiz 1913 - 1968//, http://www.rechnerlexikon.de/files/MADAS—8-2010.pdf, viewed 18 February 2012.^]

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||1890-1900 ||A. M. Stevenson Adder||Joliet, Ill.\\||2 Wheel||%height=~~75px~~%[[Stevenson1890| http://meta-studies.net/pmwiki/uploads/Stevenson.png]]||
||1903 ||Adix Adding Machine\\Original model||Manheim||Key input\\lever &\\gears||%height=~~75px~~%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/Adix.png]]||
||1910 ||Adall Adding Machine||Dreyfus\\and Levy ||Key input\\Concentric \\toothed disk\\and groove||%height=~~75px~~%[[Site.Adall1910| http://meta-studies.net/pmwiki/uploads/Adall.jpg]]||
||~1946 ||Lightning Portable\\Adding Machine||Lightning\\Adding Machine\\Co. L.A.||7 Wheels||%height=~~75px~~%[[Site.Lightning1946| http://meta-studies.net/pmwiki/uploads/Lightning.png]]||
||1968 ||SEE Demonstration\\Adding Machine||Selective Educational\\Equipment Corporation||4 Wheels||%height=~~75px~~%[[Site.SEE1968| http://meta-studies.net/pmwiki/uploads/SEE-1.jpg]]||

to:

||1890-1900 ||A. M. Stevenson Adder||Joliet, Ill.\\||2 Wheel||%height=100px%[[Stevenson1890| http://meta-studies.net/pmwiki/uploads/Stevenson.png]]||
||1903 ||Adix Adding Machine\\Original model||Manheim||Key input\\lever &\\gears||%height=100px%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/Adix.png]]||
||1910 ||Adall Adding Machine||Dreyfus\\and Levy ||Key input\\Concentric \\toothed disk\\and groove||%height=100px%[[Site.Adall1910| http://meta-studies.net/pmwiki/uploads/Adall.jpg]]||
||~1946 ||Lightning Portable\\Adding Machine||Lightning\\Adding Machine\\Co. L.A.||7 Wheels||%height=100px%[[Site.Lightning1946| http://meta-studies.net/pmwiki/uploads/Lightning.png]]||
||1968 ||SEE Demonstration\\Adding Machine||Selective Educational\\Equipment Corporation||4 Wheels||%height=100px%[[Site.SEE1968| http://meta-studies.net/pmwiki/uploads/SEE-1.jpg]]||

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||1910-20s||Comptator (9 col)||Schubert\\& Salzer||Chain||%height=~~75px~~%[[Site.Comptator1910|http://meta-studies.net/pmwiki/uploads/Comptator.png]]||
||~1915||Golden Gem Automatic\\Adding Machine||H. & H. Goldmann||Chain||%height=~~75px~~%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg]]||
||1920||Addiator Troncet adder||Ruthard & Co||Chain||%height=~~75px~~%[[Site.Addiator1920 |http://meta-studies.net/pmwiki/uploads/Addiator.png]]||
||1922||Scribola 10 column\\printing\\Adding Machine||Addiator Gesellschaft||Rod||%height=~~75px~~%[[Site.Scribola1922 |http://meta-studies.net/pmwiki/uploads/Scribola.jpg]]||
||1937||Add-O-Matic\\Adding Machine||Allied MFG. Co.||Chain||%height=~~75px~~%[[Site.Add-O-Matic1937 |http://meta-studies.net/pmwiki/uploads/AddOMatic1.jpg]]||

to:

||1910-20s||Comptator (9 col)||Schubert\\& Salzer||Chain||%height=100px%[[Site.Comptator1910|http://meta-studies.net/pmwiki/uploads/Comptator.png]]||
||~1915||Golden Gem Automatic\\Adding Machine||H. & H. Goldmann||Chain||%height=100px%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg]]||
||1920||Addiator Troncet adder||Ruthard & Co||Chain||%height=100px%[[Site.Addiator1920 |http://meta-studies.net/pmwiki/uploads/Addiator.png]]||
||1922||Scribola 10 column\\printing\\Adding Machine||Addiator Gesellschaft||Rod||%height=100px%[[Site.Scribola1922 |http://meta-studies.net/pmwiki/uploads/Scribola.jpg]]||
||1937||Add-O-Matic\\Adding Machine||Allied MFG. Co.||Chain||%height=100px%[[Site.Add-O-Matic1937 |http://meta-studies.net/pmwiki/uploads/AddOMatic1.jpg]]||

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||~1957 || Walther WSR160\\Pinwheel Calculator||Walther||Pinwheel||%height=100px%[[Site.Walther1957| http://meta-studies.net/pmwiki/uploads/Walther.png]]||
||~1957 || Walther WSR160\\Demonstration\\Pinwheel Calculator||Walther||Demonstration\\Pinwheel||%height=100px%[[Site.WaltherDemonstrator1957| http://meta-studies.net/pmwiki/uploads/WaltherDemo.png]]||

to:

||~1957 ||Walther WSR160\\Pinwheel Calculator||Walther||Pinwheel||%height=100px%[[Site.Walther1957| http://meta-studies.net/pmwiki/uploads/Walther.png]]||
||~1957 ||Walther WSR160\\Demonstration\\Pinwheel Calculator||Walther||Demonstration\\Pinwheel||%height=100px%[[Site.WaltherDemonstrator1957| http://meta-studies.net/pmwiki/uploads/WaltherDemo.png]]||

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||1909 ||TIM (Time is Money)\\ Arithmometer||Ludwig Spitz\\ & Co||Arithmometer||%height=~~75px~~%[[Site.TIM1909| http://meta-studies.net/pmwiki/uploads/TIM.JPG]]||
||~1913 ||Bunzel-Denton Arithmometer||Bunzel||Prototype\\Front Crank||%height=~~75px~~%[[Site.BunzelPrototype1913| http://meta-studies.net/pmwiki/uploads/Bunzel.JPG]]||
||~1917 ||Madas IX Maxima||Madas||Auto Division||%height=~~75px~~%[[Site.Madas-IX-Maxima| http://meta-studies.net/pmwiki/uploads/MADAS-1917.jpg]]||

to:

||1909 ||TIM (Time is Money)\\ Arithmometer||Ludwig Spitz\\ & Co||Arithmometer||%height=100px%[[Site.TIM1909| http://meta-studies.net/pmwiki/uploads/TIM.JPG]]||
||~1913 ||Bunzel-Denton Arithmometer||Bunzel||Prototype\\Front Crank||%height=100px%[[Site.BunzelPrototype1913| http://meta-studies.net/pmwiki/uploads/Bunzel.JPG]]||
||~1917 ||Madas IX Maxima||Madas||Auto Division||%height=100px%[[Site.Madas-IX-Maxima| http://meta-studies.net/pmwiki/uploads/MADAS-1917.jpg]]||

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%center% %height=~~150px~~%[[Site.Webb1869| http://meta-studies.net/pmwiki/uploads/Webb.jpg]]

to:

%center% %height=200px%[[Site.Webb1869| http://meta-studies.net/pmwiki/uploads/Webb.jpg]]

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%center%%height=~~100px~~%[[Site.Locke1901| http://meta-studies.net/pmwiki/uploads/Locke.gif]]

to:

%center%%height=150px%[[Site.Locke1901| http://meta-studies.net/pmwiki/uploads/Locke.gif]]

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!To be continued
**This essay is under construction - especially what follows. If it is ever finished (:-) it is intended to utilise this collection to shape a continuing if idiosyncratic story of the development of embodied calculation up to the introduction of personal electronic calculation. So do visit again if you have got this far, and there may (should) be more.**

Added lines 162-164:

!To be continued
**This essay is under construction - especially what follows. If it is ever finished (:-) it is intended to utilise this collection to shape a continuing if idiosyncratic story of the development of embodied calculation up to the introduction of personal electronic calculation. So do visit again if you have got this far, and there may (should) be more.**

21 July 2013 by 58.6.237.118 -

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The above three arithmometers demonstrate the sorts of improvements to the basic arithmometer design which now emerged. The first, a TIM (“Time is Money” ) arithmometer manufactured by Ludwig Spitz and Co. of Berlin-Tempelhof in 1909 was greatly strengthened from the Thomas design to create a much more robust and reliable machine. First produced in a wooden box it was later made much stronger by installing it in a cast iron frame which held all parts rigidly.[^See Ernst Martin, //The Calculating Machines (Die Rechenmaschinen): Their History and Development//, ed. and trs. by Peggy Aldridge Kidwell and Michael R. Williams, MIT Press, Mass., 1992, p. 191–4]^ Beginning a change in style that would be emulated in many other machines the brass panels were now enamelled black consistent with the management, industrial and commercial settings where it was intended to find its market.

Burkhardt in Austria produced the first Austrian version of the Thomas machine, and later improvements were marketed in association with Bunzel. Hugo Bunzel, a former caligraphy teacher in Prague, designed the machines that became known as the Bunzel-Delton. The were manufactured by the Bunzel- Delton-Werk Fabrik automatischer Schreib-und Kechenmaschinen in Vienna.[^ibid. p 198.^] The second machine above is of interest since it is a one of its kind prototype made by these workshops. It shows the "arms race" that was now underway between competitive designs. Already another radically different design of calculator (the pinwheel described below) had emerged to compete with the arithmometer. Its crank handle was mounted on the side of the machine, making it much easier to turn than the top mounted handle of the traditional arithmometer.

The ~~MADAS~~ arithmometer ~~(above, standing for “Multiplication, Addition, Division - Automatically, Substraction”) was developed by Erwin Janz and manufactured by Egli in Zurich, starting in 1913~~. ~~As the acronym suggests, this machine achieved an entirely automatic division process - the first ever for an arithmometer style calculator~~. ~~In this collection there is a MADAS IX Maxima calculator (produced in 1917) which could display 16 numbers~~ in its results register.

to:

The above three arithmometers demonstrate the sorts of improvements to the basic arithmometer design which now emerged. The first, a TIM (“Time is Money” ) arithmometer manufactured by Ludwig Spitz and Co. of Berlin-Tempelhof in 1909 was greatly strengthened from the Thomas design to create a much more robust and reliable machine. First produced in a wooden box it was later made much stronger by installing it in a cast iron frame which held all parts rigidly.[^See Ernst Martin, //The Calculating Machines (Die Rechenmaschinen): Their History and Development//, ed. and trs. by Peggy Aldridge Kidwell and Michael R. Williams, MIT Press, Mass., 1992, p. 191–4^] Beginning a change in style that would be emulated in many other machines the brass panels were now enamelled black consistent with the management, industrial and commercial settings where it was intended to find its market.

Burkhardt in Austria produced the first Austrian version of the Thomas machine, and later improvements were marketed in association with Bunzel. Hugo Bunzel, a former caligraphy teacher in Prague, designed the machines that became known as the Bunzel-Delton. The were manufactured by the Bunzel- Delton-Werk Fabrik automatischer Schreib-und Kechenmaschinen in Vienna.[^ibid. p 198.^] The second machine above is of interest since it is a one of its kind prototype made by these workshops. It shows the "arms race" that was now underway between competitive designs. Already another radically different design of calculator (the pinwheel described below) had emerged to compete with the arithmometer. Its crank handle was mounted on the side of the machine, making it much easier to turn than the top mounted handle of the traditional arithmometer. The second arithmometer in this collection above seems to encapsulate a [[http://worldwide.espacenet.com/publicationDetails/mosaics;jsessionid=344FC5328A2BB5BB997876E83E30C740.espacenet_levelx_prod_0?CC=AT&NR=64952B&KC=B&FT=D&date=19140525&DB=&&locale=en_EP|patent]] filed by Bunzel on May 25, 1914, for enabling the position of the crank to be shifted from its normal position standing upright on the deck to one where it is horizontal on the side of the machine mimicking the convenience presented by the pinwheel. Indicative though this is, the prototype was never put into production.

A much sought after goal for calculator designers was to develop a method which would completely automatically carry out division. All the previous machines required a process of "long division" where the divisor was subtracted until no more subtractions were possible. However, this required the operator to either guess when this point had been reached, or subtract one time too many (creating an "overflow") and then reversing the subtraction to get the correct outcome. In the third machine above, a method was developed which allowed the machine to anticipate when this point had been reached, and advance the carriage. The a MADAS arithmometer was developed by Erwin Janz and manufactured by Egli in Zurich, starting in 1913. The acronym MADAS was short for “Multiplication, Addition, Division - Automatically, Substraction”). As already noted this machine achieved an entirely automatic division process - the first ever for an arithmometer style calculator. In this collection there is a MADAS IX Maxima calculator (produced in 1917), an ambitious machine also in that it could accept 9 digits, up to one thousand million, as input and could display 16 digits (representing numbers up to ten thousand trillion) in its results register.

21 July 2013 by 58.6.237.118 -

Changed line 161 from:

The above three arithmometers demonstrate the sorts of improvements to the basic arithmometer design which now emerged. The first, a TIM (“Time is Money” ) arithmometer manufactured by Ludwig Spitz and Co. of Berlin-Tempelhof in 1909 was greatly strengthened from the Thomas design to create a much more robust and reliable machine. First produced in a wooden box it was later made much stronger by installing it in a cast iron frame which held all parts rigidly.[^(See Ernst Martin, //The Calculating Machines (Die Rechenmaschinen): Their History and Development//, ed. and trs. by Peggy Aldridge Kidwell and Michael R. Williams, MIT Press, Mass., 1992, p. 191–4)]^ Beginning a change in style that would be emulated in many other machines the brass panels were now enamelled black consistent with the management, industrial and commercial settings where it was intended to find its market.

to:

The above three arithmometers demonstrate the sorts of improvements to the basic arithmometer design which now emerged. The first, a TIM (“Time is Money” ) arithmometer manufactured by Ludwig Spitz and Co. of Berlin-Tempelhof in 1909 was greatly strengthened from the Thomas design to create a much more robust and reliable machine. First produced in a wooden box it was later made much stronger by installing it in a cast iron frame which held all parts rigidly.[^See Ernst Martin, //The Calculating Machines (Die Rechenmaschinen): Their History and Development//, ed. and trs. by Peggy Aldridge Kidwell and Michael R. Williams, MIT Press, Mass., 1992, p. 191–4]^ Beginning a change in style that would be emulated in many other machines the brass panels were now enamelled black consistent with the management, industrial and commercial settings where it was intended to find its market.

21 July 2013 by 58.6.237.118 -

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%center% %height=~~250px~~% [[Site.ThomasDeColmar1884|http://meta-studies.net/pmwiki/uploads/ThomasDeColmar.jpg]]

to:

%center% %height=300px% [[Site.ThomasDeColmar1884|http://meta-studies.net/pmwiki/uploads/ThomasDeColmar.jpg]]

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!!!!Comptometers
A further approach to the problem of the ~~four functions is found in the American invention by Felt,~~ of ~~a device that he called the comptometer and patented in 1887~~. ~~It performs the task of addition by a system of keys and levers. Notably no crank handle needs to be turned in order to perform the addition~~. ~~And the process of multiplication is done by multiple presses of the number~~. As already mentioned, in this collection we have one of the first models of the comptomoter - one from 1896 cased in wood? and one of the 40 oldest known to still be in existence,

%center% %height=250px% [[Site.ComptometerWoodie1896|http://meta-studies.net/pmwiki/uploads/ComptometerWoodie.png]]
%center% 1896: Felt and Tarrant Comptometer\\Earliest - wood-cased model, serial 2491\\

to:

!!!!Pinwheels
The pinwheel calculator was developed as an improvement on the arithmometer, utilising a clever ‘counting gear’ in which the number of teeth could be adjusted by sliders (and later a push-down keyboard). In this collection there is the already mentioned very early Brunsviga-Schuster pinwheel calculator from 1896 (an Ohdner Brunsviga which had been re-badged by Schuster who on-sold them).

%center% %height=250px% [[Site.BrunsvigaSchuster1896|http://meta-studies.net/pmwiki/uploads/Brunsviga1896.png]]
%center% Brunsviga Schuster Pinwheel Calculator ~1896\\Serial 3406\\

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~~Addition of~~ a ~~number automatically occurs whenever~~ a ~~corresponding key is pressed. This is fast. But subtraction must be carried out by addition of complementary numbers. Carrying of “tens” must be done by addition. The comptometer was~~ a ~~highly successful innovation and was sufficiently cheap and useful to reach a broad market~~. Characterised by extremely effective marketing and capable of being mass produced the device continued to be marketed for some 80 years unusually for such innovations leaving its inventor extremely wealthy. By then its essential mechanism was being utilised by more than one company. Shown below is the remaining comptometer in this collection, this time made of plastic in the 1950s by the British Bell Punch company. Also shown is a demonstration model showing the keys and lever system used in the Bell Punch machine.

to:

There is also a later Ohdner from 1938 and a Facit calculator from around 1945, and then from near the end of production of such machines, from the 1950s a very nice demonstration Walther 160 calculator, showing its mechanism, complemented by a complete and fully operational Walther of the same model.

Changed lines 179-180 from:

||~~1950s~~ ||~~Bell Sumlock Comptometer||Bell Sumlock~~||~~Model 909/S/117.878~~||%height=100px%[[Site.~~SumlockComptometer1950s~~| http://meta-studies.net/pmwiki/uploads/~~Sumlock~~.png]]||
||~~~1955~~||~~Bell Punch Sumlock~~ ||~~Bell Punch~~||~~Demonstration\\Comptometer~~||%height=100px%[[Site.~~SumlockDemonstrator1955~~| ~~http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png]]~~||

to:

||1945 ||Facit Model S Calculator\\serial 210652||Facit||Pinwheel||%height=100px%[[Site.Facit1945| http://meta-studies.net/pmwiki/uploads/Facit.png]]||
||~1951||Original Ohdner Model 39\\serial 39-288965||Ohdner||Pinwheel||%height=100px%[[Site.OriginalOhdner39-1951|Add Picture]]||
||~1957 || Walther WSR160\\Pinwheel Calculator||Walther||Pinwheel||%height=100px%[[Site.Walther1957| http://meta-studies.net/pmwiki/uploads/Walther.png]]||
||~1957 || Walther WSR160\\Demonstration\\Pinwheel Calculator||Walther||Demonstration\\Pinwheel||%height=100px%[[Site.WaltherDemonstrator1957| http://meta-studies.net/pmwiki/uploads/WaltherDemo.png]]||

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!!!!Pinwheels
The pinwheel calculator was developed as an improvement on the arithmometer, utilising a clever ‘counting gear’ in which the number of teeth could be adjusted by sliders (and later a push-down keyboard). In this collection there is the already mentioned very early Brunsviga-Schuster pinwheel calculator from 1896 (an Ohdner Brunsviga which had been re-badged by Schuster who on-sold them).

%center% %height=250px% [[Site.BrunsvigaSchuster1896|http://meta-studies.net/pmwiki/uploads/Brunsviga1896.png]]
%center% Brunsviga Schuster Pinwheel Calculator ~1896\\Serial 3406\\
%center% (collection Calculant)

There is also a later Ohdner from 1938 and a Facit calculator from around 1945, and then from near the end of production of such machines, from the 1950s a very nice demonstration Walther 160 calculator, showing its mechanism, complemented by a complete and fully operational Walther of the same model.

||Date||Description||Maker||Type||Device (click for greater detail)||
||1945 ||Facit Model S Calculator\\serial 210652||Facit||Pinwheel||%height=100px%[[Site.Facit1945| http://meta-studies.net/pmwiki/uploads/Facit.png]]||
||~1951||Original Ohdner Model 39\\serial 39-288965||Ohdner||Pinwheel||%height=100px%[[Site.OriginalOhdner39-1951|Add Picture]]||
||~1957 || Walther WSR160\\Pinwheel Calculator||Walther||Pinwheel||%height=100px%[[Site.Walther1957| http://meta-studies.net/pmwiki/uploads/Walther.png]]||
||~1957 || Walther WSR160\\Demonstration\\Pinwheel Calculator||Walther||Demonstration\\Pinwheel||%height=100px%[[Site.WaltherDemonstrator1957| http://meta-studies.net/pmwiki/uploads/WaltherDemo.png]]||
(collection Calculant - all above)

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!!!!Comptometers
A further approach to the problem of the four functions is found in the American invention by Felt, of a device that he called the comptometer and patented in 1887. It performs the task of addition by a system of keys and levers. Notably no crank handle needs to be turned in order to perform the addition. And the process of multiplication is done by multiple presses of the number. As already mentioned, in this collection we have one of the first models of the comptomoter - one from 1896 cased in wood? and one of the 40 oldest known to still be in existence,

%center% %height=250px% [[Site.ComptometerWoodie1896|http://meta-studies.net/pmwiki/uploads/ComptometerWoodie.png]]
%center% 1896: Felt and Tarrant Comptometer\\Earliest - wood-cased model, serial 2491\\
%center% (collection Calculant)

Addition of a number automatically occurs whenever a corresponding key is pressed. This is fast. But subtraction must be carried out by addition of complementary numbers. Carrying of “tens” must be done by addition. The comptometer was a highly successful innovation and was sufficiently cheap and useful to reach a broad market. Characterised by extremely effective marketing and capable of being mass produced the device continued to be marketed for some 80 years unusually for such innovations leaving its inventor extremely wealthy. By then its essential mechanism was being utilised by more than one company. Shown below is the remaining comptometer in this collection, this time made of plastic in the 1950s by the British Bell Punch company. Also shown is a demonstration model showing the keys and lever system used in the Bell Punch machine.

||Date||Description||Maker||Type||Device (click for greater detail)||
||1950s ||Bell Sumlock Comptometer||Bell Sumlock||Model 909/S/117.878||%height=100px%[[Site.SumlockComptometer1950s| http://meta-studies.net/pmwiki/uploads/Sumlock.png]]||
||~1955||Bell Punch Sumlock ||Bell Punch||Demonstration\\Comptometer||%height=100px%[[Site.SumlockDemonstrator1955| http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png]]||
(collection Calculant - all above)

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The above three arithmometers demonstrate the sorts of improvements to the basic arithmometer design which now emerged. The first, a TIM (“Time is Money” ) arithmometer from 1909

which was by now designed as a more robust arithmometer, mounted now in an all steel frame. Burkhardt in Austria produced the first Austrian version of the Thomas machine, and later improvements were marketed in association with Bunzel.

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The above three arithmometers demonstrate the sorts of improvements to the basic arithmometer design which now emerged. The first, a TIM (“Time is Money” ) arithmometer manufactured by Ludwig Spitz and Co. of Berlin-Tempelhof in 1909 was greatly strengthened from the Thomas design to create a much more robust and reliable machine. First produced in a wooden box it was later made much stronger by installing it in a cast iron frame which held all parts rigidly.[^(See Ernst Martin, //The Calculating Machines (Die Rechenmaschinen): Their History and Development//, ed. and trs. by Peggy Aldridge Kidwell and Michael R. Williams, MIT Press, Mass., 1992, p. 191–4)]^ Beginning a change in style that would be emulated in many other machines the brass panels were now enamelled black consistent with the management, industrial and commercial settings where it was intended to find its market.

Burkhardt in Austria produced the first Austrian version of the Thomas machine, and later improvements were marketed in association with Bunzel. Hugo Bunzel, a former caligraphy teacher in Prague, designed the machines that became known as the Bunzel-Delton. The were manufactured by the Bunzel- Delton-Werk Fabrik automatischer Schreib-und Kechenmaschinen in Vienna.[^ibid. p 198.^] The second machine above is of interest since it is a one of its kind prototype made by these workshops. It shows the "arms race" that was now underway between competitive designs. Already another radically different design of calculator (the pinwheel described below) had emerged to compete with the arithmometer. Its crank handle was mounted on the side of the machine, making it much easier to turn than the top mounted handle of the traditional arithmometer.

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The time was ripe for others to attempt to produce improved machines. The Thomas concept was developed and improved by a number of other engineers and marketed from different countries.[^P. A. Kidwell, "American Scientists and Calculating Machines- From Novelty to Commonplace", Annals of the History of Computing, Volume 12, Number 1, 1990, pp. 31^] From 1880, other manufacturers - Burkhardt, Layton, Saxonia, ~~Bunzel~~, etc entered the market. ~~Some later~~ arithmometers in this collection ~~are shown~~ below.

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The time was ripe for others to attempt to produce improved machines. The Thomas concept was developed and improved by a number of other engineers and marketed from different countries.[^P. A. Kidwell, "American Scientists and Calculating Machines- From Novelty to Commonplace", Annals of the History of Computing, Volume 12, Number 1, 1990, pp. 31^] From 1880, other European manufacturers - Burkhardt, Layton, Saxonia, Egli, Bunzel, etc entered the market. The three arithmometers from this collection, below, are products of this now enlarging set of competing manufacturers and designers.

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~~subsequent devices - TIM (“Time is Money” ) from 1909~~ which was by now designed as a more robust arithmometer, mounted now in an all steel frame. Burkhardt in Austria produced the first Austrian version of the Thomas machine, and later improvements were marketed in association with Bunzel.

to:

The above three arithmometers demonstrate the sorts of improvements to the basic arithmometer design which now emerged. The first, a TIM (“Time is Money” ) arithmometer from 1909

which was by now designed as a more robust arithmometer, mounted now in an all steel frame. Burkhardt in Austria produced the first Austrian version of the Thomas machine, and later improvements were marketed in association with Bunzel.

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Indeed the Thomas arithmometer did take off as a consumer product in France, the UK and Europe and variants continued to sell right up to the first world war. They were not cheap. For example, in 1872 British engineer Henry Brunel wrote that "I have just got what my mother irreverently calls ‘a new toy’ – to wit a calculating machine price £12 which does all the common operations of arithmetic viz addition, multiplication, subtraction & division in the twinkling of an eye. It is really a very useful article worth its weight in brass."[^ Brunel to Adams, 18 March 1866, Bristol University Library, Brunel Collection, Letter Book VII, f. 106, cited in Johnston, ibid.^] In terms of today's purchasing power, £12 from 1872

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Indeed the Thomas arithmometer did take off as a consumer product in France, the UK and Europe and variants continued to sell right up to the first world war. They were not cheap. For example, in 1872 British engineer Henry Brunel wrote that "I have just got what my mother irreverently calls ‘a new toy’ – to wit a calculating machine price £12 which does all the common operations of arithmetic viz addition, multiplication, subtraction & division in the twinkling of an eye. It is really a very useful article worth its weight in brass."[^ Brunel to Adams, 18 March 1866, Bristol University Library, Brunel Collection, Letter Book VII, f. 106, cited in Johnston, ibid.^] In terms of today's purchasing power, £12 from 1872 was the equivalent of £5,840 (~US$8,900) in 2013 (based on average earnings).[^Calculated using the [[http://www.measuringworth.com]] calculator on 21 July 2013^]

Not surprisingly, the commercial background of Thomas de Colmar gave him a head start in knowing how to manage, promote, and sell his product, and that, must in part be the clue to its success. By the turn of the century Thomas de Colmar arithmometers found homes in science laboratories (particularly astronomical observatories), insurance and engineering companies, and government departments (especially those dealing with finances).

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The ~~Thomas design was copied~~ and improved by a number of other engineers and marketed from different countries.[^P. A. Kidwell, "American Scientists and Calculating Machines- From Novelty to Commonplace", Annals of the History of Computing, Volume 12, Number 1, 1990, pp. 31^] From 1880, other manufacturers - Burkhardt, Layton, Saxonia, Bunzel, etc entered the market. Some later arithmometers in this collection are shown below.

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The repairs carried out on this machine were not uncharacteristic of what was required to keep the arithmometer in reliable working order. The machines however were subject to breakage and expensive to repair. The market for such an expensive machine was quite limited, and despite its uprecedented success, as Johnston concludes, that Thomas's work on the machine still fell "more into the category of vanity publishing than mass production".[^ibid^] Nevertheless, it formed the standard against which improvements were sought and new designs contemplated.

The time was ripe for others to attempt to produce improved machines. The Thomas concept was developed and improved by a number of other engineers and marketed from different countries.[^P. A. Kidwell, "American Scientists and Calculating Machines- From Novelty to Commonplace", Annals of the History of Computing, Volume 12, Number 1, 1990, pp. 31^] From 1880, other manufacturers - Burkhardt, Layton, Saxonia, Bunzel, etc entered the market. Some later arithmometers in this collection are shown below.

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Thomas himself was the director of an insurance company~~, which no doubt galvanised his interest in finding an efficient way~~ of ~~handling multiple calculations, but in the 1820s the insurance industry was rapidly expanding as a consequence of free trade and the transport revolution, and France had become international centres~~ of ~~the industry.[^Peter Borscheid, "Europe: Overview", in Peter Borscheid and Niels Vigo Haueter (eds), //World Insurance: The Evolution~~ of a Global Risk Network//, Oxford University Press, Oxford, 2012, p. 39.^] It is unlikely then that Thomas de Colmar spent all or even a great deal of his time on building more such machines over the next several decades. Indeed it was not until 1844 that the ~~arithmometer, very much re-designed, appeared at a French national exhibition where it was placed amongst precision instruments in~~ a category of ‘diverse measures, counters and calculating machines’.[^ibid.^] Johnston thus argues that far from being a lone pioneer, the machines of Thomas were in competition (and regarded initially as a poor second) to others. However, over a half century, the machines of Thomas, as they evolved, prevailed.~~[^As cited by Johnston, Jean Marguin~~, ~~//Histoire des instruments et machines à calculer//~~, ~~Paris, 1994, p~~. ~~111: ‘Pendant un demi-siècle, la machine y régna seule.’^] Johnston notes that to achieve this "Thomas campaigned both through the press and in commissioned publications~~. ~~He also engaged in the rituals of patronage, rituals that we might more readily associate with the decoratively elaborate calculating machines~~ of ~~the 18th century."[^Johnston, "Making the arithmometer count".^] However,~~ the ~~design of the Thomas machine was sufficiently beautifully executed to make it an appropriate gift to persons~~ of ~~high standing, a property essential to its successful~~ promotion.

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Thomas himself was the director of an insurance company. In the 1820s the insurance industry was rapidly expanding as a consequence of free trade and the transport revolution, and France had become international centres of the industry.[^Peter Borscheid, "Europe: Overview", in Peter Borscheid and Niels Vigo Haueter (eds), //World Insurance: The Evolution of a Global Risk Network//, Oxford University Press, Oxford, 2012, p. 39.^] Whilst the likely consequent intensification of work no doubt galvanised his interest in finding an efficient way of handling multiple calculations, It is unlikely then that Thomas de Colmar would have been able to spend all or even a great deal of his time on designing and building more arithmometers over the next several decades. Indeed it was not until 1844 that the arithmometer, very much re-designed, appeared at a French national exhibition where it was placed amongst precision instruments in a category of ‘diverse measures, counters and calculating machines’.[^ibid.^] Johnston thus argues that far from being a lone pioneer, the machines of Thomas were in competition (and regarded initially as a poor second) to others. However, over a half century, the machines of Thomas, as they evolved, prevailed.[^As cited by Johnston, Jean Marguin, //Histoire des instruments et machines à calculer//, Paris, 1994, p. 111: ‘Pendant un demi-siècle, la machine y régna seule.’^] Johnston notes that to achieve this "Thomas campaigned both through the press and in commissioned publications. He also engaged in the rituals of patronage, rituals that we might more readily associate with the decoratively elaborate calculating machines of the 18th century."[^Johnston, "Making the arithmometer count".^] However, the design of the Thomas machine was sufficiently beautifully executed to make it an appropriate gift to persons of high standing, a property essential to its successful promotion.

Indeed the Thomas arithmometer did take off as a consumer product in France, the UK and Europe and variants continued to sell right up to the first world war. They were not cheap. For example, in 1872 British engineer Henry Brunel wrote that "I have just got what my mother irreverently calls ‘a new toy’ – to wit a calculating machine price £12 which does all the common operations of arithmetic viz addition, multiplication, subtraction & division in the twinkling of an eye. It is really a very useful article worth its weight in brass."[^ Brunel to Adams, 18 March 1866, Bristol University Library, Brunel Collection, Letter Book VII, f. 106, cited in Johnston, ibid.^] In terms of today's purchasing power, £12 from 1872

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Thomas himself was the director of an insurance company, which no doubt galvanised his interest in finding an efficient way of handling multiple calculations, but ~~business would have been expanding with the economy and it is unlikely that he~~ spent all or even a great deal of his time on building more such machines over the next several decades. Indeed it was not until 1844 that the arithmometer, very much re-designed, appeared at a French national exhibition where it was placed amongst precision instruments in a category of ‘diverse measures, counters and calculating machines’.[^ibid.^] Johnston thus argues that far from being a lone pioneer, the machines of Thomas were in competition (and regarded initially as a poor second) to others. However, over a half century, the machines of Thomas, as they evolved, prevailed.[^As cited by Johnston, Jean Marguin, //Histoire des instruments et machines à calculer//, Paris, 1994, p. 111: ‘Pendant un demi-siècle, la machine y régna seule.’^] Johnston notes that to achieve this "Thomas campaigned both through the press and in commissioned publications. He also engaged in the rituals of patronage, rituals that we might more readily associate with the decoratively elaborate calculating machines of the 18th century."[^Johnston, "Making the arithmometer count".^] However, the design of the Thomas machine was sufficiently beautifully executed to make it an appropriate gift to persons of high standing, a property essential to its successful promotion.

to:

Thomas himself was the director of an insurance company, which no doubt galvanised his interest in finding an efficient way of handling multiple calculations, but in the 1820s the insurance industry was rapidly expanding as a consequence of free trade and the transport revolution, and France had become international centres of the industry.[^Peter Borscheid, "Europe: Overview", in Peter Borscheid and Niels Vigo Haueter (eds), //World Insurance: The Evolution of a Global Risk Network//, Oxford University Press, Oxford, 2012, p. 39.^] It is unlikely then that Thomas de Colmar spent all or even a great deal of his time on building more such machines over the next several decades. Indeed it was not until 1844 that the arithmometer, very much re-designed, appeared at a French national exhibition where it was placed amongst precision instruments in a category of ‘diverse measures, counters and calculating machines’.[^ibid.^] Johnston thus argues that far from being a lone pioneer, the machines of Thomas were in competition (and regarded initially as a poor second) to others. However, over a half century, the machines of Thomas, as they evolved, prevailed.[^As cited by Johnston, Jean Marguin, //Histoire des instruments et machines à calculer//, Paris, 1994, p. 111: ‘Pendant un demi-siècle, la machine y régna seule.’^] Johnston notes that to achieve this "Thomas campaigned both through the press and in commissioned publications. He also engaged in the rituals of patronage, rituals that we might more readily associate with the decoratively elaborate calculating machines of the 18th century."[^Johnston, "Making the arithmometer count".^] However, the design of the Thomas machine was sufficiently beautifully executed to make it an appropriate gift to persons of high standing, a property essential to its successful promotion.

21 July 2013 by 124.170.43.18 -

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Thomas himself was the director of an insurance company, which no doubt galvanised his interest in finding an efficient way of handling multiple calculations, but business would have been expanding with the economy and it is unlikely that he spent all or even a great deal of his time on building more such machines over the next several decades. Indeed it was not until 1844 that the arithmometer, very much re-designed, appeared at a French national exhibition where it was placed amongst precision instruments in a category of ‘diverse measures, counters and calculating machines’.[^ibid.^] Johnston thus argues ~~with support~~ from ~~Marguin that far from being a lone pioneer, the machines of Thomas were in competition (and regarded initially as a poor second) to others. However~~, ~~over a half century~~, ~~the machines of Thomas~~, ~~as they evolved,~~ prevailed.[^As cited by Johnston, Jean Marguin, //Histoire des instruments et machines à calculer//, Paris, 1994, p. 111: ‘Pendant un demi-siècle, la machine y régna seule.’ Johnston notes that to achieve this "Thomas campaigned both through the press and in commissioned publications. He also engaged in the rituals of patronage, rituals that we might more readily associate with the decoratively elaborate calculating machines of the 18th century."[^Johnston, "Making the arithmometer count".^] However, the design of the Thomas machine ~~still reflected this need, and was sufficiently beautifully executed~~ to ~~make it an appropriate gift to persons of high standing~~.

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Thomas himself was the director of an insurance company, which no doubt galvanised his interest in finding an efficient way of handling multiple calculations, but business would have been expanding with the economy and it is unlikely that he spent all or even a great deal of his time on building more such machines over the next several decades. Indeed it was not until 1844 that the arithmometer, very much re-designed, appeared at a French national exhibition where it was placed amongst precision instruments in a category of ‘diverse measures, counters and calculating machines’.[^ibid.^] Johnston thus argues that far from being a lone pioneer, the machines of Thomas were in competition (and regarded initially as a poor second) to others. However, over a half century, the machines of Thomas, as they evolved, prevailed.[^As cited by Johnston, Jean Marguin, //Histoire des instruments et machines à calculer//, Paris, 1994, p. 111: ‘Pendant un demi-siècle, la machine y régna seule.’^] Johnston notes that to achieve this "Thomas campaigned both through the press and in commissioned publications. He also engaged in the rituals of patronage, rituals that we might more readily associate with the decoratively elaborate calculating machines of the 18th century."[^Johnston, "Making the arithmometer count".^] However, the design of the Thomas machine was sufficiently beautifully executed to make it an appropriate gift to persons of high standing, a property essential to its successful promotion.

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Thomas de Colmar first made public his design for a calculating machine capable of doing all four functions (addition, subtraction, multiplication and division) when he was granted a patent for it in 1820.[^Patent no. 1420, 18 November 1820^]. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.[^For the most authoritative website on the Thomas de Colmar machines and history see Valéry Monier's magisterial site [[http://www.arithmometre.org]], viewed 20 July 2013.^] The first design consisted of four step drums (along the lines invented by Leibniz, but not necessarily based on having ever heard of, let alone seen the internal mechanism of Leibniz's invention[^Friedrich W. Kistermann, "When Could Anyone Have Seen Leibniz’s Stepped Wheel?", //IEEE Annals of the History of Computing//, Volume 21, Number 2, 1999, pp. 68-72.^]).

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Thomas de Colmar first made public his design for a calculating machine capable of doing all four functions (addition, subtraction, multiplication and division) when he was granted a patent for it in 1820.[^Patent no. 1420, 18 November 1820^]. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.[^For the most authoritative website on the Thomas de Colmar machines and history see Valéry Monier's magisterial site [[http://www.arithmometre.org]], viewed 20 July 2013.^] The first design consisted of four step drums (along the lines invented by Leibniz, but not necessarily based on having ever heard of, let alone seen the internal mechanism of Leibniz's invention[^see Friedrich W. Kistermann, "When Could Anyone Have Seen Leibniz’s Stepped Wheel?", //IEEE Annals of the History of Computing//, Volume 21, Number 2, 1999, pp. 68-72. However, as Stephen Johnston (see reference below) points out, images of Leibniz's machine were available from the late C18, see for example 1744 engraving in Annegret Kehrbaum and Bernhard Korte, //Calculi: Bilder des Rechnens einst und heute (Images of Computing in Olden and Modern Times)//, Opladen, 1995, p. 61.^]).

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As with previous calculating machines that commercial success of this machine was far from assured. The aesthetics of the design still reflects the high status market where it could have become just another prestigious mathematical machine in the cabinets of curiosities of those of elevated status. The somewhat circuitous route to that later success is described by Stephen Johnston. [^Stephen Johnston, "Making the arithmometer count", //Bulletin of the Scientific Instrument Society//, Volume 52, 1997, pp. 12-21.^] As Johnston notes, Thomas did not of course make these early machines. The first of his machines to survive was made by in Paris by Devrine, as usual a local clockmaker.

Thomas himself was the director of an insurance company, which no doubt galvanised his interest in finding an efficient way of handling multiple calculations, but business would have been expanding with the economy and it is unlikely that he spent all or even a great deal of his time on building more such machines over the next several decades. Indeed it was not until 1844 that the arithmometer, very much re-designed, ~~appeared at a French national~~ exhibition.[^ibid.^]

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As with previous calculating machines that commercial success of this machine was far from assured. The aesthetics of the design still reflects the high status market where it could have become just another prestigious mathematical machine in the cabinets of curiosities of those of elevated status. The somewhat circuitous route to that later success is described by Stephen Johnston. [^Stephen Johnston, "Making the arithmometer count", //Bulletin of the Scientific Instrument Society//, Volume 52, 1997, pp. 12-21.^] As Johnston notes, Thomas did not of course make these early machines. The first of his machines to survive was made by in Paris by Devrine, as usual a local clock (and instrument) maker.

Thomas himself was the director of an insurance company, which no doubt galvanised his interest in finding an efficient way of handling multiple calculations, but business would have been expanding with the economy and it is unlikely that he spent all or even a great deal of his time on building more such machines over the next several decades. Indeed it was not until 1844 that the arithmometer, very much re-designed, appeared at a French national exhibition where it was placed amongst precision instruments in a category of ‘diverse measures, counters and calculating machines’.[^ibid.^] Johnston thus argues with support from Marguin that far from being a lone pioneer, the machines of Thomas were in competition (and regarded initially as a poor second) to others. However, over a half century, the machines of Thomas, as they evolved, prevailed.[^As cited by Johnston, Jean Marguin, //Histoire des instruments et machines à calculer//, Paris, 1994, p. 111: ‘Pendant un demi-siècle, la machine y régna seule.’ Johnston notes that to achieve this "Thomas campaigned both through the press and in commissioned publications. He also engaged in the rituals of patronage, rituals that we might more readily associate with the decoratively elaborate calculating machines of the 18th century."[^Johnston, "Making the arithmometer count".^] However, the design of the Thomas machine still reflected this need, and was sufficiently beautifully executed to make it an appropriate gift to persons of high standing.

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As with previous calculating machines that commercial success of this machine was far from assured. The aesthetics of the design still reflects the high status market where it could have become just another prestigious mathematical machine in the cabinets of curiosities of those of elevated status. The somewhat circuitous route to that later success is described by Stephen Johnston. [^Stephen Johnston, "Making the arithmometer count", //Bulletin of the Scientific Instrument Society//, Volume 52, 1997, pp. 12-21.^] As Johnston notes, Thomas did not of course make these early machines. The first of his machines to survive was made by in Paris by Devrine, as usual a local clockmaker. ~~Thomas~~ himself was the director of an insurance company and it is unlikely that he spent all or even a great deal of his time on building more such machines over the next several decades. Indeed it was not until 1844 that the arithmometer, very much re-designed, appeared at a French national exhibition.[^ibid.^]

to:

As with previous calculating machines that commercial success of this machine was far from assured. The aesthetics of the design still reflects the high status market where it could have become just another prestigious mathematical machine in the cabinets of curiosities of those of elevated status. The somewhat circuitous route to that later success is described by Stephen Johnston. [^Stephen Johnston, "Making the arithmometer count", //Bulletin of the Scientific Instrument Society//, Volume 52, 1997, pp. 12-21.^] As Johnston notes, Thomas did not of course make these early machines. The first of his machines to survive was made by in Paris by Devrine, as usual a local clockmaker.

Thomas himself was the director of an insurance company, which no doubt galvanised his interest in finding an efficient way of handling multiple calculations, but business would have been expanding with the economy and it is unlikely that he spent all or even a great deal of his time on building more such machines over the next several decades. Indeed it was not until 1844 that the arithmometer, very much re-designed, appeared at a French national exhibition.[^ibid.^]

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As with previous calculating machines that commercial success of this machine was far from assured. The aesthetics of the design still reflects the high status market where it could have become just another prestigious mathematical machine in the cabinets of curiosities of those of elevated status. ~~Indeed many of the early Thomas machines did~~ ~~The somewhat circuitous route to that later success is described by Stephen Johnston. [^Stephen Johnston~~, ~~"Making the arithmometer count", //Bulletin of the Scientific Instrument Society//, Volume 52, 1997, pp. 12-21~~.^]

to:

As with previous calculating machines that commercial success of this machine was far from assured. The aesthetics of the design still reflects the high status market where it could have become just another prestigious mathematical machine in the cabinets of curiosities of those of elevated status. The somewhat circuitous route to that later success is described by Stephen Johnston. [^Stephen Johnston, "Making the arithmometer count", //Bulletin of the Scientific Instrument Society//, Volume 52, 1997, pp. 12-21.^] As Johnston notes, Thomas did not of course make these early machines. The first of his machines to survive was made by in Paris by Devrine, as usual a local clockmaker. Thomas himself was the director of an insurance company and it is unlikely that he spent all or even a great deal of his time on building more such machines over the next several decades. Indeed it was not until 1844 that the arithmometer, very much re-designed, appeared at a French national exhibition.[^ibid.^]

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By the time Thomas died, in May 1870, some 800 arithmometers had been made. His son, Thomas de Bojano then took over manufacturing. Thomas de Bojano died in 1881 and Thomas's grandson, the Compte de Ronseray, continued manufacturing arithmometers under the management of Payen. By 1878 some 1500 Thomas arithmometers had been constructed. Some 180 Thomas arithmometers are known to have survived to the present, of which 110 are in public collections and 50 in private collections. Below is ~~shown~~ the Thomas Arithmometer in this collection, which is from 1884.

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By the time Thomas died, in May 1870, some 800 arithmometers had been made. His son, Thomas de Bojano then took over manufacturing. Thomas de Bojano died in 1881 and Thomas's grandson, the Compte de Ronseray, continued manufacturing arithmometers under the management of Payen. By 1878 some 1500 Thomas arithmometers had been constructed. Some 180 Thomas arithmometers are known to have survived to the present, of which 110 are in public collections and 50 in private collections. Below is the Thomas Arithmometer in this collection, which is from 1884.

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By the time Thomas died, in May 1870, some 800 arithmometers had been made. His son, Thomas de Bojano then took over manufacturing. Thomas de Bojano died in 1881 and Thomas's grandson, the Compte de Ronseray, continued manufacturing arithmometers under the management of Payen. By 1878 some 1500 Thomas arithmometers had been constructed. Below is shown the Thomas Arithmometer in this collection, which is from 1884.

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By the time Thomas died, in May 1870, some 800 arithmometers had been made. His son, Thomas de Bojano then took over manufacturing. Thomas de Bojano died in 1881 and Thomas's grandson, the Compte de Ronseray, continued manufacturing arithmometers under the management of Payen. By 1878 some 1500 Thomas arithmometers had been constructed. Some 180 Thomas arithmometers are known to have survived to the present, of which 110 are in public collections and 50 in private collections. Below is shown the Thomas Arithmometer in this collection, which is from 1884.

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The above arithmometer demonstrates the high level of usability that the firm of Thomas had now achieved. It allows the multiplication of two numbers each as large as 9 million and the result can be read out to 16 places. Ivory markers are provided for the decimal point (and to delineate hundreds, thousands and millions for ease of use). The clearing and carry mechanisms are entirely reliable. Indeed, ~~this particular machine still operates reliably some 125 years after it was made. Indicating that its owner was serious about~~ its ~~use~~ the machine appears to have been re-mounted by the famous instrument maker, Stanley, (sometime after 1900) in a better quality and stronger box fixed to a cast iron frame. This allows the machine to be tilted at a suitable angle for easy use. As the only surviving Thomas known to have this improvement, this machine seems to stand as a precursor to later innovations under Payen when he added a (rather less robust) hinged tilt base to his machines.

to:

The above arithmometer demonstrates the high level of usability that the firm of Thomas had now achieved. It allows the multiplication of two numbers each as large as 9 million and the result can be read out to 16 places. Ivory markers are provided for the decimal point (and to delineate hundreds, thousands and millions for ease of use). The clearing and carry mechanisms are entirely reliable. Indeed, still bearing its original varnish, this particular machine operates reliably some 125 years after it was made. Indicating that its owner was serious about its use in practice the machine appears to have been re-mounted by the famous instrument maker, Stanley, (sometime after 1900) in a better quality and stronger box fixed to a cast iron frame. This allows the machine to be tilted at a suitable angle for easy use. As the only surviving Thomas known to have this improvement, this machine seems to stand as a precursor to later innovations under Payen when he added a (rather less robust) hinged tilt base to his machines.

21 July 2013 by 124.170.43.18 -

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The above arithmometer demonstrates the high level of usability that the firm of Thomas had now achieved. This particular machine still operates reliably some 125 years after it was made. Indicating that its owner was serious about its use the machine appears to have been re-mounted by the famous instrument maker, ~~Stanley (sometime after 1900), in a better quality~~ and ~~stronger box fixed to a cast iron frame which~~ allows the machine to be tilted at a suitable angle for easy use. As the only surviving Thomas known to have this improvement, this machine seems to stand as a precursor to later innovations under Payen when he added a (rather less robust) hinged tilt base to his machines.

to:

The above arithmometer demonstrates the high level of usability that the firm of Thomas had now achieved. It allows the multiplication of two numbers each as large as 9 million and the result can be read out to 16 places. Ivory markers are provided for the decimal point (and to delineate hundreds, thousands and millions for ease of use). The clearing and carry mechanisms are entirely reliable. Indeed, this particular machine still operates reliably some 125 years after it was made. Indicating that its owner was serious about its use the machine appears to have been re-mounted by the famous instrument maker, Stanley, (sometime after 1900) in a better quality and stronger box fixed to a cast iron frame. This allows the machine to be tilted at a suitable angle for easy use. As the only surviving Thomas known to have this improvement, this machine seems to stand as a precursor to later innovations under Payen when he added a (rather less robust) hinged tilt base to his machines.

21 July 2013 by 124.170.43.18 -

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The above arithmometer demonstrates the high level of usability that the firm of Thomas had now achieved. This particular machine still operates reliably some 125 years after it was made. Indicating that its owner was serious about its use the machine appears to have been re-mounted by the famous instrument maker, Stanley (sometime after 1900), in a better quality and stronger box fixed to a cast iron ~~tilt~~ frame ~~for ease of use. As the only Thomas~~ to have this improvement, this machine seems to stand as a precursor to later innovations under Payen when he added a (rather less robust) hinged tilt base to his machines.

to:

The above arithmometer demonstrates the high level of usability that the firm of Thomas had now achieved. This particular machine still operates reliably some 125 years after it was made. Indicating that its owner was serious about its use the machine appears to have been re-mounted by the famous instrument maker, Stanley (sometime after 1900), in a better quality and stronger box fixed to a cast iron frame which allows the machine to be tilted at a suitable angle for easy use. As the only surviving Thomas known to have this improvement, this machine seems to stand as a precursor to later innovations under Payen when he added a (rather less robust) hinged tilt base to his machines.

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Thomas de Colmar first made public his design for a calculating machine capable of doing all four functions (addition, subtraction, multiplication and division) when he was granted a patent for it in 1820.[^Patent no. 1420, 18 November 1820^]. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.[^For the most authoritative website on the Thomas de Colmar machines and history see Valéry Monier's magisterial site [[http://www.arithmometre.org]], viewed 20 July 2013.^] The somewhat circuitous route to that later success is described by Stephen Johnston. [^Stephen Johnston, "Making the arithmometer count", //Bulletin of the Scientific Instrument Society//, Volume 52, 1997, pp. 12-21.^] The first design consisted of four step drums (along the lines invented by Leibniz, but not necessarily based on having ever heard of, let alone seen the internal mechanism of Leibniz's invention[^Friedrich W. Kistermann, "When Could Anyone Have Seen Leibniz’s Stepped Wheel?", //IEEE Annals of the History of Computing//, Volume 21, Number 2, 1999, pp. 68-72.^]).

to:

Thomas de Colmar first made public his design for a calculating machine capable of doing all four functions (addition, subtraction, multiplication and division) when he was granted a patent for it in 1820.[^Patent no. 1420, 18 November 1820^]. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.[^For the most authoritative website on the Thomas de Colmar machines and history see Valéry Monier's magisterial site [[http://www.arithmometre.org]], viewed 20 July 2013.^] The first design consisted of four step drums (along the lines invented by Leibniz, but not necessarily based on having ever heard of, let alone seen the internal mechanism of Leibniz's invention[^Friedrich W. Kistermann, "When Could Anyone Have Seen Leibniz’s Stepped Wheel?", //IEEE Annals of the History of Computing//, Volume 21, Number 2, 1999, pp. 68-72.^]).

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The above diagram shows the crank handle on the right top which drives the rotation of the step drum (shown centre right). In front of the crank handle can be seen a "slider nob" which moves the cog along the axle to engage with correct number of teeth of the step drum. To the ~~right~~ is a ~~clearing~~ mechanism ~~and output~~ dial. The ~~lever for~~ the ~~carry mechanism is also shown. But~~ the Thomas arithmometer did not really have a reliable carry mechanism until a patented mechanism was introduced in 1865, and this remained the fundamental system for carry arithmometers for the next 50 years.

to:

The above diagram shows the crank handle on the right top which drives the rotation of the step drum (shown centre right). In front of the crank handle can be seen a "slider nob" which moves the cog along the axle to engage with correct number of teeth of the step drum. To the left is a reversing mechanism connected to an output dial. The reversing mechanism allows the output dial to be rotated in the opposite direction, if the nob that activates it (situated above) is shifted from the "addition" to the "subtraction" position.

The Thomas was arranged so that the input mechanism could be shifted in relation to the output dials. In this way it was possible to carry out "long multiplications" (by repeated additions) or "long division" (by repeated subtraction). However, in the early decades the machine was not particularly reliable. In particular, the Thomas arithmometer did not really have a reliable carry mechanism until a patented mechanism was introduced in 1865, and this remained the fundamental system for carry arithmometers for the next 50 years.

As with previous calculating machines that commercial success of this machine was far from assured. The aesthetics of the design still reflects the high status market where it could have become just another prestigious mathematical machine in the cabinets of curiosities of those of elevated status. Indeed many of the early Thomas machines did The somewhat circuitous route to that later success is described by Stephen Johnston. [^Stephen Johnston, "Making the arithmometer count", //Bulletin of the Scientific Instrument Society//, Volume 52, 1997, pp. 12-21.^]

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The above arithmometer demonstrates the high level of usability that the firm of Thomas had now achieved. This particular machine still operates reliably some 125 years after it was made. Indicating that its owner was serious about its use the machine appears to have been re-mounted by the famous instrument maker, Stanley (sometime after 1900), in a better quality and stronger box fixed to a cast iron tilt frame for ease of use. As the only Thomas to have this improvement, this machine seems to stand as a precursor to later innovations under Payen when he added a (rather less robust) hinged tilt base to his machines.

21 July 2013 by 124.170.43.18 -

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Whether or not Thomas reinvented the step drum, even in this first design, the four integers to be added (or subtracted) were set by sliding four corresponding cogs to the appropriate position on such drums. The cogs were moved by sliding nobs along four (square section) axles which were in turn attached to output ~~cylinders~~ which showed the correct number through small windows. A carry mechanism was incorporated. Rather than being turned by a crank handle the stepped drums were turned by a ribbon that was pulled out from the side. All later designs used a crank handle to turn the drums as is shown in the diagram by Franz Reuleaux in 1862.

to:

Whether or not Thomas reinvented the step drum, even in this first design, the four integers to be added (or subtracted) were set by sliding four corresponding cogs to the appropriate position on such drums. The cogs were moved by sliding nobs along four (square section) axles which were in turn attached to output dial wheels which showed the correct number through small windows. A carry mechanism was incorporated. Rather than being turned by a crank handle the stepped drums were turned by a ribbon that was pulled out from the side. All later designs used a crank handle to turn the drums as is shown in the diagram by Franz Reuleaux in 1862.

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%center%1862: Diagram of the Thomas de Colmar arithmometer mechanism.[^ Franz Reuleaux, //Die Thomas’sche Rechenmaschine//, Freiberg, 1862 reproduced in Reuleaux’s article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^]\\(~~Source: Museum of~~ the ~~History of Science, University of Oxford.~~)

The Thomas design was copied and improved by a number of other engineers and marketed from different countries.[^P. A. Kidwell, "American Scientists and Calculating Machines- From Novelty to Commonplace", Annals of the History of ~~Computing, Volume 12, Number 1, 1990, pp.~~ ~~31^]~~

to:

%center%1862: Diagram of the Thomas de Colmar arithmometer mechanism.[^ Franz Reuleaux, //Die Thomas’sche Rechenmaschine//, Freiberg, 1862 reproduced in Reuleaux’s article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^]\\ (click on the image for an enlargement)\\(Source: Museum of the History of Science, University of Oxford.)

The above diagram shows the crank handle on the right top which drives the rotation of the step drum (shown centre right). In front of the crank handle can be seen a "slider nob" which moves the cog along the axle to engage with correct number of teeth of the step drum. To the right is a clearing mechanism and output dial. The lever for the carry mechanism is also shown. But the Thomas arithmometer did not really have a reliable carry mechanism until a patented mechanism was introduced in 1865, and this remained the fundamental system for carry arithmometers for the next 50 years.

By the time Thomas died, in May 1870, some 800 arithmometers had been made. His son, Thomas de Bojano then took over manufacturing. Thomas de Bojano died in 1881 and Thomas's grandson, the Compte de Ronseray, continued manufacturing arithmometers under the management of Payen. By 1878 some 1500 Thomas arithmometers had been constructed. Below is shown the Thomas Arithmometer in this collection, which is from 1884.

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subsequent devices - TIM (“Time is Money” ) from 1909 which was by now designed as a more robust arithmometer, mounted now in an all steel frame. Burkhardt in Austria produced the first Austrian version of the Thomas machine, ~~and later improvements were marketed in association with Bunzel.~~

to:

The Thomas design was copied and improved by a number of other engineers and marketed from different countries.[^P. A. Kidwell, "American Scientists and Calculating Machines- From Novelty to Commonplace", Annals of the History of Computing, Volume 12, Number 1, 1990, pp. 31^] From 1880, other manufacturers - Burkhardt, Layton, Saxonia, Bunzel, etc entered the market. Some later arithmometers in this collection are shown below.

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subsequent devices - TIM (“Time is Money” ) from 1909 which was by now designed as a more robust arithmometer, mounted now in an all steel frame. Burkhardt in Austria produced the first Austrian version of the Thomas machine, and later improvements were marketed in association with Bunzel.

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%center%1862: Diagram of the Thomas de Colmar arithmometer mechanism.[^ Franz Reuleaux, //Die Thomas’sche Rechenmaschine//, Freiberg, 1862 reproduced in Reuleaux’s article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^]

Source: Museum of the History of Science, University of ~~Oxford~~

to:

%center%1862: Diagram of the Thomas de Colmar arithmometer mechanism.[^ Franz Reuleaux, //Die Thomas’sche Rechenmaschine//, Freiberg, 1862 reproduced in Reuleaux’s article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^]\\(Source: Museum of the History of Science, University of Oxford.)

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Whether or not Thomas reinvented the step drum, even in this first design, the four integers to be added (or subtracted) were set by sliding four corresponding cogs to the appropriate position on such drums. The cogs were moved by sliding nobs along four (square section) axles which were in turn attached to output cylinders which showed the correct number through small windows. A carry mechanism was incorporated. Rather than being turned by a crank handle the stepped drums were turned by a ribbon that was pulled out from the side.

to:

Whether or not Thomas reinvented the step drum, even in this first design, the four integers to be added (or subtracted) were set by sliding four corresponding cogs to the appropriate position on such drums. The cogs were moved by sliding nobs along four (square section) axles which were in turn attached to output cylinders which showed the correct number through small windows. A carry mechanism was incorporated. Rather than being turned by a crank handle the stepped drums were turned by a ribbon that was pulled out from the side. All later designs used a crank handle to turn the drums as is shown in the diagram by Franz Reuleaux in 1862.

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%center%1862: Diagram of the Thomas de Colmar arithmometer mechanism.[^ Franz Reuleaux, //Die Thomas’sche Rechenmaschine//, Freiberg, 1862 reproduced in Reuleaux’s article in //Der Civilingenieur//, 8, 1862, and reproduced in turn by Johnston, "Making the arithmometer count", figure 2.^]

Source: Museum of the History of Science, University of Oxford

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%center%%height=200px%[[Site.ThomasMechanism|http://meta-studies.net/pmwiki/uploads/Misc/ThomasMechRel.jpg]]

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Thomas de Colmar first made public his design for a calculating machine capable of doing all four functions (addition, subtraction, multiplication and division) when he was granted a patent for it in 1820.[^Patent no. 1420, 18 November 1820^]. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.[^For the most authoritative website on the Thomas de Colmar machines and history see Valéry Monier's magisterial site [[http://www.arithmometre.org]], viewed 20 July 2013.^] The somewhat circuitous route to that later success is described by Stephen Johnston. [^Stephen Johnston, "Making the arithmometer count", //Bulletin of the Scientific Instrument Society//, Volume 52, 1997, pp. 12-21.^]

~~Thomas de Colmar arithmometer (1884) Each represents a different mechanical approach to digitally carrying out the four functions, with an easy input~~, ~~and a digital readout. Each then was improved through a series of innovations, first by the original inventors, and then as more players across the world competed to produce and market better variants~~.~~%0a %0aThomas de Colmar was~~ the ~~first person to produce a commercially useable calculator based on Leibnitz’s stepped drum principle, and he named his machine the “arithmometer”.~~ The Thomas design was copied and improved by a number of other engineers and marketed from different countries.[^P. A. Kidwell, "American Scientists and Calculating Machines- From Novelty to Commonplace", Annals of the History of Computing, Volume 12, Number 1, 1990, pp. 31^]

to:

Thomas de Colmar first made public his design for a calculating machine capable of doing all four functions (addition, subtraction, multiplication and division) when he was granted a patent for it in 1820.[^Patent no. 1420, 18 November 1820^]. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.[^For the most authoritative website on the Thomas de Colmar machines and history see Valéry Monier's magisterial site [[http://www.arithmometre.org]], viewed 20 July 2013.^] The somewhat circuitous route to that later success is described by Stephen Johnston. [^Stephen Johnston, "Making the arithmometer count", //Bulletin of the Scientific Instrument Society//, Volume 52, 1997, pp. 12-21.^] The first design consisted of four step drums (along the lines invented by Leibniz, but not necessarily based on having ever heard of, let alone seen the internal mechanism of Leibniz's invention[^Friedrich W. Kistermann, "When Could Anyone Have Seen Leibniz’s Stepped Wheel?", //IEEE Annals of the History of Computing//, Volume 21, Number 2, 1999, pp. 68-72.^]).

Whether or not Thomas reinvented the step drum, even in this first design, the four integers to be added (or subtracted) were set by sliding four corresponding cogs to the appropriate position on such drums. The cogs were moved by sliding nobs along four (square section) axles which were in turn attached to output cylinders which showed the correct number through small windows. A carry mechanism was incorporated. Rather than being turned by a crank handle the stepped drums were turned by a ribbon that was pulled out from the side.

The Thomas design was copied and improved by a number of other engineers and marketed from different countries.[^P. A. Kidwell, "American Scientists and Calculating Machines- From Novelty to Commonplace", Annals of the History of Computing, Volume 12, Number 1, 1990, pp. 31^]

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||%center% July1972~~: Hewlett Packard~~\\~~HP 35 Calculator~~\\~~serial 1230A 79429, 1972~~\\ ~~(second version)\\(collection Calculant)~~||%center% December 1973~~: Hewlett Packard~~\\~~HP 45 Calculator~~\\~~serial 1350A~~ 36719, 1973||

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||%center% July1972\\Hewlett Packard\\HP 35 Calculator\\serial 1230A 79429, 1972||%center% December 1973\\Hewlett Packard\\HP 45 Calculator\\serial 1350A 36719, 1973||
||(collection Calculant)|| ||

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*The slide rule had used the motion of sliding along a straight line to add distances representing a logarithmic scale. *The devices of Schickard, Pascal and Leibniz had used rotation of dials to achieve addition of rotations. Schickard's machine had the capacity to subtract by turning the dials backwards, but had not fully resolved how to carry from one dial to another.

to:

*The slide rule had used the motion of sliding along a straight line to add distances representing a logarithmic scale.
*The devices of Schickard, Pascal and Leibniz had used rotation of dials to achieve addition of rotations. Schickard's machine had the capacity to subtract by turning the dials backwards, but had not fully resolved how to carry from one dial to another.

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~1929 “Herzstark” electric Calculating Machine serial 6549, badged by Herzstark, Vienna; essentially Badenia Model TE 13 Duplex

It features an electric motor, still in good working order, and with a keyboard instead of sliders for input. The features of it were not only that it had a keyboard for input, but also a control mechanism consisting of a column of keys which enabled a number to be entered and then added through 0 to 8 repeats representing multiplication by one to nine.

to:

This calculator features its original electric motor, still in good working order, and with a keyboard instead of sliders for input. The features of it were not only that it had a keyboard for input, but also a control mechanism consisting of a column of keys which enabled a number to be entered and then added through 0 to 8 repeats representing multiplication by one to nine.

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~~As well as Haman (and the Mercedes-Euklid) mentioned earlier, H.W. Egli also began~~ the chain of innovation to mechanise this process, but only by abandonning the sophistication of the Millionaire and like Haman returning to the principles of the arithmometer. The result was the MADAS calculator, first produced in manual form, which could advance the carriage automatically one place at a time as division and multiplication were carried out. With progressive further modifications, including the insertion of an electric motor, the MADAS became the highly effective electric mechanical calculating machine whose use continued right into the 1960s. The late MADAS 20BTG calculator which is part of this collection represents a classic exemplar of the late stages of this evolutionary development. Its mechanism was also adopted in its essentials, then with many innovations (but with less of the Swiss robust construction of the Madas), in the US Frieden calculators. As it turned out, this final class of machines represented the pinacle of achievement in motorised mechanical calculation.

to:

H.W. Egli now approached the chain of innovation to mechanise this process, but only by abandonning the sophistication of the Millionaire and like Haman returning to the principles of the arithmometer. The result was the MADAS calculator, first produced in manual form, which could advance the carriage automatically one place at a time as division and multiplication were carried out. With progressive further modifications, including the insertion of an electric motor, the MADAS became the highly effective electric mechanical calculating machine whose use continued right into the 1960s. The late MADAS 20BTG calculator which is part of this collection represents a classic exemplar of the late stages of this evolutionary development. Its mechanism was also adopted in its essentials, then with many innovations (but with less of the Swiss robust construction of the Madas), in the US Frieden calculators. As it turned out, this final class of machines represented the pinacle of achievement in motorised mechanical calculation.

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~~%center%~~||%center% %height=250px%[[Site.HP-35-1972|http://meta-studies.net/pmwiki/uploads/HP35.jpg]]||%center% %height=250px%[[Site.HP-45-1973|http://meta-studies.net/pmwiki/uploads/HP-45.jpg]]||
~~%center%~~||%center% July1972: Hewlett Packard\\HP 35 Calculator\\serial 1230A 79429, 1972\\ (second version)\\(collection Calculant)||%center% December 1973: Hewlett Packard\\HP 45 Calculator\\serial 1350A 36719, 1973||

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||%center% %height=250px%[[Site.HP-35-1972|http://meta-studies.net/pmwiki/uploads/HP35.jpg]]||%center% %height=250px%[[Site.HP-45-1973|http://meta-studies.net/pmwiki/uploads/HP-45.jpg]]||
||%center% July1972: Hewlett Packard\\HP 35 Calculator\\serial 1230A 79429, 1972\\ (second version)\\(collection Calculant)||%center% December 1973: Hewlett Packard\\HP 45 Calculator\\serial 1350A 36719, 1973||

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||%center% %~~height=250px~~%[[Site.HP-35-1972|http://meta-studies.net/pmwiki/uploads/HP35.jpg]]||%center% %height=250px%[[Site.HP-45-1973|http://meta-studies.net/pmwiki/uploads/HP-45.jpg]]||
||%center% July1972: Hewlett Packard\\HP 35 Calculator\\serial 1230A 79429, 1972\\ (second version)\\(collection Calculant)||%center% December 1973: Hewlett Packard\\HP 45 Calculator\\serial 1350A 36719, 1973||

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%center%||%center% %height=250px%[[Site.HP-35-1972|http://meta-studies.net/pmwiki/uploads/HP35.jpg]]||%center% %height=250px%[[Site.HP-45-1973|http://meta-studies.net/pmwiki/uploads/HP-45.jpg]]||
%center%||%center% July1972: Hewlett Packard\\HP 35 Calculator\\serial 1230A 79429, 1972\\ (second version)\\(collection Calculant)||%center% December 1973: Hewlett Packard\\HP 45 Calculator\\serial 1350A 36719, 1973||

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The Millionaire calculating machine combines the idea of the physical embodiment of multiplication tables with that of the proportional rack. It is able to interrogate a multiplication table represented by metal rods, and in a single crank of the handle multiplies the multiplicand by a number set between 1 and 9 then advancing its internal carriage one place ready for the next multiplier to be set and applied. Manufactured by H.W. Egli, some 4,655 of these were sold. The Millionaire calculating machine in this collection is from 1912, and is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

to:

The Millionaire calculating machine combines the idea of the physical embodiment of multiplication tables with that of the proportional rack. It is able to interrogate a multiplication table represented by metal rods, and in a single crank of the handle multiplies the multiplicand by a number set between 1 and 9 then advancing its internal carriage one place ready for the next multiplier to be set and applied. Manufactured by H.W. Egli, some 4,655 of these were sold. The Millionaire calculating machine in this collection is from 1912, and is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

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!!!**To be continued~~....~~ This essay is under construction - especially what follows. If it is ever finished (:-) it is intended to utilise this collection to shape a continuing if idiosyncratic story of the development of embodied calculation up to the introduction of personal electronic calculation. So do visit again if you have got this far, and there may (should) be more.**

to:

!To be continued
**This essay is under construction - especially what follows. If it is ever finished (:-) it is intended to utilise this collection to shape a continuing if idiosyncratic story of the development of embodied calculation up to the introduction of personal electronic calculation. So do visit again if you have got this far, and there may (should) be more.**

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!!!**To be continued.... This essay is under construction - especially what follows. If it is ever finished (:-) it is intended to utilise this collection to shape a continuing if idiosyncratic story of the development of embodied calculation up to the introduction of personal electronic calculation. So do visit again if you have got this far, and there may (should) be more.**

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Thomas de Colmar first made public his design for a calculating machine capable of doing all four functions (addition, subtraction, multiplication and division) when he was granted a patent for it in 1820.[^Patent no. 1420, 18 November 1820^]. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.[^For the most authoritative website on the Thomas de Colmar machines and history see Valéry Monier's magisterial site [[http://www.arithmometre.org]], viewed 20 July 2013.^] The somewhat circuitous route to that later success is described by Stephen Johnston [^Stephen Johnston, "Making the arithmometer count", //Bulletin of the Scientific Instrument Society//, Volume 52, 1997, pp. 12-21.^]

to:

Thomas de Colmar first made public his design for a calculating machine capable of doing all four functions (addition, subtraction, multiplication and division) when he was granted a patent for it in 1820.[^Patent no. 1420, 18 November 1820^]. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.[^For the most authoritative website on the Thomas de Colmar machines and history see Valéry Monier's magisterial site [[http://www.arithmometre.org]], viewed 20 July 2013.^] The somewhat circuitous route to that later success is described by Stephen Johnston. [^Stephen Johnston, "Making the arithmometer count", //Bulletin of the Scientific Instrument Society//, Volume 52, 1997, pp. 12-21.^]

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Thomas de Colmar first made public his design for a calculating machine capable of doing all four functions (addition, subtraction, multiplication and division) when he was granted a patent for ~~his design~~ in 1820.[^Patent no. 1420, 18 November 1820^]. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.[^For the most authoritative website on the Thomas de Colmar machines and history see Valéry Monier's magisterial site [[http://www.arithmometre.org]], viewed 20 July 2013.^] The somewhat circuitous route to that later success is described by Stephen Johnston [^Stephen Johnston, "Making the arithmometer count", //Bulletin of the Scientific Instrument Society//, Volume 52, 1997, pp. 12-21.^]

Thomas de Colmar arithmometer (1884) Each represents a different mechanical approach to digitally carrying out the four functions, with an easy input, and a digital readout. Each then was improved through a series of innovations, first by the original inventors, and then as more players across the world competed to produce and market better variants.%0a %0aThomas de Colmar was the first person to produce a commercially useable calculator based on Leibnitz’s stepped drum principle, and he named his machine the “arithmometer”. The Thomas design was copied and improved by a number of other engineers and marketed from different countries.[^P. A. Kidwell, "American Scientists and Calculating Machines- From Novelty to Commonplace", Annals of the History of Computing, Volume 12, Number 1, 1990, pp. 31^]

to:

Thomas de Colmar first made public his design for a calculating machine capable of doing all four functions (addition, subtraction, multiplication and division) when he was granted a patent for it in 1820.[^Patent no. 1420, 18 November 1820^]. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.[^For the most authoritative website on the Thomas de Colmar machines and history see Valéry Monier's magisterial site [[http://www.arithmometre.org]], viewed 20 July 2013.^] The somewhat circuitous route to that later success is described by Stephen Johnston [^Stephen Johnston, "Making the arithmometer count", //Bulletin of the Scientific Instrument Society//, Volume 52, 1997, pp. 12-21.^]

Thomas de Colmar arithmometer (1884) Each represents a different mechanical approach to digitally carrying out the four functions, with an easy input, and a digital readout. Each then was improved through a series of innovations, first by the original inventors, and then as more players across the world competed to produce and market better variants.%0a %0aThomas de Colmar was the first person to produce a commercially useable calculator based on Leibnitz’s stepped drum principle, and he named his machine the “arithmometer”. The Thomas design was copied and improved by a number of other engineers and marketed from different countries.[^P. A. Kidwell, "American Scientists and Calculating Machines- From Novelty to Commonplace", Annals of the History of Computing, Volume 12, Number 1, 1990, pp. 31^]

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~~It was Thomas de Colmar who decisively built~~ Thomas de Colmar arithmometer (1884) Each represents a different mechanical approach to digitally carrying out the four functions, with an easy input, and a digital readout. Each then was improved through a series of innovations, first by the original inventors, and then as more players across the world competed to produce and market better variants.%0a %0aThomas de Colmar was the first person to produce a commercially useable calculator based on Leibnitz’s stepped drum principle, and he named his machine the “arithmometer”. The Thomas design was copied and improved by a number of other engineers and marketed from different countries.[^P. A. Kidwell, "American Scientists and Calculating Machines- From Novelty to Commonplace", Annals of the History of Computing, Volume 12, Number 1, 1990, pp. 31^]

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Thomas de Colmar first made public his design for a calculating machine capable of doing all four functions (addition, subtraction, multiplication and division) when he was granted a patent for his design in 1820.[^Patent no. 1420, 18 November 1820^]. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.[^For the most authoritative website on the Thomas de Colmar machines and history see Valéry Monier's magisterial site [[http://www.arithmometre.org]], viewed 20 July 2013.^] The somewhat circuitous route to that later success is described by Stephen Johnston [^Stephen Johnston, "Making the arithmometer count", //Bulletin of the Scientific Instrument Society//, Volume 52, 1997, pp. 12-21.^]

Thomas de Colmar arithmometer (1884) Each represents a different mechanical approach to digitally carrying out the four functions, with an easy input, and a digital readout. Each then was improved through a series of innovations, first by the original inventors, and then as more players across the world competed to produce and market better variants.%0a %0aThomas de Colmar was the first person to produce a commercially useable calculator based on Leibnitz’s stepped drum principle, and he named his machine the “arithmometer”. The Thomas design was copied and improved by a number of other engineers and marketed from different countries.[^P. A. Kidwell, "American Scientists and Calculating Machines- From Novelty to Commonplace", Annals of the History of Computing, Volume 12, Number 1, 1990, pp. 31^]

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||%center% %height=~~200px~~%[[Site.HP-35-1972|http://meta-studies.net/pmwiki/uploads/HP35.jpg]]||%center% %height=~~200px~~%[[Site.HP-45-1973|http://meta-studies.net/pmwiki/uploads/HP-45.jpg]]||

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||%center% %height=250px%[[Site.HP-35-1972|http://meta-studies.net/pmwiki/uploads/HP35.jpg]]||%center% %height=250px%[[Site.HP-45-1973|http://meta-studies.net/pmwiki/uploads/HP-45.jpg]]||

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~~July1972: Hewlett Packard~~ HP 35 ~~Calculator serial 1230A 79429,~~ 1972 (second version)

December 1973: ~~Hewlett Packard~~ HP 45 ~~Calculator serial 1350A 36719, 1973~~

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||%center% %height=200px%[[Site.HP-35-1972|http://meta-studies.net/pmwiki/uploads/HP35.jpg]]||%center% %height=200px%[[Site.HP-45-1973|http://meta-studies.net/pmwiki/uploads/HP-45.jpg]]||
||%center% July1972: Hewlett Packard\\HP 35 Calculator\\serial 1230A 79429, 1972\\ (second version)\\(collection Calculant)||%center% December 1973: Hewlett Packard\\HP 45 Calculator\\serial 1350A 36719, 1973||

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%center% %height=250px% [[Site.Hertstark1929|http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometer.png]]
%center% ~1929 “Herzstark” electric Calculating Machine serial 6549\\badged by Herzstark, Vienna\\(essentially a Badenia Model TE 13 Duplex)\\
%center% (collection Calculant)

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~~1950s-1960s: MADAS Model 20BTG serial 94046 electric calculator with true automatic division~~

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%center% %height=250px% [[Site.MADAS1950-60s|http://meta-studies.net/pmwiki/uploads/MADAS_Smaller.png]]
%center% 1950s-1960s: MADAS Model 20BTG serial 94046\\electric calculator with true automatic division\\
%center% (collection Calculant)

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%center% %height=250px% [[http://meta-studies.net/pmwiki/uploads/BolleeMAB1890.jpg]]

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%center% %height=250px% [[Site.Bollee1890|http://meta-studies.net/pmwiki/uploads/BolleeMAB1890.jpg]]

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1855: “Messrs. Scheutz’s New Calculating Machine”, The Illustrated London News, 30 June 1855, p. 661. Original print article.

1890: Leon Bollée Calculating Machine, “A New Calculating Machine of very General Applicability”, The Manufacturer and Builder, July 1890, p. 156. Original print article.

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Similar principles were however utilised by Otto Steiger who patented a rather more practical “Millionaire calculating machine” which had a simple enough mechanism to enable production on a commercial scale.

%center% %height=250px% [[Site.Millionaire1912|http://~~meta-studies~~.~~net/pmwiki/uploads/Millionair~~.png]]
%center% 1912: Millionaire Calculating Machine\\serial 2015 (10x10x20)\\

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%center% %height=250px% [[http://meta-studies.net/pmwiki/uploads/BolleeMAB1890.jpg]]
%center% Leon Bollée Calculating Machine\\"A New Calculating Machine of very General Applicability”\\//The Manufacturer and Builder 1890//[^1890: Leon Bollée Calculating Machine, “A New Calculating Machine of very General Applicability”, //The Manufacturer and Builder//, July 1890, p. 156. Original print article.^]\\

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Similar principles were however utilised by Otto Steiger who patented a rather more practical “Millionaire calculating machine” which had a simple enough mechanism to enable production on a commercial scale.

%center% %height=250px% [[Site.Millionaire1912|http://meta-studies.net/pmwiki/uploads/Millionair.png]]
%center% 1912: Millionaire Calculating Machine\\serial 2015 (10x10x20)\\
%center% (collection Calculant)

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Scheutz and Babbage - difference engines

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%center% %height=250px% [[Site.BambergerOmega1904|http://meta-studies.net/pmwiki/uploads/BambergerOmega.~~pngg~~]]

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%center% %height=250px% [[Site.BambergerOmega1904|http://meta-studies.net/pmwiki/uploads/BambergerOmega.png]]

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The MADAS arithmometer (above, standing for “Multiplication, Addition, Division - Automatically, Substraction”) was developed by Erwin Janz and manufactured by Egli in Zurich, starting in 1913. As the acronym suggests, this machine achieved an entirely automatic division process - the first ever for an arithmometer style calculator. In this collection there is a MADAS IX Maxima calculator (produced in 1917) which could display 16 numbers in its results register.

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~ 1955
1950s: (made in Great Britain by Bell Punch Company Ltd)

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~~Many variations. Eg Frieden's cam timed "Frieden wheel"~~.

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Of course this is a broad brush description of the various mechanisms. Many variations. Eg Frieden's cam timed "Frieden wheel". Described very well elsewhere - eg Martin, Rechnerlexicon and Wolff.

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One helpful development in design was the development of a proportional rack which moved cogs through a series of increments depending on the length of a toothed rack with which they engaged. Different lengths thus represented different numbers to be added. In 1906 Christel Haman founded the Mercedes-Euklid company who adopted this principle to create a machine that after a process of development eventually could automate the process of division. There is both a demonstration Mercedes-Euklid (model 29 from 1934) and then a fully working Mercedes-Euklid 29 in this collection.

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%center% %height=250px% [[Site.BambergerOmega1904|http://meta-studies.net/pmwiki/uploads/BambergerOmega.pngg]]
%center% 1904-1905: Bamberger’s Omega Calculating Machine\\
%center% (collection Calculant)

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1904-1905: Bamberger’s Omega Calculating Machine

1912: Millionaire Calculating Machine serial 2015 (10x10x20)

One helpful development in ~~design was the development of~~ a proportional rack which moved cogs through a series of increments depending on the length of a toothed rack with which they engaged. Different lengths thus represented different numbers to be added. In 1906 Christel Haman founded the Mercedes-Euklid company who adopted this principle to create a machine that after a process of development eventually could automate the process of division. There is both a demonstration Mercedes-Euklid (model 29 from 1934) and then a fully working Mercedes-Euklid 29 in this collection.

~~An arithmometer, the MADAS (standing for “Multiplication, Addition, Division~~ - ~~Automatically, Substraction”) was developed by Erwin Janz and manufactured by Egli in Zurich, starting in 1913. As~~ the ~~acronym suggests, this machine achieved an entirely automatic division process - the first ever for an arithmometer style calculator. In this collection there is~~ a MADAS IX Maxima calculator (produced in 1917) which could display 16 numbers in its results register.

A much heavier and complex mechanical approach was also explored. First it was embodied in Léon Bollée’s calculating machine which won a gold medal at the Paris Exposition of 1889. One surviving example of this bulky but beautiful machine can be seen at the Musée des Arts et Métiers in Paris. This collection has only an article on this “New Calculating Machine of very General Applicability” from the Manufacturer and Builder of 1890. Similar principles were however utilised by Otto Steiger who patented a rather more practical “Millionaire calculating machine” which had a simple enough mechanism to enable production on a commercial scale. The Millionaire calculating machine combines the idea of the physical embodiment of multiplication tables with that of the proportional rack. It is able to interrogate a multiplication table represented by metal rods, and in a single crank of the handle multiplies the multiplicand by a number set between 1 and 9 then advancing its internal carriage one place ready for the next multiplier to be set and applied. Manufactured by H.W. Egli, some 4,655 of these were sold. The Millionaire calculating machine in this collection is from 1912, and is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.
One step backward, many steps forward: applying the electric motor (C20)

to:

A much heavier and complex mechanical approach was also explored. First it was embodied in Léon Bollée’s calculating machine which won a gold medal at the Paris Exposition of 1889. One surviving example of this bulky but beautiful machine can be seen at the Musée des Arts et Métiers in Paris. This collection has only an article on this “New Calculating Machine of very General Applicability” from the Manufacturer and Builder of 1890.

Similar principles were however utilised by Otto Steiger who patented a rather more practical “Millionaire calculating machine” which had a simple enough mechanism to enable production on a commercial scale.

%center% %height=250px% [[Site.Millionaire1912|http://meta-studies.net/pmwiki/uploads/Millionair.png]]
%center% 1912: Millionaire Calculating Machine\\serial 2015 (10x10x20)\\
%center% (collection Calculant)

The Millionaire calculating machine combines the idea of the physical embodiment of multiplication tables with that of the proportional rack. It is able to interrogate a multiplication table represented by metal rods, and in a single crank of the handle multiplies the multiplicand by a number set between 1 and 9 then advancing its internal carriage one place ready for the next multiplier to be set and applied. Manufactured by H.W. Egli, some 4,655 of these were sold. The Millionaire calculating machine in this collection is from 1912, and is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.

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In this collection there is an arithmometer branded by Samuel Hertzstark from 1929, although by then he was not making machines. It is actually a Badenia (manufactured by the German Company Math. Bauerle in the Black Forest) which Hertzstark was by then re-badging (not long before he died). It features an electric motor, still in good working order, and with a keyboard instead of sliders for input. The features of it were not only that it had a keyboard for input, but also a control mechanism consisting of a column of keys which enabled a number to be entered and then added through 0 to 8 repeats representing multiplication by one to nine.

Whilst the above was an obvious innovation, the clumsiest approach in all the calculating devices - from the first arithmometer through to the Millionaire was division, which could only be done by a process along the lines of that done in long division. That is, the number to be divided (the dividend) is considered sequentially from the highest power of ten, and thus decomposed into a series of partial products of the successive parts of the dividend with the divisor. This required a process of guessing each partial product and then trying it out, the result being subtracted from the dividend to give a remainder, exactly as is done in pen and paper long division.

As well as Haman (and the Mercedes-Euklid) mentioned earlier, H.W. Egli also began the chain of innovation to mechanise this process, but only by abandonning the sophistication of the Millionaire and like Haman returning to the principles of the arithmometer. The result was the MADAS calculator, first produced in manual form, which could advance the carriage automatically one place at a time as division and multiplication were carried out. With progressive further modifications, including the insertion of an electric motor, the MADAS became the highly effective electric mechanical calculating machine whose use continued right into the 1960s. The late MADAS 20BTG calculator which is part of this collection represents a classic exemplar of the late stages of this evolutionary development. Its mechanism was also adopted in its essentials, then with many innovations (but with less of the Swiss robust construction of the Madas), in the US Frieden calculators. As it turned out, this final class of machines represented the pinacle of achievement in motorised mechanical calculation.

to:

In this collection there is an arithmometer branded by Samuel Hertzstark from 1929, although by then he was not making machines. It is actually a Badenia (manufactured by the German Company Math. Bauerle in the Black Forest) which Hertzstark was by then re-badging (not long before he died).

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It features an electric motor, still in good working order, and with a keyboard instead of sliders for input. The features of it were not only that it had a keyboard for input, but also a control mechanism consisting of a column of keys which enabled a number to be entered and then added through 0 to 8 repeats representing multiplication by one to nine.

Whilst the above was an obvious innovation, the clumsiest approach in all the calculating devices - from the first arithmometer through to the Millionaire was division, which could only be done by a process along the lines of that done in long division. That is, the number to be divided (the dividend) is considered sequentially from the highest power of ten, and thus decomposed into a series of partial products of the successive parts of the dividend with the divisor. This required a process of guessing each partial product and then trying it out, the result being subtracted from the dividend to give a remainder, exactly as is done in pen and paper long division.

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As well as Haman (and the Mercedes-Euklid) mentioned earlier, H.W. Egli also began the chain of innovation to mechanise this process, but only by abandonning the sophistication of the Millionaire and like Haman returning to the principles of the arithmometer. The result was the MADAS calculator, first produced in manual form, which could advance the carriage automatically one place at a time as division and multiplication were carried out. With progressive further modifications, including the insertion of an electric motor, the MADAS became the highly effective electric mechanical calculating machine whose use continued right into the 1960s. The late MADAS 20BTG calculator which is part of this collection represents a classic exemplar of the late stages of this evolutionary development. Its mechanism was also adopted in its essentials, then with many innovations (but with less of the Swiss robust construction of the Madas), in the US Frieden calculators. As it turned out, this final class of machines represented the pinacle of achievement in motorised mechanical calculation.

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Variety of electronic desk calculators from the ANITA on. But these could not replace the portable slide rules and other mathematical aids that were still in use in parallel with the large mechanical desktop calculators that these electronic machines began to replace. It was in July 1972 however, that the old ways for scientists and citizen alike were definitively undermined. In that month

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!!!In Lieu of a Conclusion

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||%center% ~July 1948: CURTA Type 1\\(pin sliders) earliest\\model calculator\\serial 5424||%center% 1967: CURTA Type I\\calculator serial 76436\\& cardboard box||%center% 1963: CURTA Type II\\calculator ~~with\\Leather Case~~||

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||%center% ~July 1948: CURTA Type 1\\(pin sliders) earliest\\model calculator\\serial 5424||%center% 1967: CURTA Type I\\calculator serial 76436\\& cardboard box||%center% 1963: CURTA Type II\\calculator||

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1967: CURTA Type I calculator serial 76436, near mint, with original case, cardboard box and instructions

1963: CURTA Type II calculator with Leather Case, serial 554765

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~~~July~~ 1948: ~~CURTA Type~~ 1 ~~(pin sliders) earliest model calculator serial 5424~~

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||%center% %height=200px%[[Site.Curta-1-1948|http://meta-studies.net/pmwiki/uploads/Curta1-1948.png]]||%center% %height=200px%[[Site.Curta-1-1967|http://meta-studies.net/pmwiki/uploads/Curta1-1967.png]]||%center% %height=200px%[[Site.Curta-2-1963|http://meta-studies.net/pmwiki/uploads/Curta2.png]]||
||%center% ~July 1948: CURTA Type 1\\(pin sliders) earliest\\model calculator\\serial 5424||%center% 1967: CURTA Type I\\calculator serial 76436\\& cardboard box||%center% 1963: CURTA Type II\\calculator with\\Leather Case||
||(collection Calculant)|| || ||

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||%center% 1923: Mercedes-Euklid Model 29 calculator||%center% 1923: Mercedes-Euklid Model 29\\Demonstration calculator||
||(collection Calculant)|| ||

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||%center% 1923: Mercedes-Euklid Model 29 calculator\\(collection Calculant)||%center% 1923: Mercedes-Euklid Model 29\\Demonstration calculator||

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||%center% 1923: Mercedes-Euklid Model 29 calculator||%center% 1923: Mercedes-Euklid Model 29 Demonstration calculator||

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||%center% 1923: Mercedes-Euklid Model 29 calculator||%center% 1923: Mercedes-Euklid Model 29\\Demonstration calculator||

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||%center% %height=~~250px~~%[[Site.Mercedes291923|http://meta-studies.net/pmwiki/uploads/Mercedes.png]]||%center% %height=~~250px~~%[[Site.Mercedes29Demonstrator1923|http://meta-studies.net/pmwiki/uploads/MercedesDemo.png]]||
||%center% 1923: Mercedes-Euklid Model 29 calculator||%center% 1923: Mercedes-Euklid Model 29 Demonstration calculator||\\
(collection Calculant)

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||%center% %height=200px%[[Site.Mercedes291923|http://meta-studies.net/pmwiki/uploads/Mercedes.png]]||%center% %height=200px%[[Site.Mercedes29Demonstrator1923|http://meta-studies.net/pmwiki/uploads/MercedesDemo.png]]||
||%center% 1923: Mercedes-Euklid Model 29 calculator||%center% 1923: Mercedes-Euklid Model 29 Demonstration calculator||
||(collection Calculant)|| ||

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%center% ||%~~center~~% ~~%height=250px%~~[[Site.Mercedes291923| http://meta-studies.net/pmwiki/uploads/Mercedes.png]]||%center% %height=250px%[[Site.Mercedes29Demonstrator1923| http://meta-studies.net/pmwiki/uploads/MercedesDemo.png]]||
%center% ~~||%center%~~ 1923: Mercedes-Euklid Model 29 calculator||%center% 1923: Mercedes-Euklid Model 29 Demonstration calculator||

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||%center% %height=250px%[[Site.Mercedes291923|http://meta-studies.net/pmwiki/uploads/Mercedes.png]]||%center% %height=250px%[[Site.Mercedes29Demonstrator1923|http://meta-studies.net/pmwiki/uploads/MercedesDemo.png]]||
||%center% 1923: Mercedes-Euklid Model 29 calculator||%center% 1923: Mercedes-Euklid Model 29 Demonstration calculator||\\

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||~1951||Original Ohdner Model 39\\serial 39-288965||Ohdner||Pinwheel||%height=100px%[[Site.OriginalOhdner39-1951|Add Picture||

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||~1951||Original Ohdner Model 39\\serial 39-288965||Ohdner||Pinwheel||%height=100px%[[Site.OriginalOhdner39-1951|Add Picture]]||

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1957: Walther Demonstration WSR160 Pinwheel Calculator
~1957: Walther WSR160 Pinwheel Calculator

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!To be continued....
This essay is under construction. If it is ever finished (:-) it is intended to utilise this collection to shape a continuing if idiosyncratic story of the development of embodied calculation up to the introduction of personal electronic calculation. So do visit again if you have got this far, and there may (should) be more.

!Reshaping style

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1923: Mercedes-Euklid Model 29 Demonstration calculator

1923: ~~Mercedes~~-~~Euklid Model 29 calculator~~

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%center% ||%center% %height=250px%[[Site.Mercedes291923| http://meta-studies.net/pmwiki/uploads/Mercedes.png]]||%center% %height=250px%[[Site.Mercedes29Demonstrator1923| http://meta-studies.net/pmwiki/uploads/MercedesDemo.png]]||
%center% ||%center% 1923: Mercedes-Euklid Model 29 calculator||%center% 1923: Mercedes-Euklid Model 29 Demonstration calculator||
(collection Calculant)

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%center% %height=250px% [[Site.BrunsvigaSchuster1896|http://meta-studies.net/pmwiki/uploads/~~ComptometerWoodie~~.png]]

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%center% %height=250px% [[Site.BrunsvigaSchuster1896|http://meta-studies.net/pmwiki/uploads/Brunsviga1896.png]]

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||~1951||Original Ohdner Model 39\\serial 39-288965||Ohdner||Pinwheel||%height=100px%[[Site.OriginalOhdner39-1951| ~~http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png]]~~||

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||~1951||Original Ohdner Model 39\\serial 39-288965||Ohdner||Pinwheel||%height=100px%[[Site.OriginalOhdner39-1951|Add Picture||

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The pinwheel calculator was developed as an improvement on the arithmometer, utilising a clever ‘counting gear’ in which the number of teeth could be adjusted by sliders (and later a push-down keyboard). In this collection there is the already mentioned very early Brunsviga-Schuster pinwheel calculator from 1896 (an Ohdner Brunsviga which had been re-badged by Schuster who on-sold them). ~~There is also a later Ohdner from 1938 and a Facit calculator from around 1945, and then~~ from ~~near the end of production of such machines~~, ~~from the 1950s a very nice demonstration Walther 160 calculator, showing its mechanism, complemented by~~ a ~~complete and fully operational~~ Walther of the same model.

~1896: Ohdner Brunsviga Schuster Calculator serial 3406
1945: Facit Model S Calculator serial 210652
~1951: Original Ohdner Model 39, Calculator serial 39-~~288965~~

to:

The pinwheel calculator was developed as an improvement on the arithmometer, utilising a clever ‘counting gear’ in which the number of teeth could be adjusted by sliders (and later a push-down keyboard). In this collection there is the already mentioned very early Brunsviga-Schuster pinwheel calculator from 1896 (an Ohdner Brunsviga which had been re-badged by Schuster who on-sold them).

%center% %height=250px% [[Site.BrunsvigaSchuster1896|http://meta-studies.net/pmwiki/uploads/ComptometerWoodie.png]]
%center% Brunsviga Schuster Pinwheel Calculator ~1896\\Serial 3406\\
%center% (collection Calculant)

There is also a later Ohdner from 1938 and a Facit calculator from around 1945, and then from near the end of production of such machines, from the 1950s a very nice demonstration Walther 160 calculator, showing its mechanism, complemented by a complete and fully operational Walther of the same model.

||Date||Description||Maker||Type||Device (click for description)||
||1945 ||Facit Model S Calculator\\serial 210652||Facit||Pinwheel||%height=100px%[[Site.Facit1945| http://meta-studies.net/pmwiki/uploads/Facit.png]]||
||~1951||Original Ohdner Model 39\\serial 39-288965||Ohdner||Pinwheel||%height=100px%[[Site.OriginalOhdner39-1951| http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png]]||
||~1957 || Walther WSR160\\Pinwheel Calculator||Walther||Pinwheel||%height=100px%[[Site.Walther1957| http://meta-studies.net/pmwiki/uploads/Walther.png]]||
||~1957 || Walther WSR160\\Demonstration\\Pinwheel Calculator||Walther||Demonstration\\Pinwheel||%height=100px%[[Site.WaltherDemonstrator1957| http://meta-studies.net/pmwiki/uploads/WaltherDemo.png]]||
(collection Calculant - all above)

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!!!"Arms races" and mechanical evolution
In this collection there is a rare and probably unique Bunzel-Delton arithmometer (1913) - the only known one existing with a forward crank, and from this fact, and the expert way in which the modification has been made, almost certainly a prototype created in the Bunzel workshops to match a patent, also reproduced int his site.

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||1950s ||Bell Sumlock Comptometer||Bell Sumlock||Model 909/S/117.878||%height=100px%[[Site.~~SumlockComptometer1950slPrototype1913~~| http://meta-studies.net/pmwiki/uploads/Sumlock.png]]||

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||1950s ||Bell Sumlock Comptometer||Bell Sumlock||Model 909/S/117.878||%height=100px%[[Site.SumlockComptometer1950s| http://meta-studies.net/pmwiki/uploads/Sumlock.png]]||

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||1950s ||Bell Sumlock Comptometer||Bell Sumlock||Model 909/S/117.878||%height=~~75px~~%[[Site.SumlockComptometer1950slPrototype1913| http://meta-studies.net/pmwiki/uploads/Sumlock.png]]||

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||1950s ||Bell Sumlock Comptometer||Bell Sumlock||Model 909/S/117.878||%height=100px%[[Site.SumlockComptometer1950slPrototype1913| http://meta-studies.net/pmwiki/uploads/Sumlock.png]]||

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A further approach to the problem of the four functions is found in the American invention by Felt, of a device that he called the comptometer and patented in 1887. It performs the task of addition by a system of keys and levers. Notably no crank handle needs to be turned in order to perform the addition. ~~Addition of a number automatically occurs whenever a corresponding key is pressed. This is fast~~. ~~But the difficulty is that subtraction must be carried out by a process~~ of ~~addition of complementary numbers. Carrying of “tens” must be done by addition also. And the process of multiplication is done by multiple presses of the number. As already mentioned~~, in this collection we have one of the first models of the comptomoter - one from 1896 cased in wood? and one of the 40 oldest known to still be in existence, as well as a later demonstration machine from Bell Punch, and then its embodiment in a fully working Bell Punch Sumlock (from the 1950s).-

to:

A further approach to the problem of the four functions is found in the American invention by Felt, of a device that he called the comptometer and patented in 1887. It performs the task of addition by a system of keys and levers. Notably no crank handle needs to be turned in order to perform the addition. And the process of multiplication is done by multiple presses of the number. As already mentioned, in this collection we have one of the first models of the comptomoter - one from 1896 cased in wood? and one of the 40 oldest known to still be in existence,

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Addition of a number automatically occurs whenever a corresponding key is pressed. This is fast. But subtraction must be carried out by addition of complementary numbers. Carrying of “tens” must be done by addition. The comptometer was a highly successful innovation and was sufficiently cheap and useful to reach a broad market. Characterised by extremely effective marketing and capable of being mass produced the device continued to be marketed for some 80 years unusually for such innovations leaving its inventor extremely wealthy. By then its essential mechanism was being utilised by more than one company. Shown below is the remaining comptometer in this collection, this time made of plastic in the 1950s by the British Bell Punch company. Also shown is a demonstration model showing the keys and lever system used in the Bell Punch machine.

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~~||~1955||Bell Punch Sumlock ||Bell Punch||Demonstration\\Comptometer||%height=75px%[[Site.SumlockDemonstrator1955| http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png]]||~~

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||~1955||Bell Punch Sumlock ||Bell Punch||Demonstration\\Comptometer||%height=100px%[[Site.SumlockDemonstrator1955| http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png]]||

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||~1955||Bell Punch Sumlock ||~~Demonstration Comptometer~~||%height=75px%[[Site.SumlockDemonstrator1955| http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png]]||
||1950s ||Bell Sumlock Comptometer||Model 909/S/117.878||%height=75px%[[Site.SumlockComptometer1950slPrototype1913| http://meta-studies.net/pmwiki/uploads/Sumlock.png]]||

to:

||~1955||Bell Punch Sumlock ||Bell Punch||Demonstration\\Comptometer||%height=75px%[[Site.SumlockDemonstrator1955| http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png]]||
||1950s ||Bell Sumlock Comptometer||Bell Sumlock||Model 909/S/117.878||%height=75px%[[Site.SumlockComptometer1950slPrototype1913| http://meta-studies.net/pmwiki/uploads/Sumlock.png]]||

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||Date||Maker||Type||Device (click for description)

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||Date||Description||Maker||Type||Device (click for description)

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||Date||~~Maker~~||~~Type~~||Device (click for description)||
||~ 1955 ||Bell Punch Sumlock ||Demonstration Comptometer||%height=75px%[[Site.SumlockDemonstrator1955| http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png]]||
||1950s ||Bell Sumlock Comptometer|| Model 909/S/117.878||%height=75px%[[Site.SumlockComptometer1950slPrototype1913| http://meta-studies.net/pmwiki/uploads/Sumlock.png]]||

to:

||Date||Description||Maker||Type||Device (click for description)||
||~1955||Bell Punch Sumlock ||Demonstration Comptometer||%height=75px%[[Site.SumlockDemonstrator1955| http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png]]||
||1950s ||Bell Sumlock Comptometer||Model 909/S/117.878||%height=75px%[[Site.SumlockComptometer1950slPrototype1913| http://meta-studies.net/pmwiki/uploads/Sumlock.png]]||

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~~||Note~~||Date||Maker||Type||Device (click for description)

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||Date||Maker||Type||Device (click for description)

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||Date||Maker||Type||Device (click for description)

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||Date||Maker||Type||Device (click for description)||

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%center% %height=~~200px~~% [[Site.ComptometerWoodie1896|http://meta-studies.net/pmwiki/uploads/ComptometerWoodie.png]]

to:

%center% %height=250px% [[Site.ComptometerWoodie1896|http://meta-studies.net/pmwiki/uploads/ComptometerWoodie.png]]

Changed lines 145-147 from:

~ 1907: Comptometer oil bottle, marked with patent 23 April 1905; 6 April 1907
~ 1955 Bell Punch Sumlock Demonstration Comptometer
1950s: ~~Bell Sumlock Comptometer Model 909~~/S/~~117~~.~~878~~ (made in Great Britain by Bell Punch Company Ltd)

to:

||Date||Maker||Type||Device (click for description)||
||~ 1955 ||Bell Punch Sumlock ||Demonstration Comptometer||%height=75px%[[Site.SumlockDemonstrator1955| http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png]]||
||1950s ||Bell Sumlock Comptometer|| Model 909/S/117.878||%height=75px%[[Site.SumlockComptometer1950slPrototype1913| http://meta-studies.net/pmwiki/uploads/Sumlock.png]]||
(collection Calculant - all above)

~ 1955
1950s: (made in Great Britain by Bell Punch Company Ltd)

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%center% %height=~~250px~~% [[Site.ComptometerWoodie1896|http://meta-studies.net/pmwiki/uploads/ComptometerWoodie.png]]

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%center% %height=200px% [[Site.ComptometerWoodie1896|http://meta-studies.net/pmwiki/uploads/ComptometerWoodie.png]]

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Similar simple devices were developed which utilised simple rotation of cogs, with a crude carry process (usually along the lines of that used by Schickard). They relied for their success on having but a small number of interacting cogs, so that the carry mechanism would not jam, or adopting the use of springs (in place of Pascal's weights) which would store rotary motion to then be utilised when a carry was required. ~~Those in this collection are shown below. (Once more, clicking on the image will take you to a larger image on the description page~~.)

to:

Similar simple devices were developed which utilised simple rotation of cogs, with a crude carry process (usually along the lines of that used by Schickard). They relied for their success on having but a small number of interacting cogs, so that the carry mechanism would not jam, or adopting the use of springs (in place of Pascal's weights) which would store rotary motion to then be utilised when a carry was required. The device shown below was the first model made by C.H. Webb (from New York) who began marketing it in 1869. It is made of brass and is set on a heavy wooden base.

Changed lines 96-100 from:

to:

%center%Web Patent Adder and Talley Board 1869\\
%center%(collection Calculant)

Other simple rotational adding devices in this collection are shown below. (Once more, clicking on the image will take you to a larger image on the description page.)

Deleted line 101:

~~||1869 ||Web Patent\\Adder and\\Talley Board||C.H. Webb\\ NY||2 Wheel||%height=75px%[[Site.Webb1869| http://meta-studies.net/pmwiki/uploads/Webb.jpg]]||~~

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%center%Locke Adder 1905-10

to:

%center%Locke Adder 1905-10\\

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One such line of development was based on the possibility of adding linear displacements of strips of metal. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe, later to be known as the Addiator (of which there is one in this collection), of which a bewildering number of different designs appeared in the late C19 and early C20. Some used strips or rods, and some used chains which were more versatile. ~~Those in this collection are shown below. (Clicking on the image will take you to a larger image on the description page~~.)

to:

One such line of development was based on the possibility of adding linear displacements of strips of metal. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe, later to be known as the Addiator (of which there is one in this collection), of which a bewildering number of different designs appeared in the late C19 and early C20. Some used strips or rods, and some used chains which were more versatile. A rather beautiful Locke Adder which uses strips moved by knobs, from 1905-10, sold by Clarence Locke, is shown below.

Changed lines 77-81 from:

to:

%center%Locke Adder 1905-10
%center%(collection Calculant)

Other simple linear devices in this collection are shown below. (Clicking on the image will take you to a larger image on the description page.)

Deleted line 82:

~~||1905-11 ||Locke Adder||Clarence\\Locke\\||Rod||%height=75px%[[Site.Locke1901| http://meta-studies.net/pmwiki/uploads/Locke.gif]]||~~

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%height=~~150px~~%[[Site.Locke1901| http://meta-studies.net/pmwiki/uploads/Locke.gif]]||

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%center%%height=100px%[[Site.Locke1901| http://meta-studies.net/pmwiki/uploads/Locke.gif]]

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%~~height=150px~~%~~[[Site.Webb1869|~~ http://meta-studies.net/pmwiki/uploads/Webb.jpg]]||

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%center% %height=150px%[[Site.Webb1869| http://meta-studies.net/pmwiki/uploads/Webb.jpg]]

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%height=150px%[[Site.Locke1901| http://meta-studies.net/pmwiki/uploads/Locke.gif]]||

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%height=150px%[[Site.Webb1869| http://meta-studies.net/pmwiki/uploads/Webb.jpg]]||

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%height=250px%[[Site.Locke1901| http://meta-studies.net/pmwiki/uploads/Locke.gif]]||

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%center% %height=~~300px~~% [[Site.ThomasDeColmar1884|http://meta-studies.net/pmwiki/uploads/ThomasDeColmar.jpg]]

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%center% %height=250px% [[Site.ThomasDeColmar1884|http://meta-studies.net/pmwiki/uploads/ThomasDeColmar.jpg]]

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%center% %height=~~300px~~% [[Site.ComptometerWoodie1896|http://meta-studies.net/pmwiki/uploads/ComptometerWoodie.png]]

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%center% %height=250px% [[Site.ComptometerWoodie1896|http://meta-studies.net/pmwiki/uploads/ComptometerWoodie.png]]

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%center% %height=300px% [[~~Site.~~Site.ComptometerWoodie1896|http://meta-studies.net/pmwiki/uploads/ComptometerWoodie.png]]

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%center% %height=300px% [[Site.ComptometerWoodie1896|http://meta-studies.net/pmwiki/uploads/ComptometerWoodie.png]]

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~~Sept 1896: Felt and Tarrant Comptometer~~: ~~Earliest~~ - ~~wood-cased “Woodie” model, serial 2491~~ - ~~a "~~model ~~T" for industrial calculation.~~

to:

%center% %height=300px% [[Site.Site.ComptometerWoodie1896|http://meta-studies.net/pmwiki/uploads/ComptometerWoodie.png]]
%center% 1896: Felt and Tarrant Comptometer\\Earliest - wood-cased model, serial 2491\\
%center% (collection Calculant)

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Popular though some of these were as they became cheaper and more accessible not only to shopkeepers but ordinary citizens who might value the assistance they offered, for example in their role as taxpayers,[^See for example,"‘Yours for Improvement’—The Adding Machines of Chicago, 1884–1930", //IEEE Annals of the History of Computing//, July-September, 2001, pp. 3-6.^] they suffered from the same problems of clumsy input and slow operation that afflicted the simple linear machines. Some such as the Adall could only add, others had no provision for zeroing, and all were slow to use. Further, such adders, whilst simple in concept and cheap to manufacture, were so slow to use for repetitive calculation that they were virtually useless for the key arithmetic operations of multiplication and division. A quick method repeated addition and subtraction was required at minimum to achieve these other two functions. That required a more expensive approach and a much more elaborate machine, the first commercial variant of which was designed and sold as the "Arithmometer" by Thomas de Colmar.

to:

Popular though some of these were as they became cheaper and more accessible not only to shopkeepers but ordinary citizens who might value the assistance they offered, for example in their role as taxpayers,[^See for example, A.P. Kidwell, "‘Yours for Improvement’—The Adding Machines of Chicago, 1884–1930", //IEEE Annals of the History of Computing//, July-September, 2001, pp. 3-6.^] they suffered from the same problems of clumsy input and slow operation that afflicted the simple linear machines. Some such as the Adall could only add, others had no provision for zeroing, and all were slow to use. Further, such adders, whilst simple in concept and cheap to manufacture, were so slow to use for repetitive calculation that they were virtually useless for the key arithmetic operations of multiplication and division. A quick method repeated addition and subtraction was required at minimum to achieve these other two functions. That required a more expensive approach and a much more elaborate machine, the first commercial variant of which was designed and sold as the "Arithmometer" by Thomas de Colmar.

20 July 2013 by 124.170.43.18 -

Changed lines 103-105 from:

Popular though some of these were as they became cheaper and more accessible they suffered from the same problems of clumsy input and slow operation that afflicted the simple linear machines. Some such as the Adall could only add, others had no provision for zeroing, and all were slow to use. Further, such adders, whilst simple in concept and cheap to manufacture, were so slow to use for repetitive calculation that they were virtually useless for the key arithmetic operations of multiplication and division. A quick method repeated addition and subtraction was required at minimum to achieve these other two functions. That required a more expensive approach and a much more elaborate machine, the first commercial variant of which was designed and sold as the "Arithmometer" by Thomas de Colmar.

to:

Popular though some of these were as they became cheaper and more accessible not only to shopkeepers but ordinary citizens who might value the assistance they offered, for example in their role as taxpayers,[^See for example,"‘Yours for Improvement’—The Adding Machines of Chicago, 1884–1930", //IEEE Annals of the History of Computing//, July-September, 2001, pp. 3-6.^] they suffered from the same problems of clumsy input and slow operation that afflicted the simple linear machines. Some such as the Adall could only add, others had no provision for zeroing, and all were slow to use. Further, such adders, whilst simple in concept and cheap to manufacture, were so slow to use for repetitive calculation that they were virtually useless for the key arithmetic operations of multiplication and division. A quick method repeated addition and subtraction was required at minimum to achieve these other two functions. That required a more expensive approach and a much more elaborate machine, the first commercial variant of which was designed and sold as the "Arithmometer" by Thomas de Colmar.

Changed line 110 from:

It was Thomas de Colmar who decisively built Thomas de Colmar arithmometer (1884) Each represents a different mechanical approach to digitally carrying out the four functions, with an easy input, and a digital readout. Each then was improved through a series of innovations, first by the original inventors, and then as more players across the world competed to produce and market better variants.%0a %0aThomas de Colmar was the first person to produce a commercially useable calculator based on Leibnitz’s stepped drum principle, and he named his machine the “arithmometer”. The Thomas design was copied and improved by a number of other engineers and marketed from different countries.

to:

It was Thomas de Colmar who decisively built Thomas de Colmar arithmometer (1884) Each represents a different mechanical approach to digitally carrying out the four functions, with an easy input, and a digital readout. Each then was improved through a series of innovations, first by the original inventors, and then as more players across the world competed to produce and market better variants.%0a %0aThomas de Colmar was the first person to produce a commercially useable calculator based on Leibnitz’s stepped drum principle, and he named his machine the “arithmometer”. The Thomas design was copied and improved by a number of other engineers and marketed from different countries.[^P. A. Kidwell, "American Scientists and Calculating Machines- From Novelty to Commonplace", Annals of the History of Computing, Volume 12, Number 1, 1990, pp. 31^]

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||1909 ||TIM (Time is Money)\\ Arithmometer||Ludwig Spitz\\ & Co||Arithmometer||%height=~~100px~~%[[Site.TIM1909| http://meta-studies.net/pmwiki/uploads/TIM.JPG]]||
||~1913 ||Bunzel-Denton Arithmometer||Bunzel||Prototype\\Front Crank||%height=~~100px~~%[[Site.BunzelPrototype1913| http://meta-studies.net/pmwiki/uploads/Bunzel.JPG]]||
||~1917 ||Madas IX Maxima||Madas||Auto Division||%height=~~100px~~%[[Site.Madas-IX-Maxima| http://meta-studies.net/pmwiki/uploads/MADAS-1917.jpg]]||

to:

||1909 ||TIM (Time is Money)\\ Arithmometer||Ludwig Spitz\\ & Co||Arithmometer||%height=75px%[[Site.TIM1909| http://meta-studies.net/pmwiki/uploads/TIM.JPG]]||
||~1913 ||Bunzel-Denton Arithmometer||Bunzel||Prototype\\Front Crank||%height=75px%[[Site.BunzelPrototype1913| http://meta-studies.net/pmwiki/uploads/Bunzel.JPG]]||
||~1917 ||Madas IX Maxima||Madas||Auto Division||%height=75px%[[Site.Madas-IX-Maxima| http://meta-studies.net/pmwiki/uploads/MADAS-1917.jpg]]||

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||Note||Date||Maker||Type||Device (click for description)
||1909 ||TIM (Time is Money)\\ Arithmometer||Ludwig Spitz\\ & Co||Arithmometer||%height=~~200px~~%[[Site.TIM1909| http://meta-studies.net/pmwiki/uploads/TIM.JPG]]||
||~1913 ||Bunzel-Denton Arithmometer||Bunzel||Prototype\\Front Crank||%height=~~200px~~%[[Site.BunzelPrototype1913| http://meta-studies.net/pmwiki/uploads/Bunzel.JPG]]||
||~1917 ||Madas IX Maxima||Madas||Auto Division||%height=~~200px~~%[[Site.Madas-IX-Maxima| http://meta-studies.net/pmwiki/uploads/MADAS-1917.jpg]]||

to:

||Note||Date||Maker||Type||Device (click for description)||
||1909 ||TIM (Time is Money)\\ Arithmometer||Ludwig Spitz\\ & Co||Arithmometer||%height=100px%[[Site.TIM1909| http://meta-studies.net/pmwiki/uploads/TIM.JPG]]||
||~1913 ||Bunzel-Denton Arithmometer||Bunzel||Prototype\\Front Crank||%height=100px%[[Site.BunzelPrototype1913| http://meta-studies.net/pmwiki/uploads/Bunzel.JPG]]||
||~1917 ||Madas IX Maxima||Madas||Auto Division||%height=100px%[[Site.Madas-IX-Maxima| http://meta-studies.net/pmwiki/uploads/MADAS-1917.jpg]]||

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1884: Thomas de Colmar Arithmometer Model T1878 B, serial 2083

1909: Ludwig Spitz & Co.~~, G~~.m.~~b.H., Berlin~~-~~Tempelhof TIM (Time is Money)~~ Arithmometer

~~~1913:~~ Bunzel~~-Denton Arithmometer~~ Prototype with crank moved to front

1917: Madas IX Maxima ~~calculator, serial 5532~~

to:

||Note||Date||Maker||Type||Device (click for description)
||1909 ||TIM (Time is Money)\\ Arithmometer||Ludwig Spitz\\ & Co||Arithmometer||%height=200px%[[Site.TIM1909| http://meta-studies.net/pmwiki/uploads/TIM.JPG]]||
||~1913 ||Bunzel-Denton Arithmometer||Bunzel||Prototype\\Front Crank||%height=200px%[[Site.BunzelPrototype1913| http://meta-studies.net/pmwiki/uploads/Bunzel.JPG]]||
||~1917 ||Madas IX Maxima||Madas||Auto Division||%height=200px%[[Site.Madas-IX-Maxima| http://meta-studies.net/pmwiki/uploads/MADAS-1917.jpg]]||
(collection Calculant - all above)

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%center% %height=300px% http://meta-studies.net/pmwiki/uploads/ThomasDeColmar.~~jpg~~

to:

%center% %height=300px% [[Site.ThomasDeColmar1884|http://meta-studies.net/pmwiki/uploads/ThomasDeColmar.jpg]]

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%center% http://meta-studies.net/pmwiki/uploads/ThomasDeColmar.jpg
%center% 1884: Thomas de Colmar Arithmometer ~~Serial~~ 2083 Model T1878 B

to:

%center% %height=300px% http://meta-studies.net/pmwiki/uploads/ThomasDeColmar.jpg
%center% 1884: Thomas de Colmar Arithmometer\\Serial 2083 Model T1878 B\\

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to:

(collection Calculant - all above)

Changed lines 97-98 from:

to:

(collection Calculant - all above)

Added lines 111-115:

%center% http://meta-studies.net/pmwiki/uploads/ThomasDeColmar.jpg
%center% 1884: Thomas de Colmar Arithmometer Serial 2083 Model T1878 B
%center% (collection Calculant)

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Changed lines 101-105 from:

Popular though some of these were as they became cheaper and more accessible they suffered from the same problems of clumsy input and slow operation that afflicted the simple linear machines. Some such as the Adall could only add, others had no provision for zeroing, and all were slow to use. Further, such adders, whilst simple in concept and cheap to manufacture, were so slow to use for repetitive calculation that they were virtually useless for the key arithmetic operations of multiplication and division.

~~!!!Commercial~~ calculating machines

to:

Popular though some of these were as they became cheaper and more accessible they suffered from the same problems of clumsy input and slow operation that afflicted the simple linear machines. Some such as the Adall could only add, others had no provision for zeroing, and all were slow to use. Further, such adders, whilst simple in concept and cheap to manufacture, were so slow to use for repetitive calculation that they were virtually useless for the key arithmetic operations of multiplication and division. A quick method repeated addition and subtraction was required at minimum to achieve these other two functions. That required a more expensive approach and a much more elaborate machine, the first commercial variant of which was designed and sold as the "Arithmometer" by Thomas de Colmar.

!!!Commercial "four function" calculating machines

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|1910 ||Adall Adding Machine||Dreyfus\\and Levy ||Key input\\Concentric \\toothed disk\\and groove||%height=75px%[[Site.Adall1910| http://meta-studies.net/pmwiki/uploads/Adall.jpg]]||

to:

||1910 ||Adall Adding Machine||Dreyfus\\and Levy ||Key input\\Concentric \\toothed disk\\and groove||%height=75px%[[Site.Adall1910| http://meta-studies.net/pmwiki/uploads/Adall.jpg]]||

Changed lines 97-110 from:

The main advantage of these devices was that they were cheap to manufacture and could be easily mass-produced. ~~The most obvious development was not only in the subtleties of carry mechanism (and in the case of the Adix the use of key input) but also progress~~ in the ~~use of materials. Here we see the heavy two wheel mechanism~~ of the Webb Adder, in brass and wood, counterposed against the Adix Adding Machine which for the first time incorporates aluminium amongst its 122 parts, whilst the SEE Adding Machine which is entirely composed of plastic, has a Pascaline-like weighted carry mechanism, but is built so lightly utilising a materials evolution over three centuries, that a much simplified approach was by now implementable.

!!!!Other simple approaches
A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which simply used successive rotations of a wheel to wind on successive numbers whilst a ball bearing, moving in a spiral groove, tracked the successive rotations. Such adders, whilst simple in concept and cheap to manufacture, are slow and virtually useless for efficient multiplication and division. Early experiments with keyboards can be seen in the Adix adding machine of 1903, but as the one in this collection shows, it can only add and is very hard even to zero.

~1910 Adall Concentric-disk Adding Machine

!To be continued....
This essay is under construction. If it is ever finished (:-) it is intended to utilise this collection to ~~shape a continuing if idiosyncratic story of the development of embodied calculation up to~~ the ~~introduction of personal electronic calculation. So do visit again if you have got this far, and there may (should) be more~~.
~~!Reshaping style~~

to:

The main advantage of these devices was that they were cheap to manufacture and could be easily mass-produced. We can of course see a lot of innovation in the detail of these machines. A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which simply used successive rotations of a wheel to wind on successive numbers whilst a ball bearing, moving in a spiral groove, tracked the successive rotations. Early experiments with keyboards can be seen in the Adix adding machine of 1903.

The most obvious other development beyond the subtleties of carry mechanism was the developments in the use of materials. Here we see the heavy two wheel mechanism of the Webb Adder, in brass and wood, counterposed against the Adix Adding Machine which for the first time incorporates aluminium amongst its 122 parts, whilst the SEE Adding Machine which is entirely composed of plastic, has a Pascaline-like weighted carry mechanism, but is built so lightly utilising a materials evolution over three centuries, that a much simplified approach was by now implementable.

Popular though some of these were as they became cheaper and more accessible they suffered from the same problems of clumsy input and slow operation that afflicted the simple linear machines. Some such as the Adall could only add, others had no provision for zeroing, and all were slow to use. Further, such adders, whilst simple in concept and cheap to manufacture, were so slow to use for repetitive calculation that they were virtually useless for the key arithmetic operations of multiplication and division.

Added lines 143-147:

!To be continued....
This essay is under construction. If it is ever finished (:-) it is intended to utilise this collection to shape a continuing if idiosyncratic story of the development of embodied calculation up to the introduction of personal electronic calculation. So do visit again if you have got this far, and there may (should) be more.

!Reshaping style

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||1890-1900 || A. M. Stevenson Adder||Joliet, Ill.\\||2 Wheel||%height=75px%[[Stevenson1890| http://meta-studies.net/pmwiki/uploads/Stevenson.png]]||

to:

||1890-1900 ||A. M. Stevenson Adder||Joliet, Ill.\\||2 Wheel||%height=75px%[[Stevenson1890| http://meta-studies.net/pmwiki/uploads/Stevenson.png]]||

Added line 93:

|1910 ||Adall Adding Machine||Dreyfus\\and Levy ||Key input\\Concentric \\toothed disk\\and groove||%height=75px%[[Site.Adall1910| http://meta-studies.net/pmwiki/uploads/Adall.jpg]]||

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Changed lines 96-99 from:

The main advantage of these devices was that they were cheap to manufacture and could be easily mass-produced. The most obvious development was not only in the subtleties of carry mechanism (and in the case of the Adix the use of key input) but also progress in the use of materials. Here we see the heavy two wheel mechanism of the Webb Adder, in brass and wood, counterposed against the Adix Adding Machine which for the first time incorporates aluminium amongst its 122 parts, whilst the SEE Adding Machine which is entirely composed of plastic, has a Pascaline-like weighted carry mechanism, but is built so lightly utilising a materials evolution over three centuries, that a much simplified approach is now implementable.

to:

The main advantage of these devices was that they were cheap to manufacture and could be easily mass-produced. The most obvious development was not only in the subtleties of carry mechanism (and in the case of the Adix the use of key input) but also progress in the use of materials. Here we see the heavy two wheel mechanism of the Webb Adder, in brass and wood, counterposed against the Adix Adding Machine which for the first time incorporates aluminium amongst its 122 parts, whilst the SEE Adding Machine which is entirely composed of plastic, has a Pascaline-like weighted carry mechanism, but is built so lightly utilising a materials evolution over three centuries, that a much simplified approach was by now implementable.

Added lines 99-100:

A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which simply used successive rotations of a wheel to wind on successive numbers whilst a ball bearing, moving in a spiral groove, tracked the successive rotations. Such adders, whilst simple in concept and cheap to manufacture, are slow and virtually useless for efficient multiplication and division. Early experiments with keyboards can be seen in the Adix adding machine of 1903, but as the one in this collection shows, it can only add and is very hard even to zero.

Changed line 103 from:

A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which simply used successive rotations of a wheel to wind on successive numbers whilst a ball bearing, moving in a spiral groove, tracked the successive rotations. Such adders, whilst simple in concept and cheap to manufacture, are slow and virtually useless for efficient multiplication and division. Early experiments with keyboards can be seen in the Adix adding machine of 1903, but as the one in this collection shows, it can only add and is very hard even to zero.

to:

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||1890-1900 || A. M. Stevenson Adder||Joliet, Ill.\\||2 Wheel||%height=75px%[[Stevenson1890| http://meta-studies.net/pmwiki/uploads/Stevenson.png]]|
||1903 ||Adix Adding Machine\\Original model||Manheim||Key input\\lever &\\gears||%height=75px%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/Adix.png]]|
||~1946 ||Lightning Portable\\Adding Machine||Lightning\\Adding Machine\\Co. L.A.||7 Wheels||%height=75px%[[Site.Lightning1946| http://meta-studies.net/pmwiki/uploads/Lightning.png]]|
||1968 ||SEE Demonstration\\Adding Machine||Selective Educational\\Equipment Corporation||4 Wheels||%height=75px%[[Site.SEE1968| http://meta-studies.net/pmwiki/uploads/SEE-1.jpg]]|

The main advantage of these devices was that they were cheap to manufacture and could be easily mass-produced. ~~They were however little more than gimmicks which were too slow to be used as a practical means of addition or subtraction for which they were designed~~.

to:

||1890-1900 || A. M. Stevenson Adder||Joliet, Ill.\\||2 Wheel||%height=75px%[[Stevenson1890| http://meta-studies.net/pmwiki/uploads/Stevenson.png]]||
||1903 ||Adix Adding Machine\\Original model||Manheim||Key input\\lever &\\gears||%height=75px%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/Adix.png]]||
||~1946 ||Lightning Portable\\Adding Machine||Lightning\\Adding Machine\\Co. L.A.||7 Wheels||%height=75px%[[Site.Lightning1946| http://meta-studies.net/pmwiki/uploads/Lightning.png]]||
||1968 ||SEE Demonstration\\Adding Machine||Selective Educational\\Equipment Corporation||4 Wheels||%height=75px%[[Site.SEE1968| http://meta-studies.net/pmwiki/uploads/SEE-1.jpg]]||

The main advantage of these devices was that they were cheap to manufacture and could be easily mass-produced. The most obvious development was not only in the subtleties of carry mechanism (and in the case of the Adix the use of key input) but also progress in the use of materials. Here we see the heavy two wheel mechanism of the Webb Adder, in brass and wood, counterposed against the Adix Adding Machine which for the first time incorporates aluminium amongst its 122 parts, whilst the SEE Adding Machine which is entirely composed of plastic, has a Pascaline-like weighted carry mechanism, but is built so lightly utilising a materials evolution over three centuries, that a much simplified approach is now implementable.

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||1968 ||SEE Demonstration\\Adding Machine||Selective Educational\\Equipment Corporation||4 Wheels||%height=75px%[[Site.SEE1968| http://meta-studies.net/pmwiki/uploads/~~Locke~~.~~gif~~]]|

to:

||1968 ||SEE Demonstration\\Adding Machine||Selective Educational\\Equipment Corporation||4 Wheels||%height=75px%[[Site.SEE1968| http://meta-studies.net/pmwiki/uploads/SEE-1.jpg]]|

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~~1869 model Web Patent Adder~~ and ~~Talley~~ Board serial B2040

1890-1900: A. M. Stevenson Adder

1903: ~~Adix Adding Machine~~. Original model

~1946: Lightning Portable Adding Machine

1968: SEE Demonstration Adding ~~Machine~~

to:

||Note||Date||Maker||Type||Device (click for description)
||1869 ||Web Patent\\Adder and\\Talley Board||C.H. Webb\\ NY||2 Wheel||%height=75px%[[Site.Webb1869| http://meta-studies.net/pmwiki/uploads/Webb.jpg]]||
||1890-1900 || A. M. Stevenson Adder||Joliet, Ill.\\||2 Wheel||%height=75px%[[Stevenson1890| http://meta-studies.net/pmwiki/uploads/Stevenson.png]]|
||1903 ||Adix Adding Machine\\Original model||Manheim||Key input\\lever &\\gears||%height=75px%[[Site.Adix1903| http://meta-studies.net/pmwiki/uploads/Adix.png]]|
||~1946 ||Lightning Portable\\Adding Machine||Lightning\\Adding Machine\\Co. L.A.||7 Wheels||%height=75px%[[Site.Lightning1946| http://meta-studies.net/pmwiki/uploads/Lightning.png]]|
||1968 ||SEE Demonstration\\Adding Machine||Selective Educational\\Equipment Corporation||4 Wheels||%height=75px%[[Site.SEE1968| http://meta-studies.net/pmwiki/uploads/Locke.gif]]|

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||Note||Date||~~Type~~||~~Maker~~||Device (click for description)

to:

||Note||Date||Maker||Type||Device (click for description)

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||1905-11 ||Locke Adder||Clarence\\~~Lock~~\\||Rod||%height=75px%[[Site.Locke1901| http://meta-studies.net/pmwiki/uploads/Locke.gif]]||

to:

||1905-11 ||Locke Adder||Clarence\\Locke\\||Rod||%height=75px%[[Site.Locke1901| http://meta-studies.net/pmwiki/uploads/Locke.gif]]||

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||~1915||Golden Gem Automatic Adding Machine||H. & H. Goldmann||Chain||%height=75px%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg]]||

to:

||~1915||Golden Gem Automatic\\Adding Machine||H. & H. Goldmann||Chain||%height=75px%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg]]||

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||1937||Add-O-Matic Adding Machine||Allied MFG. Co.||Chain||%height=75px%[[Site.Add-O-Matic1937 |http://meta-studies.net/pmwiki/uploads/AddOMatic1.jpg]]||

to:

||1937||Add-O-Matic\\Adding Machine||Allied MFG. Co.||Chain||%height=75px%[[Site.Add-O-Matic1937 |http://meta-studies.net/pmwiki/uploads/AddOMatic1.jpg]]||

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||~1915||Golden Gem Automatic Adding Machine||~~Chain||~~H. & H. Goldmann||%height=75px%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg]]||

to:

||~1915||Golden Gem Automatic Adding Machine||H. & H. Goldmann||Chain||%height=75px%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg]]||

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The above relied either on the movement by a stylus or knobs of strips, rods or chains to create addition. Some (such as the Locke adder) used a simplified form of complementary arithmetic for subtraction,t others allowed a such as the Golden Gem allowed reverse motion, and others again such as the Addiator could be turned over to perform the subtraction. Most (but not the Locke Adder) had a simple provision for carries and some (such as the Scribola - which also had a very early printout) had clearing levers to bring the display back to zero for the next calculation. All however, whilst affordable, were cumbersome and slow to use since each digit had to be individually entered by performing a sliding motion. It was much quicker to add the numbers on paper using mental arithmetic, but of course, here that capability was lacking, or where the effort of doing it was considered tedious, then these devices began to find a market in the first half of the C20, and thousands were produced and sold.

to:

The above relied either on the movement by a stylus or knobs of strips, rods or chains to create addition. Some (such as the Locke adder) used a simplified form of complementary arithmetic for subtraction,t others allowed a such as the Golden Gem allowed reverse motion, and others again such as the Addiator could be turned over to perform the subtraction. Most (but not the Locke Adder) had a simple provision for carries and some (such as the Scribola - which also had a very early printout) had clearing levers to bring the display back to zero for the next calculation. All however, whilst affordable, were cumbersome and slow to use since each digit had to be individually entered by performing a sliding motion. It was much quicker to add the numbers on paper using mental arithmetic, but of course, here that capability was lacking, or where the effort of doing it was considered tedious, then these devices began to find a market in the first half of the C20, and thousands were produced and sold across the more industrialised countries of Europe, the British Empire and the USA.

20 July 2013 by 124.170.43.18 -

Changed lines 84-85 from:

The above relied either on the movement by a stylus of strips, rods or chains to create addition. Some such as the Locke ~~Adder required~~

to:

The above relied either on the movement by a stylus or knobs of strips, rods or chains to create addition. Some (such as the Locke adder) used a simplified form of complementary arithmetic for subtraction,t others allowed a such as the Golden Gem allowed reverse motion, and others again such as the Addiator could be turned over to perform the subtraction. Most (but not the Locke Adder) had a simple provision for carries and some (such as the Scribola - which also had a very early printout) had clearing levers to bring the display back to zero for the next calculation. All however, whilst affordable, were cumbersome and slow to use since each digit had to be individually entered by performing a sliding motion. It was much quicker to add the numbers on paper using mental arithmetic, but of course, here that capability was lacking, or where the effort of doing it was considered tedious, then these devices began to find a market in the first half of the C20, and thousands were produced and sold.

Changed line 87 from:

Similar simple devices were developed which utilised simple rotation of cogs, with a crude carry process (usually along the lines of that used by Schickard). They relied for their success on having but a small number of interacting cogs, so that the carry mechanism would not jam. In this sense (despite often being referred to as of the style of the Pascaline) they were extensions of the idea of the adding component of Schickard's instrument and lacked the centrally important innovation of Pascal where the ~~carry was achieved by~~ a ~~weighted sorter~~.

to:

Similar simple devices were developed which utilised simple rotation of cogs, with a crude carry process (usually along the lines of that used by Schickard). They relied for their success on having but a small number of interacting cogs, so that the carry mechanism would not jam, or adopting the use of springs (in place of Pascal's weights) which would store rotary motion to then be utilised when a carry was required. Those in this collection are shown below. (Once more, clicking on the image will take you to a larger image on the description page.)

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One such line of development was based on the possibility of adding linear displacements of strips of metal. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe, later to be known as the Addiator (of which there is one in this collection), of which a bewildering number of different designs appeared in the late C19 and early C20. Those in this collection are shown below. (Clicking on the image will take you to a larger image on the description page.)

to:

One such line of development was based on the possibility of adding linear displacements of strips of metal. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe, later to be known as the Addiator (of which there is one in this collection), of which a bewildering number of different designs appeared in the late C19 and early C20. Some used strips or rods, and some used chains which were more versatile. Those in this collection are shown below. (Clicking on the image will take you to a larger image on the description page.)

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The above relied either on the movement by a stylus of strips, rods or chains to create addition. Some such as the Locke Adder required

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||Note||Date||Type||Maker||

to:

||Note||Date||Type||Maker||Device (click for description)

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||1937||Add-O-Matic Adding Machine||Allied MFG. Co.||Chain||%height=75px%[[Site.Add-O-Matic1937 |http://meta-studies.net/pmwiki/uploads/~~AddOMatic2~~.jpg]]||

to:

||1937||Add-O-Matic Adding Machine||Allied MFG. Co.||Chain||%height=75px%[[Site.Add-O-Matic1937 |http://meta-studies.net/pmwiki/uploads/AddOMatic1.jpg]]||

20 July 2013 by 124.170.43.18 -

Changed lines 74-75 from:

One such line of development was based on the possibility of adding linear displacements of strips of metal. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe, later to be known as the Addiator (of which there is one in this collection), of which a bewildering number of different designs appeared in the late C19 and early C20.

to:

One such line of development was based on the possibility of adding linear displacements of strips of metal. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe, later to be known as the Addiator (of which there is one in this collection), of which a bewildering number of different designs appeared in the late C19 and early C20. Those in this collection are shown below. (Clicking on the image will take you to a larger image on the description page.)

Changed lines 80-87 from:

: , serial 73158

1920: Addiator Troncet adder

1922: Scribola 10 column printing Adding Machine

1937: Add-~~O-Matic Adding Machine~~

to:

||1920||Addiator Troncet adder||Ruthard & Co||Chain||%height=75px%[[Site.Addiator1920 |http://meta-studies.net/pmwiki/uploads/Addiator.png]]||
||1922||Scribola 10 column\\printing\\Adding Machine||Addiator Gesellschaft||Rod||%height=75px%[[Site.Scribola1922 |http://meta-studies.net/pmwiki/uploads/Scribola.jpg]]||
||1937||Add-O-Matic Adding Machine||Allied MFG. Co.||Chain||%height=75px%[[Site.Add-O-Matic1937 |http://meta-studies.net/pmwiki/uploads/AddOMatic2.jpg]]||

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||1905-11 ||Locke Adder||Clarence\\Lock\\||Rod||%height=~~100px~~%[[Site.Locke1901| http://meta-studies.net/pmwiki/uploads/Locke.gif]]||
||1910-20s||Comptator (9 col)||Schubert\\& Salzer||Chain||%height=~~100px~~%[[Site.Comptator1910|http://meta-studies.net/pmwiki/uploads/Comptator.png]]||
||~1915||Golden Gem Automatic Adding Machine||Chain||H. & H. Goldmann||%height=~~100px~~%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg]]||

to:

||1905-11 ||Locke Adder||Clarence\\Lock\\||Rod||%height=75px%[[Site.Locke1901| http://meta-studies.net/pmwiki/uploads/Locke.gif]]||
||1910-20s||Comptator (9 col)||Schubert\\& Salzer||Chain||%height=75px%[[Site.Comptator1910|http://meta-studies.net/pmwiki/uploads/Comptator.png]]||
||~1915||Golden Gem Automatic Adding Machine||Chain||H. & H. Goldmann||%height=75px%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg]]||

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||1905-11 ||Locke Adder||Clarence\\Lock\\||Rod||%~~width~~=~~300px~~%[[Site.Locke1901| http://meta-studies.net/pmwiki/uploads/Locke.gif]]||
||1910-20s||Comptator (9 col)||Schubert\\& Salzer||Chain||%~~width~~=~~300px~~%[[Site.Comptator1910|http://meta-studies.net/pmwiki/uploads/Comptator.png]]||
||~1915||Golden Gem Automatic Adding Machine||Chain||H. & H. Goldmann||[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg]]||

to:

||1905-11 ||Locke Adder||Clarence\\Lock\\||Rod||%height=100px%[[Site.Locke1901| http://meta-studies.net/pmwiki/uploads/Locke.gif]]||
||1910-20s||Comptator (9 col)||Schubert\\& Salzer||Chain||%height=100px%[[Site.Comptator1910|http://meta-studies.net/pmwiki/uploads/Comptator.png]]||
||~1915||Golden Gem Automatic Adding Machine||Chain||H. & H. Goldmann||%height=100px%[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg]]||

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||Note||Date||~~Maker~~||
||1905-11 ||Locke Adder||Clarence\\Lock\\||%width=300px%[[Site.Locke1901| http://meta-studies.net/pmwiki/uploads/Locke.gif]]||

||~~[[#ii]](ii)~~||~~1759-69~~||~~Edward~~\\~~Roberts\\Everard\\pattern\\gauger's\\rule\\\\~~||%width=300px% http://meta-studies.net/pmwiki/uploads/~~Everard~~.~~jpg~~||
1905-1911: Locke Adder

1910-1920s Comptator, 9 column

~1915: Golden Gem Automatic Adding Machine, serial 73158

to:

||Note||Date||Type||Maker||
||1905-11 ||Locke Adder||Clarence\\Lock\\||Rod||%width=300px%[[Site.Locke1901| http://meta-studies.net/pmwiki/uploads/Locke.gif]]||
||1910-20s||Comptator (9 col)||Schubert\\& Salzer||Chain||%width=300px%[[Site.Comptator1910|http://meta-studies.net/pmwiki/uploads/Comptator.png]]||
||~1915||Golden Gem Automatic Adding Machine||Chain||H. & H. Goldmann||[[Site.GoldenGem1915|http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg]]||

: , serial 73158

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to:

||Note||Date||Maker||
||1905-11 ||Locke Adder||Clarence\\Lock\\||%width=300px%[[Site.Locke1901| http://meta-studies.net/pmwiki/uploads/Locke.gif]]||

||[[#ii]](ii)||1759-69||Edward\\Roberts\\Everard\\pattern\\gauger's\\rule\\\\||%width=300px% http://meta-studies.net/pmwiki/uploads/Everard.jpg||

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!!!Proportional Rack Calculators

to:

!!!!Proportional Rack Calculators

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!!Evolutionary cul-de-sac: the search for true multiplication and division

to:

!!!Evolutionary cul-de-sac: the search for true multiplication and division

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!!Harnessing electricity

to:

!!!Harnessing electricity

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!The Vanishing point: electronics and the arrival of the HP35

to:

!!!The Vanishing point: electronics and the arrival of the HP35

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!!Commercial calculating machines

!!!Arithmometers

to:

!!!Commercial calculating machines

!!!!Arithmometers

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!!!Comptometers

to:

!!!!Comptometers

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!!!Pinwheels

to:

!!!!Pinwheels

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!!!Curta: The peak of minituarisation (1947–1970)

to:

!!!!Curta: The peak of minituarisation (1947–1970)

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!!!!Arithmometers

to:

!!!Arithmometers

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!!!!Comptometers

to:

!!!Comptometers

20 July 2013 by 124.170.43.18 -

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!!!Commercial calculating machines

!Arithmometers

to:

!!Commercial calculating machines

!!!!Arithmometers

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!Comptometers

to:

!!!!Comptometers

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!Pinwheels

to:

!!!Pinwheels

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!Proportional Rack Calculators

to:

!!!Proportional Rack Calculators

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!Curta: The peak of minituarisation (1947–1970)

to:

!!!Curta: The peak of minituarisation (1947–1970)

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!"Arms races" and mechanical evolution

to:

!!!"Arms races" and mechanical evolution

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!!!Evolutionary cul-de-sac: the search for true multiplication and division

to:

!!Evolutionary cul-de-sac: the search for true multiplication and division

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!!!Harnessing electricity

to:

!!Harnessing electricity

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Added lines 111-115:

!To be continued....
This essay is under construction. If it is ever finished (:-) it is intended to utilise this collection to shape a continuing if idiosyncratic story of the development of embodied calculation up to the introduction of personal electronic calculation. So do visit again if you have got this far, and there may (should) be more.
!Reshaping style

Deleted lines 131-137:

!To be continued....
This essay is under construction. If it is ever finished (:-) it is intended to utilise this collection to shape a continuing if idiosyncratic story of the development of embodied calculation up to the introduction of personal electronic calculation. So do visit again if you have got this far, and there may (should) be more.
!Reshaping style

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1903: Adix Adding Machine. Original model

Changed lines 112-118 from:

It was Thomas de Colmar who decisively built

~~!Thomas de Colmar - a commercial calculator~~

Thomas de Colmar arithmometer (1884) Each represents a different mechanical approach to digitally carrying out the four functions, with an easy input, and a digital readout. Each then was improved through a series of innovations, first by the original inventors, and then as more players across the world competed to produce and market better variants.%0a %0aThomas de Colmar was the first person to produce a commercially useable calculator based on Leibnitz’s stepped drum principle, and he named his machine the “arithmometer”. The Thomas design was copied and improved by a number of other engineers and marketed from different countries.

to:

!Arithmometers

It was Thomas de Colmar who decisively built Thomas de Colmar arithmometer (1884) Each represents a different mechanical approach to digitally carrying out the four functions, with an easy input, and a digital readout. Each then was improved through a series of innovations, first by the original inventors, and then as more players across the world competed to produce and market better variants.%0a %0aThomas de Colmar was the first person to produce a commercially useable calculator based on Leibnitz’s stepped drum principle, and he named his machine the “arithmometer”. The Thomas design was copied and improved by a number of other engineers and marketed from different countries.

Changed lines 119-122 from:

to:

1884: Thomas de Colmar Arithmometer Model T1878 B, serial 2083

1909: Ludwig Spitz & Co., G.m.b.H., Berlin-Tempelhof TIM (Time is Money) Arithmometer

~1913: Bunzel-Denton Arithmometer Prototype with crank moved to front

1917: Madas IX Maxima calculator, serial 5532

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!~~Felt and Tarrant - a "model T" for industrial calculation.~~

to:

!Comptometers

Changed lines 139-142 from:

~~!Ohdner's~~ Pinwheels

to:

Sept 1896: Felt and Tarrant Comptometer: Earliest - wood-cased “Woodie” model, serial 2491 - a "model T" for industrial calculation.
~ 1907: Comptometer oil bottle, marked with patent 23 April 1905; 6 April 1907
~ 1955 Bell Punch Sumlock Demonstration Comptometer
1950s: Bell Sumlock Comptometer Model 909/S/117.878 (made in Great Britain by Bell Punch Company Ltd)

!Pinwheels

Added lines 148-154:

~1896: Ohdner Brunsviga Schuster Calculator serial 3406
1945: Facit Model S Calculator serial 210652
~1951: Original Ohdner Model 39, Calculator serial 39-288965
1957: Walther Demonstration WSR160 Pinwheel Calculator
~1957: Walther WSR160 Pinwheel Calculator

Added lines 157-163:

!Proportional Rack Calculators

1923: Mercedes-Euklid Model 29 Demonstration calculator

1923: Mercedes-Euklid Model 29 calculator

Added lines 167-173:

~July 1948: CURTA Type 1 (pin sliders) earliest model calculator serial 5424

1967: CURTA Type I calculator serial 76436, near mint, with original case, cardboard box and instructions

1963: CURTA Type II calculator with Leather Case, serial 554765

Added lines 185-188:

1904-1905: Bamberger’s Omega Calculating Machine

1912: Millionaire Calculating Machine serial 2015 (10x10x20)

Changed lines 209-214 from:

to:

~1929 “Herzstark” electric Calculating Machine serial 6549, badged by Herzstark, Vienna; essentially Badenia Model TE 13 Duplex

1950s-1960s: MADAS Model 20BTG serial 94046 electric calculator with true automatic division

Added lines 216-219:

July1972: Hewlett Packard HP 35 Calculator serial 1230A 79429, 1972 (second version)

December 1973: Hewlett Packard HP 45 Calculator serial 1350A 36719, 1973

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Changed line 73 from:

!!!!Simple linear ~~mechanisms~~

to:

!!!!Simple linear devices

Changed lines 75-80 from:

Addiator,
Golden Gem,
Locke Adder
Slide Rule

!!!!Simple rotational mechanisms

to:

1905-1911: Locke Adder

1910-1920s Comptator, 9 column

~1915: Golden Gem Automatic Adding Machine, serial 73158

1920: Addiator Troncet adder

1922: Scribola 10 column printing Adding Machine

1937: Add-O-Matic Adding Machine

!!!!Simple rotational devices

Changed lines 92-96 from:

Webb Patent Adder (1869)
Stevens Adder (1890s)
Lightning (1940s)
SEE

to:

1869 model Web Patent Adder and Talley Board serial B2040

1890-1900: A. M. Stevenson Adder

~1946: Lightning Portable Adding Machine

1968: SEE Demonstration Adding Machine

Changed lines 105-106 from:

to:

~1910 Adall Concentric-disk Adding Machine

Changed lines 147-151 from:

An entirely different evolutionary path which has already been mentioned was attempted to solving the problem of mechanising the four arithmetic operations (+, -, x, /), with emphasis on finding ways to directly perform the more difficult two operations of multiplication and division. This developed from the Napier’s rods - or “bones” (developed by John Napier (1550–1617) to which we have already referred. As already mentioned calculational approaches were designed around them by Wilhelm Schickard in 1623, Charles Cotterel in 1667, Gaspard Schott in 1668, and Samuel Morland between 1625 and 1695. A late and unique expression of these in this collection is Justin Bamberger’s Omega Calculating Machine (1903-6). It combines a stylus operated adding machine (complete with provision for automatic carry) with a sophisticated Napier bones based machine for discovering the partial products of two multiplied numbers (a bit like that in Schickard’s much earlier device), which can then be added in the adding machine to find corresponding products and quotients. ~~I am working on an English language set of instructions for its use have been devised and are available~~. ~~For that, watch this space~~.

to:

An entirely different evolutionary path which has already been mentioned was attempted to solving the problem of mechanising the four arithmetic operations (+, -, x, /), with emphasis on finding ways to directly perform the more difficult two operations of multiplication and division. This developed from the Napier’s rods - or “bones” (developed by John Napier (1550–1617) to which we have already referred. As already mentioned calculational approaches were designed around them by Wilhelm Schickard in 1623, Charles Cotterel in 1667, Gaspard Schott in 1668, and Samuel Morland between 1625 and 1695. A late and unique expression of these in this collection is Justin Bamberger’s Omega Calculating Machine (1903-6). It combines a stylus operated adding machine (complete with provision for automatic carry) with a sophisticated Napier bones based machine for discovering the partial products of two multiplied numbers (a bit like that in Schickard’s much earlier device), which can then be added in the adding machine to find corresponding products and quotients.

1855: “Messrs. Scheutz’s New Calculating Machine”, The Illustrated London News, 30 June 1855, p. 661. Original print article.

1890: Leon Bollée Calculating Machine, “A New Calculating Machine of very General Applicability”, The Manufacturer and Builder, July 1890, p. 156. Original print article.

20 July 2013 by 124.170.43.18 -

Deleted lines 97-102:

!To be continued....
This essay is under construction. If it is ever finished (:-) it is intended to utilise this collection to shape a continuing if idiosyncratic story of the development of embodied calculation up to the introduction of personal electronic calculation. So do visit again if you have got this far, and there may (should) be more.

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!To be continued....
This essay is under construction. If it is ever finished (:-) it is intended to utilise this collection to shape a continuing if idiosyncratic story of the development of embodied calculation up to the introduction of personal electronic calculation. So do visit again if you have got this far, and there may (should) be more.

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*movement of a point along a line (implemented for example by a sliding rod, moving chain, or ~~something~~ similar)
*rotations of wheels
*something else (for example, although it was not used, ~~additions to~~ columns of water).

to:

*movement of a point along a line (implemented for example by a sliding rod, moving chain or strap, or something similar)
*rotations of wheels and cogs
*something else that can be moved (for example, although it was barely used,[^An exception is the ingenious MONIAC hydraulic computer used to demonstrate macroeconomic theory. See for example, Anna Corkhill ‘A superb explanatory device’ //University of Melbourne Collections//, issue 10, June 2012^] the height of columns of water).

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!!!!Simple linear mechanisms

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~~Similar simple devices were developed which utilised~~ simple rotation of cogs, with a crude carry process (usually along the lines of that used by Schickard). They relied for their success on having but a small number of interacting cogs, so that the carry mechanism would not jam. In this sense (despite often being referred to as of the style of the Pascaline) they were extensions of the ~~idea of the adding component~~ of ~~Schickard's instrument and lacked~~ the ~~centrally important innovation~~ of ~~Pascal where the carry was achieved by a weighted sorter. Devices using variations of this principle in this collection start with the Webb Patent Adder~~ (~~1869~~) ~~and Stevens Adder~~ (~~1890s~~)

Other devices such as the Golden Gem, Addiator, and Lightning (1940s) calculators provide further illustrations of course of the wide range of different types and shapes of such devices that were sold. All of these work by adding movements (of cogs, chains, or straps) imprinted on which are the equivalent numbers. The devices in this collection are shown below.

to:

Addiator,
Golden Gem,
Locke Adder
Slide Rule

!!!!Simple rotational mechanisms
Similar simple devices were developed which utilised simple rotation of cogs, with a crude carry process (usually along the lines of that used by Schickard). They relied for their success on having but a small number of interacting cogs, so that the carry mechanism would not jam. In this sense (despite often being referred to as of the style of the Pascaline) they were extensions of the idea of the adding component of Schickard's instrument and lacked the centrally important innovation of Pascal where the carry was achieved by a weighted sorter.
Webb Patent Adder (1869)
Stevens Adder (1890s)
Lightning (1940s)
SEE

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!!!!Other simple approaches

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to:

!!!Commercial calculating machines

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%center% http://meta-studies.net/pmwiki/uploads/Convertiseur.png

to:

%center% %height=200px% http://meta-studies.net/pmwiki/uploads/Convertiseur.png

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It is useful to recapitulate the available principles which had been discovered upon which devices for more sophisticated arithmetic tasks could be devised. Key to all of these was the idea, already embodied in calculi and counting tables, or the abacus, that addition of numbers represents the addition of units of something physical. Bearing this in mind, adding units of motion in space could do the same job, whether the movement was of a point along a line~~, or rotations of wheels (or indeed, although it was not used, columns of water~~)~~. Subtraction could be achieved by units of motion in the opposite direction.~~ ~~Multiplication~~ could be achieved by repeated additions, and divisions by repeated subtractions. Alternatively tables of multiplication (or logarithms) could be utilised to replace these steps. Where the mechanism did not permit reverse motion, [[Site.OperatingInstructionsForAPascaline|complementary numbers]] could be added to achieve subtraction through addition.

The slide rule had used the motion of sliding along a straight line to add distances representing a logarithmic scale. ~~The devices of Schickard, Pascal and Leibniz had used rotation of dials to achieve addition of rotations~~. ~~Schickard's machine had the capacity to subtract by turning the dials backwards, but had not fully resolved how to carry from one dial~~ to ~~another. Pascal had developed a very efficient carry mechanism but at the expense of the dials not being able to be rotated backwards. Both of these relied on a stylus for input.~~ Leibniz had developed his step drum to improve the input process and repeated additions were facilitated by the capacity of the machine to be turned with a crank handle. But his carry mechanism needed further development to work when this occurred.

to:

It is useful to recapitulate the available principles which had been discovered upon which devices for more sophisticated arithmetic tasks could be devised. Key to all of these was the idea, already embodied in calculi and counting tables, or the abacus, that addition of numbers represents the addition of units of something physical. Bearing this in mind, adding units of motion in space could do the same job, whether the movement was units of:
*movement of a point along a line (implemented for example by a sliding rod, moving chain, or something similar)
*rotations of wheels
*something else (for example, although it was not used, additions to columns of water).

Subtraction could be achieved by units of motion in the opposite direction, or where that was not possible, the addition of [[Site.OperatingInstructionsForAPascaline|complementary numbers]].

Multiplication could be achieved by repeated additions, and divisions by repeated subtractions. Alternatively tables of multiplication (or logarithms) could be utilised to replace these steps.

Examples utilising these analogue motions to aid arithmetic were already available from as early as the C17.

*The slide rule had used the motion of sliding along a straight line to add distances representing a logarithmic scale. *The devices of Schickard, Pascal and Leibniz had used rotation of dials to achieve addition of rotations. Schickard's machine had the capacity to subtract by turning the dials backwards, but had not fully resolved how to carry from one dial to another.
*Pascal had developed a very efficient carry mechanism but at the expense of the dials not being able to be rotated backwards. Both of these relied on a stylus for input.
*Leibniz had developed his step drum to improve the input process and repeated additions were facilitated by the capacity of the machine to be turned with a crank handle. But his carry mechanism needed further development to work when this occurred.

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The dominant role of ready reckoners at this period is indicated by M. Norton Wise's comment in relation to Victorian England that:
->By the 1860’s, the favorite device for lessening the work of the computer (human), the mathematical table, had become an object whose dizzying rows of printed figures would fascinate the Victorian public. These tables displayed the limitless fecundity of numbers, and transformed them into a commodity that would bring the power of calculation within the reach of the ordinary citizen. The centrality of tables of numbers and calculation to mid-Victorian life was famously portrayed by Charles Dickens’ character Thomas Gradgrind, who always had a rule and a pair of scales and the multiplication table in his pocket.[^M.N. Wise, //The Values of Precision//, Princeton University Press, USA, 1995, p. 318.^]

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As the above suggests, historical periods do not easily fit together as simply defined blocks of time with nice clear boundaries. Rather they are useful labels for different times of change, which whilst usefully distinguished, overlap each other to allow for the transitions which take place across them. The process of technological change in particular, in any particular period, has roots back before and layers on innovations which precede it.

to:

As the above suggests, historical periods do not easily fit together as simply defined blocks of time with nice clear boundaries. Rather they are useful labels for different times of change, which whilst usefully distinguished, overlap each other to allow for the transitions which take place across them. The process of technological change in particular, in any particular period, has roots back before and layers on innovations which precede it. Indeed, not only did prior inventions provide a base on which new more commercially successful devices might be built, but also old methods could be persistently found in use sometimes right through the late Modern period. One of the most common of these, which may still be found in use in some places, was ready reckoners.

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Ready reckoners were in widespread use by shopkeepers and many others from the C17 on. They presented tables of precalculated results of many kinds of multiplication. These included the much needed calculations of the price for multiples of an item for sale, or per unit of weight. They could also be used to look up the calculations needed for wages and interest.[^see Bruce O.B. Williams and Roger G. Johnson, "Ready Reckoners", //IEEE Annals of the History of Computing//, October-December, 2005, pp. 64-80.^] One such, from 1892, shown below is "Ropp's Commercial Calculator: a practical arithmetic for practical purposes, containing a complete system of useful, accurate, and convenient tables, together with simple, short, and practical methods for rapid calculation", a published in the US and used widely into the early C20. This one is the 1892 World's Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.

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%center% Ropp's Commercial Calculator, ~~1892~~

to:

%center% Ropp's Commercial Calculator, 1892\\

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Ropp's Commercial Calculator: a practical arithmetic for practical purposes, containing a complete system of useful, accurate, and convenient tables, together with simple, short, and practical methods for rapid calculation", 1892

Until reliable and cheap calculators could become broadly available most calculation was carried out with the help of tables published in ready reckoners of one sort or another. The Ropp ready reckoners were widely used for this purpose in the USA right into the twentieth century.

The 1892 World's Fair Edition of Ropp's Commercial Calculator book in this collection contains 128 pages of useful mathematical facts, formulas and tables. The covers have creases, rubbing and edge and corner wear. The spine has been torn at the top and bottom. The edges of the pages are colored with red ink which is not unusual in a late 1800's reference book. The book shows its age but is all intact with no loose pages or obvious decay.

to:

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~~As an example, the early new mathematical devices to gain broader use were not calculating machines but rather various simple adaptations of tables of numbers~~. There was an ever more extensive need to be able to measure and compare especially in the expanding processes of trade and commerce. The bane of earlier centuries (and even still) is lack of standardisation across localities in which trade took place. In particular, quantities were often not measured in the same units. As a result, special purpose devices, basically just forms of mechanical look-up tables were devised to enable conversion, needed not the least since performing associated conversion calculations each time was not only time consuming but beyond the skill of many who might need them. A particularly stark need for such devices was created, following the French Revolution, when the Revolutionary Government introduced metric measures. A “Convertisseur” from (1780–1810) designed by clock maker Gabrielle Chaix in Paris to assist in converting between the old measure of distance (the “Aune”) to the new metric metre that was introduced in 1791, is shown below.

to:

Other early new mathematical devices to gain broader use were simple adaptations of the sorts of tables that might be found in ready reckoners. There was an ever more extensive need to be able to measure and compare especially in the expanding processes of trade and commerce. The bane of earlier centuries (and even still) is lack of standardisation across localities in which trade took place. In particular, quantities were often not measured in the same units. As a result, special purpose devices, basically just forms of mechanical look-up tables were devised to enable conversion, needed not the least since performing associated conversion calculations each time was not only time consuming but beyond the skill of many who might need them. A particularly stark need for such devices was created, following the French Revolution, when the Revolutionary Government introduced metric measures. A “Convertisseur” from (1780–1810) designed by clock maker Gabrielle Chaix in Paris to assist in converting between the old measure of distance (the “Aune”) to the new metric metre that was introduced in 1791, is shown below.

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%center% %height=~~300px~~% http://meta-studies.net/pmwiki/uploads/Ropp.~~jpg~~

to:

%center% %height=200px% http://meta-studies.net/pmwiki/uploads/Ropp.jpg
%center% Ropp's Commercial Calculator, 1892
%center% (collection Calculant)

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%center% http://meta-studies.net/pmwiki/uploads/Ropp.jpg

to:

%center% %height=300px% http://meta-studies.net/pmwiki/uploads/Ropp.jpg

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!!!!Ready reckoners
%center% http://meta-studies.net/pmwiki/uploads/Ropp.jpg

Ropp's Commercial Calculator: a practical arithmetic for practical purposes, containing a complete system of useful, accurate, and convenient tables, together with simple, short, and practical methods for rapid calculation", 1892

Until reliable and cheap calculators could become broadly available most calculation was carried out with the help of tables published in ready reckoners of one sort or another. The Ropp ready reckoners were widely used for this purpose in the USA right into the twentieth century.

The 1892 World's Fair Edition of Ropp's Commercial Calculator book in this collection contains 128 pages of useful mathematical facts, formulas and tables. The covers have creases, rubbing and edge and corner wear. The spine has been torn at the top and bottom. The edges of the pages are colored with red ink which is not unusual in a late 1800's reference book. The book shows its age but is all intact with no loose pages or obvious decay.

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of complementary numbers where reverse displacement was rendered mechanically impossible. Then - either do this faster and more effectively, or in some way incorporate multiplication tables (or logarithms in the case of slide rules).

Very simple deviceswhose basic mechanism using metal strips or cogs which can be used by ~~means of a stylis can be moved linearly or circularly the distance displaced standing for added numbers~~. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe,4 later to be known as the Addiator (of which there is one in this collection). Other devices used variations of this principle start with the Webb Patent Adder (1869) and Stevens Adder (1890s), and then proceeding through the Golden Gem, Addiator, and Lightning (1940s) - just illustrations of course of the wide range of different types and shapes of such devices that were sold. All of these work by adding movements (of cogs, chains, or straps) imprinted on which are the equivalent numbers.

One using rods - a Comptator from 1910 is in this collection. In a sense the above devices are linear digital sliding rules. One of the key innovations achieved by most of these devices (but not by the ‘Troncets’) was to develop a mechanical means of ‘carrying’ (interestingly already solved by ~~Shickard) when~~ a ~~sum of two numbers in the same ‘column’ was greater than 9.~~

to:

The slide rule had used the motion of sliding along a straight line to add distances representing a logarithmic scale. The devices of Schickard, Pascal and Leibniz had used rotation of dials to achieve addition of rotations. Schickard's machine had the capacity to subtract by turning the dials backwards, but had not fully resolved how to carry from one dial to another. Pascal had developed a very efficient carry mechanism but at the expense of the dials not being able to be rotated backwards. Both of these relied on a stylus for input. Leibniz had developed his step drum to improve the input process and repeated additions were facilitated by the capacity of the machine to be turned with a crank handle. But his carry mechanism needed further development to work when this occurred.

It would be tempting to present the subsequent development devices as a single linear track of improvement from these promising beginnings more than a century before. But this would be artificial. Rather a genealogical tree of innovations spread out from these earlier inventions as a niche for their use began to be uncovered.

One such line of development was based on the possibility of adding linear displacements of strips of metal. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe, later to be known as the Addiator (of which there is one in this collection), of which a bewildering number of different designs appeared in the late C19 and early C20.

Similar simple devices were developed which utilised simple rotation of cogs, with a crude carry process (usually along the lines of that used by Schickard). They relied for their success on having but a small number of interacting cogs, so that the carry mechanism would not jam. In this sense (despite often being referred to as of the style of the Pascaline) they were extensions of the idea of the adding component of Schickard's instrument and lacked the centrally important innovation of Pascal where the carry was achieved by a weighted sorter. Devices using variations of this principle in this collection start with the Webb Patent Adder (1869) and Stevens Adder (1890s)

Other devices such as the Golden Gem, Addiator, and Lightning (1940s) calculators provide further illustrations of course of the wide range of different types and shapes of such devices that were sold. All of these work by adding movements (of cogs, chains, or straps) imprinted on which are the equivalent numbers. The devices in this collection are shown below.

The main advantage of these devices was that they were cheap to manufacture and could be easily mass-produced. They were however little more than gimmicks which were too slow to be used as a practical means of addition or subtraction for which they were designed.

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It was Thomas de Colmar who decisively built

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The resemblance between the design of the above and that of a prestigious gentleman's pocket watch is probably not coincidental. Mechanisation can come in the most basic forms and still carry the allure of the new whilst usefully substituting for otherwise necessary mental skill. Many conversion devices of similarly simple construction continued to be manufactured ~~right up to the end~~ of the ~~Modern period~~.

to:

The resemblance between the design of the above and that of a prestigious gentleman's pocket watch is probably not coincidental. Mechanisation can come in the most basic forms and still carry the allure of the new whilst usefully substituting for otherwise necessary mental skill. Many conversion devices of similarly simple construction continued to be manufactured into the second half of the twentieth century.

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The resemblance between the design of the above and that of a prestigious gentleman's pocket watch is probably not coincidental. Mechanisation can come in the most basic forms and still carry the allure of the new whilst usefully substituting for otherwise necessary mental skill.

to:

The resemblance between the design of the above and that of a prestigious gentleman's pocket watch is probably not coincidental. Mechanisation can come in the most basic forms and still carry the allure of the new whilst usefully substituting for otherwise necessary mental skill. Many conversion devices of similarly simple construction continued to be manufactured right up to the end of the Modern period.

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It is useful to recapitulate the available principles if more sophisticated arithmetic tasks were to be mechanised. Displacement as an analog for addition and subtraction. Repeated additiondisplacement as multiplication or subtraction displacement for division (with tests for overflow). Combinations of these for powers or roots. Use of complementary numbers where reverse displacement was rendered mechanically impossible. Then - either do this faster and more effectively, or in some way incorporate multiplication tables (or logarithms in the case of slide rules).

to:

It is useful to recapitulate the available principles which had been discovered upon which devices for more sophisticated arithmetic tasks could be devised. Key to all of these was the idea, already embodied in calculi and counting tables, or the abacus, that addition of numbers represents the addition of units of something physical. Bearing this in mind, adding units of motion in space could do the same job, whether the movement was of a point along a line, or rotations of wheels (or indeed, although it was not used, columns of water). Subtraction could be achieved by units of motion in the opposite direction. Multiplication could be achieved by repeated additions, and divisions by repeated subtractions. Alternatively tables of multiplication (or logarithms) could be utilised to replace these steps. Where the mechanism did not permit reverse motion, [[Site.OperatingInstructionsForAPascaline|complementary numbers]] could be added to achieve subtraction through addition.

of complementary numbers where reverse displacement was rendered mechanically impossible. Then - either do this faster and more effectively, or in some way incorporate multiplication tables (or logarithms in the case of slide rules).

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!!!!Lookup ~~devices~~

to:

!!!!Lookup tables in new form

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~~Thus, for~~ example, the early new mathematical devices to gain broader use were not calculating machines but rather various simple adaptations of tables of numbers. There was an ever more extensive need to be able to measure and compare especially in the expanding processes of trade and commerce. The bane of earlier centuries (and even still) is lack of standardisation across localities in which trade took place. In particular, quantities were often not measured in the same units. As a result, special purpose devices, basically just forms of mechanical look-up tables were devised to enable conversion, needed not the least since performing associated conversion calculations each time was not only time consuming but beyond the skill of many who might need them. A particularly stark need for such devices was created, following the French Revolution, when the Revolutionary Government introduced metric measures. A “Convertisseur” from (1780–1810) designed by clock maker Gabrielle Chaix in Paris to assist in converting between the old measure of distance (the “Aune”) to the new metric metre that was introduced in 1791, is shown below. ~~The resemblance between the design and that of a prestigious gentleman's pocket watch is probably not coincidental.~~

to:

!!!!Lookup devices
As an example, the early new mathematical devices to gain broader use were not calculating machines but rather various simple adaptations of tables of numbers. There was an ever more extensive need to be able to measure and compare especially in the expanding processes of trade and commerce. The bane of earlier centuries (and even still) is lack of standardisation across localities in which trade took place. In particular, quantities were often not measured in the same units. As a result, special purpose devices, basically just forms of mechanical look-up tables were devised to enable conversion, needed not the least since performing associated conversion calculations each time was not only time consuming but beyond the skill of many who might need them. A particularly stark need for such devices was created, following the French Revolution, when the Revolutionary Government introduced metric measures. A “Convertisseur” from (1780–1810) designed by clock maker Gabrielle Chaix in Paris to assist in converting between the old measure of distance (the “Aune”) to the new metric metre that was introduced in 1791, is shown below.

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~~Relationship~~ between ~~mechanisation~~ of ~~arithmetic~~ and ~~more general love of mechanisation. Most notably the huge reforms of the French revolution and~~ the ~~more steady but important innovations of England and elsewhere. The displacement of the ancienne regime changes the relationship of science (and calculation)~~ to society. Most dramatic in France, but elsewhere too the secular but accelerating increase in the power of merchant and market over the last several centuries has a similar effect.

Mechanisation can come in the most basic forms and still carry the allure of the new. It can also be a useful substitute for mental skill.

General revamp of the concept behind mechanical calculation. Displacement as an analog for addition and subtraction. Repeated additiondisplacement as multiplication or subtraction displacement for division (with tests for overflow). Combinations of these for powers or roots. Use of complementary numbers where reverse displacement was rendered mechanically impossible. Then - either do this faster and more effectively, or in some way incorporate multiplication tables (or logarithms in the case of slide rules).

to:

The resemblance between the design of the above and that of a prestigious gentleman's pocket watch is probably not coincidental. Mechanisation can come in the most basic forms and still carry the allure of the new whilst usefully substituting for otherwise necessary mental skill.

!!!!Available principles
It is useful to recapitulate the available principles if more sophisticated arithmetic tasks were to be mechanised. Displacement as an analog for addition and subtraction. Repeated additiondisplacement as multiplication or subtraction displacement for division (with tests for overflow). Combinations of these for powers or roots. Use of complementary numbers where reverse displacement was rendered mechanically impossible. Then - either do this faster and more effectively, or in some way incorporate multiplication tables (or logarithms in the case of slide rules).

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Thus, for example, the early new mathematical devices to gain broader use were not calculating machines but rather various simple adaptations of tables of numbers. There was an ever more extensive need to be able to measure and compare especially in the expanding processes of trade and commerce. The bane of earlier centuries (and even still) is lack of standardisation across localities in which trade took place. In particular, quantities were often not measured in the same units. As a result, special purpose devices, basically just forms of mechanical look-up tables were devised to enable conversion, needed not the least since performing associated conversion calculations each time was not only time consuming but beyond the skill of many who might need them. A particularly stark need for such devices was created, following the French Revolution, when the Revolutionary Government introduced metric measures. A “Convertisseur” from (1780–1810) designed by clock maker Gabrielle Chaix in Paris to assist in converting between the old measure of distance (the “Aune”) to the new metric metre that was introduced in 1791, is shown below.

to:

Thus, for example, the early new mathematical devices to gain broader use were not calculating machines but rather various simple adaptations of tables of numbers. There was an ever more extensive need to be able to measure and compare especially in the expanding processes of trade and commerce. The bane of earlier centuries (and even still) is lack of standardisation across localities in which trade took place. In particular, quantities were often not measured in the same units. As a result, special purpose devices, basically just forms of mechanical look-up tables were devised to enable conversion, needed not the least since performing associated conversion calculations each time was not only time consuming but beyond the skill of many who might need them. A particularly stark need for such devices was created, following the French Revolution, when the Revolutionary Government introduced metric measures. A “Convertisseur” from (1780–1810) designed by clock maker Gabrielle Chaix in Paris to assist in converting between the old measure of distance (the “Aune”) to the new metric metre that was introduced in 1791, is shown below. The resemblance between the design and that of a prestigious gentleman's pocket watch is probably not coincidental.

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Thus, for example, ~~whilst Thus for example, we have the development from tables to simple mechanical devices which did the same thing.~~ ~~The bane of earlier centuries, and even still, is the fact that quantities were often measured~~ in ~~different incompatible units. Special purpose devices, basically just forms~~ of ~~mechanical look-up tables were devised to deal with this sort of issue, since performing the calculation each time was time consuming, and many did not have~~ the skills in any case to do it. The need to be able to measure and compare occurred extensively in shipping and commerce rather early. In this collection we have a “Convertisseur” from (1780–1810) designed by Gabrielle Chaix in Paris, to assist merchants and artisans to convert between the old measure of distance (the “Aune”) and the new measure introduced by the Revolutionary Government ~~of the metre in~~ 1791.

to:

Thus, for example, the early new mathematical devices to gain broader use were not calculating machines but rather various simple adaptations of tables of numbers. There was an ever more extensive need to be able to measure and compare especially in the expanding processes of trade and commerce. The bane of earlier centuries (and even still) is lack of standardisation across localities in which trade took place. In particular, quantities were often not measured in the same units. As a result, special purpose devices, basically just forms of mechanical look-up tables were devised to enable conversion, needed not the least since performing associated conversion calculations each time was not only time consuming but beyond the skill of many who might need them. A particularly stark need for such devices was created, following the French Revolution, when the Revolutionary Government introduced metric measures. A “Convertisseur” from (1780–1810) designed by clock maker Gabrielle Chaix in Paris to assist in converting between the old measure of distance (the “Aune”) to the new metric metre that was introduced in 1791, is shown below.

%center% http://meta-studies.net/pmwiki/uploads/Convertiseur.png
%center%Conversion device (from Aunes to Metres) ~1790\\(collection Calculant)

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!To be continued....
This essay is under construction. If it is ever finished (:-) it is intended to utilise this collection to shape a continuing if idiosyncratic story of the development of embodied calculation up to the introduction of personal electronic calculation. So do visit again if you have got this far, and there may (should) be more.

!!Notes as I think about what I will write next!

Centrally increasing role of science, engineering, mathematics in production, governance and civil society.

Transformation from the old aristocratic machines to those of mass production.

Style, tyle, "usability". Break into mechanism, role, .....

Refs: WIT. NSOT.

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~~Comment - historical epochs do not come with nice clear boundaries. All transitions with interleaving and layering.~~ Thus for example, we have the development from tables to simple mechanical devices which did the same thing. The bane of earlier centuries, and even still, is the fact that quantities were often measured in different incompatible units. Special purpose devices, basically just forms of mechanical look-up tables were devised to deal with this sort of issue, since performing the calculation each time was time consuming, and many did not have the skills in any case to do it. The need to be able to measure and compare occurred extensively in shipping and commerce rather early. In this collection we have a “Convertisseur” from (1780–1810) designed by Gabrielle Chaix in Paris, to assist merchants and artisans to convert between the old measure of distance (the “Aune”) and the new measure introduced by the Revolutionary Government of the metre in 1791.

to:

As the above suggests, historical periods do not easily fit together as simply defined blocks of time with nice clear boundaries. Rather they are useful labels for different times of change, which whilst usefully distinguished, overlap each other to allow for the transitions which take place across them. The process of technological change in particular, in any particular period, has roots back before and layers on innovations which precede it.

Thus, for example, whilst Thus for example, we have the development from tables to simple mechanical devices which did the same thing. The bane of earlier centuries, and even still, is the fact that quantities were often measured in different incompatible units. Special purpose devices, basically just forms of mechanical look-up tables were devised to deal with this sort of issue, since performing the calculation each time was time consuming, and many did not have the skills in any case to do it. The need to be able to measure and compare occurred extensively in shipping and commerce rather early. In this collection we have a “Convertisseur” from (1780–1810) designed by Gabrielle Chaix in Paris, to assist merchants and artisans to convert between the old measure of distance (the “Aune”) and the new measure introduced by the Revolutionary Government of the metre in 1791.

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!To be continued....
This essay is under construction. If it is ever finished (:-) it is intended to utilise this collection to shape a continuing if idiosyncratic story of the development of embodied calculation up to the introduction of personal electronic calculation. So do visit again if you have got this far, and there may (should) be more.

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<<|[[HistoryTrail|History Contents]]|>>

[^#^]

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->In the period that followed, science began its victorious march on a broad front even into those distant realms of nature which could be entered only by technology.... Even the phrase 'description of nature' lost more and more of its original significance of a living and meaningful account of nature. Increasingly it came to mean the mathematical description of nature.[^Werner Heisenberg, //The Physicist's Conception of Nature//, Hutchinson Scientific and Technical, London, 1958, p. 11.

to:

->In the period that followed, science began its victorious march on a broad front even into those distant realms of nature which could be entered only by technology.... Even the phrase 'description of nature' lost more and more of its original significance of a living and meaningful account of nature. Increasingly it came to mean the mathematical description of nature.[^Werner Heisenberg, //The Physicist's Conception of Nature//, Hutchinson Scientific and Technical, London, 1958, p. 11.^]

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!!!~~Dynamic~~ change.

to:

!!!A time of change.

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Usefulness arises in a context, and the social, political, economic and technological context was in a process of unprecedented transformation across Europe. The late C18 was characterised most dramatically with the execution of Louis XVI in 1793 by a transition between the power of the ancienne regime to new political forces. Into the following century across Europe the emerging power of merchant and market increasingly swept aside the old aristocracy in the shaping of the politics, economics and infrastructure of what, in a process evolving from the Treaty of Westphalia (1648) had emerged as 'sovereign' nation states. Improving systems of transportation facilitated a process of ever intensifying trade across and between states was involving monarchs, peasants, artisans, merchants and financiers alike.[^For more on this see Camilleri and Falk, //Worlds in Transition//, pp. 134-44.^] Ever more efficient processes of printing and dissemination facilitated production and dissemination of ideas. A period of comparative peace between nations in the late C18 was marked by a revolution in agricultural production. But this was just one way in which a synergy between scientific and technological innovation was finding purchase within transforming systems of production, commerce, governance and more broadly lived experience. ~~Accompanying this the understanding of the world, and even the conception of meaning in existence~~, ~~was being transformed in conjunction with~~ the emergence of new scientific insights in mathematics, physics and astronomy. As Werner Heisenberg, a founding physicist in quantum mechanics has summarised it:

->In the period that followed, science began

was enormous change taking place...... market, industrialisation, mass production, complexification of ~~governance, solidification (temporarily) of the nation state, rapidly growing trade..... Mass education and the extension of childhood, two world wars, developments in materials, precision~~, ~~design, mass production and use~~.

to:

Usefulness arises in a context, and the social, political, economic and technological context was in a process of unprecedented transformation across Europe. The late C18 was characterised most dramatically with the execution of Louis XVI in 1793 by a transition between the power of the ancienne regime to new political forces. Into the following century across Europe the emerging power of merchant and market increasingly swept aside the old aristocracy in the shaping of the politics, economics and infrastructure of what, in a process evolving from the Treaty of Westphalia (1648) had emerged as 'sovereign' nation states. Improving systems of transportation facilitated a process of ever intensifying trade across and between states was involving monarchs, peasants, artisans, merchants and financiers alike.[^For more on this see Camilleri and Falk, //Worlds in Transition//, pp. 134-44.^] Ever more efficient processes of printing and dissemination facilitated production and dissemination of ideas. A period of comparative peace between nations in the late C18 was marked by a revolution in agricultural production. But this was just one way in which a synergy between scientific and technological innovation was finding purchase within transforming systems of production, commerce, governance and more broadly lived experience. In addition, science was beginning to be harnessed to actual production. Steam replaced horse, and then from the mid C-19 to the mid-C20, electrical networks spread across Europe and then much of the rest of the modern world allowing the introduction of many new technologies.

Accompanying this the understanding of the world, and even the conception of meaning in existence, was being transformed in conjunction with the emergence of new scientific insights in mathematics, physics and astronomy. As Werner Heisenberg, a founding physicist in quantum mechanics has summarised it:

->In the period that followed, science began its victorious march on a broad front even into those distant realms of nature which could be entered only by technology.... Even the phrase 'description of nature' lost more and more of its original significance of a living and meaningful account of nature. Increasingly it came to mean the mathematical description of nature.[^Werner Heisenberg, //The Physicist's Conception of Nature//, Hutchinson Scientific and Technical, London, 1958, p. 11.

Not only was the conception of nature being transformed through a more technical, and indeed mathematical account, but new literacies and cognitive skills required to deal with an economy that was ever more shaped by the market, production that was ever more shaped by science, and products whose use required continual processes of cultural learning. Mass education in reading and basic mathematical skills were now an increasing necessity and steadily the period of "childhood" was extended including the invention of the "teenager", to allow an extended period of socially conceded time in which this personal development could take place.

Finally, technological development and the role of science was greatly accelerated by the two world wars, which became wars of science, as evidenced by leaps in aviation, rocketry, electronic communication, encryption, and detection - to name just a few - and cumulating in the harnessing of the process of nuclear fission itself to bomb Hiroshima and Nagasaki. Pressed forward by the onward thrust of market and military priority, the systematic research, development and deployment of new techniques, powerful precision tools, and diverse materials, often emerging in new goods, produced through evolving processes of mass production and social organisation, became a constant theme of the times.

It was then in this remarkable period of dynamic change that the insights into calculation technology finally found purchase.

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Usefulness arises in a context, and the social, political, economic and technological context was in a process of unprecedented transformation across Europe. The late C18 was characterised most dramatically with the execution of Louis XVI in 1793 by a transition between the power of the ancienne regime to new political forces. Into the following century across Europe the emerging power of merchant and market increasingly swept aside the old aristocracy in the shaping of the politics, economics and infrastructure of what, in a process evolving from the Treaty of Westphalia (1648) had emerged as 'sovereign' nation states. Improving systems of transportation facilitated a process of ever intensifying trade across and between states was involving monarchs, peasants, artisans, merchants and financiers alike.[^For more on this see Camilleri and Falk, //Worlds in Transition//, pp. 134-44.^] Ever more efficient processes of printing and dissemination facilitated production and dissemination of ideas. A period of comparative peace between nations in the late C18 was marked by a revolution in agricultural production. But this was just one way in which a synergy between scientific and technological innovation was finding purchase within transforming systems of production, commerce, governance and more broadly lived experience.

to:

Usefulness arises in a context, and the social, political, economic and technological context was in a process of unprecedented transformation across Europe. The late C18 was characterised most dramatically with the execution of Louis XVI in 1793 by a transition between the power of the ancienne regime to new political forces. Into the following century across Europe the emerging power of merchant and market increasingly swept aside the old aristocracy in the shaping of the politics, economics and infrastructure of what, in a process evolving from the Treaty of Westphalia (1648) had emerged as 'sovereign' nation states. Improving systems of transportation facilitated a process of ever intensifying trade across and between states was involving monarchs, peasants, artisans, merchants and financiers alike.[^For more on this see Camilleri and Falk, //Worlds in Transition//, pp. 134-44.^] Ever more efficient processes of printing and dissemination facilitated production and dissemination of ideas. A period of comparative peace between nations in the late C18 was marked by a revolution in agricultural production. But this was just one way in which a synergy between scientific and technological innovation was finding purchase within transforming systems of production, commerce, governance and more broadly lived experience. Accompanying this the understanding of the world, and even the conception of meaning in existence, was being transformed in conjunction with the emergence of new scientific insights in mathematics, physics and astronomy. As Werner Heisenberg, a founding physicist in quantum mechanics has summarised it:

->In the period that followed, science began

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Usefulness arises in a context, and the social, political, economic and technological context was in a process of unprecedented transformation~~. Most dramatically the execution of Louis XVI in 1793 marked~~ the ~~triumph~~ of ~~transformation of power from the ancienne regime to new political forces. But across Europe the emerging power of merchant and market increasingly swept aside~~ the ~~old aristocracy in the shaping of the politics, economics and infrastructure of what,~~ in ~~a process evolving from~~ the ~~Treaty of Westphalia (1648) had emerged as 'sovereign' nation states. A process~~ of ~~ever intensifying trade across and between~~ states ~~was involving monarchs, peasants, artisans, merchants and financiers alike.[^For more on this see Camilleri and Falk, //Worlds in Transition//~~, ~~pp. 134^] Ever~~ more ~~efficient processes of printing facilitated production and dissemination of ideas~~. A period of comparative peace between nations in the late C18 was marked by a revolution in agricultural production based around imported species and improved farming techniques, whilst expanding markets, increasing access to resources

to:

Usefulness arises in a context, and the social, political, economic and technological context was in a process of unprecedented transformation across Europe. The late C18 was characterised most dramatically with the execution of Louis XVI in 1793 by a transition between the power of the ancienne regime to new political forces. Into the following century across Europe the emerging power of merchant and market increasingly swept aside the old aristocracy in the shaping of the politics, economics and infrastructure of what, in a process evolving from the Treaty of Westphalia (1648) had emerged as 'sovereign' nation states. Improving systems of transportation facilitated a process of ever intensifying trade across and between states was involving monarchs, peasants, artisans, merchants and financiers alike.[^For more on this see Camilleri and Falk, //Worlds in Transition//, pp. 134-44.^] Ever more efficient processes of printing and dissemination facilitated production and dissemination of ideas. A period of comparative peace between nations in the late C18 was marked by a revolution in agricultural production. But this was just one way in which a synergy between scientific and technological innovation was finding purchase within transforming systems of production, commerce, governance and more broadly lived experience.

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Usefulness arises in a context, and the social, political, economic and technological context was in a process of unprecedented transformation. ~~From~~

to:

Usefulness arises in a context, and the social, political, economic and technological context was in a process of unprecedented transformation. Most dramatically the execution of Louis XVI in 1793 marked the triumph of transformation of power from the ancienne regime to new political forces. But across Europe the emerging power of merchant and market increasingly swept aside the old aristocracy in the shaping of the politics, economics and infrastructure of what, in a process evolving from the Treaty of Westphalia (1648) had emerged as 'sovereign' nation states. A process of ever intensifying trade across and between states was involving monarchs, peasants, artisans, merchants and financiers alike.[^For more on this see Camilleri and Falk, //Worlds in Transition//, pp. 134^] Ever more efficient processes of printing facilitated production and dissemination of ideas. A period of comparative peace between nations in the late C18 was marked by a revolution in agricultural production based around imported species and improved farming techniques, whilst expanding markets, increasing access to resources

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!To be continued....
This essay is under construction. If it is ever finished (:-) it is intended to utilise this collection to shape a continuing if idiosyncratic story of the development of embodied calculation up to the introduction of personal electronic calculation. So do visit again if you have got this far, and there may (should) be more.

!!Notes as I think about what I will write next!

!!!The expansion of the market in the late Modern period.

to:

!!!Dynamic change.

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As already ~~suggersted~~, none of these devices that were created during this period sprung from their inventors minds completely unprecedented. The roots spread back into the early Modern period from the earliest forms of embodied calculation (for example, the use of calculi). The period following the inventions already mentioned of Schickard, Pascal, Moreland and Leibniz were followed by a multitude of devices built on similar basic principles, but all with the limitation that they were not widely taken up because as yet need had not developed to resonate with the limited capabilities and often high cost of the inventions. Nevertheless, as time passed a web of developments would continue to emerge that would eventually create that moment when such a resonance might take place.

~~Perhaps more important~~ was the use to which these devices might be put. ~~There was enormous change taking place...... market, industrialisation, mass production, complexification of governance, solidification (temporarily) of the nation state, rapidly growing trade~~..... ~~Mass education and the extension of childhood~~, ~~two world wars~~, ~~developments in materials, precision, design, mass production and use~~.

to:

As already suggested, none of these devices that were created during this period sprung from their inventors minds completely unprecedented. The roots spread back into the early Modern period from the earliest forms of embodied calculation (for example, the use of calculi). The period following the inventions already mentioned of Schickard, Pascal, Moreland and Leibniz were followed by a multitude of devices built on similar basic principles, but all with the limitation that they were not widely taken up because as yet need had not developed to resonate with the limited capabilities and often high cost of the inventions. Nevertheless, as time passed a web of developments would continue to emerge that would eventually create that moment when such a resonance might take place. Central to this was the use to which these devices might be put.

Usefulness arises in a context, and the social, political, economic and technological context was in a process of unprecedented transformation. From

was enormous change taking place...... market, industrialisation, mass production, complexification of governance, solidification (temporarily) of the nation state, rapidly growing trade..... Mass education and the extension of childhood, two world wars, developments in materials, precision, design, mass production and use.

!To be continued....
This essay is under construction. If it is ever finished (:-) it is intended to utilise this collection to shape a continuing if idiosyncratic story of the development of embodied calculation up to the introduction of personal electronic calculation. So do visit again if you have got this far, and there may (should) be more.

!!Notes as I think about what I will write next!

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Perhaps more important was the use to which these devices might be put. There was enormous change taking place...... market, industrialisation, mass production, complexification of governance, solidification (temporarily) of the nation state, rapidly growing trade..... Mass education and the extension of childhood, two world wars, developments in materials, precision, design, mass production and use.

to:

Perhaps more important was the use to which these devices might be put. There was enormous change taking place...... market, industrialisation, mass production, complexification of governance, solidification (temporarily) of the nation state, rapidly growing trade..... Mass education and the extension of childhood, two world wars, developments in materials, precision, design, mass production and use.

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The late modern period, spanning ~~roughly~~ the ~~mid-~~nineteenth century through ~~to the two world wars of the twentieth century, was a time~~ of ~~enormous economic~~, ~~technological, cultural and political change. The role of calculators, from one point~~ of ~~view~~, ~~was a comparatively minor part of this panoramic and turbulent time, and yet, it also was profoundly shaped by~~ it, and helped facilitate its development.

As already suggersted, none of these devices that were created during this period sprung from their inventors minds completely unprecedented. The roots spread back into the early Modern period from the earliest forms of embodied calculation (for example, the ~~use~~ of ~~calculi). The period following~~ the inventions already mentioned of Schickard, Pascal, Moreland and Leibniz were followed by a multitude of devices which built on the same basic principles.

So it was not just the process of invention that was developing.

to:

The late modern period, spanning the nineteenth century through the two world wars of the twentieth century and ending roughly in the middle of that century, was a time of enormous economic, technological, cultural and political change. The role of calculators, from one point of view, was a comparatively minor part of this panoramic and turbulent time, and yet, it also was profoundly shaped by it, and helped facilitate its development.

As already suggersted, none of these devices that were created during this period sprung from their inventors minds completely unprecedented. The roots spread back into the early Modern period from the earliest forms of embodied calculation (for example, the use of calculi). The period following the inventions already mentioned of Schickard, Pascal, Moreland and Leibniz were followed by a multitude of devices built on similar basic principles, but all with the limitation that they were not widely taken up because as yet need had not developed to resonate with the limited capabilities and often high cost of the inventions. Nevertheless, as time passed a web of developments would continue to emerge that would eventually create that moment when such a resonance might take place.

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None of these devices that were created during this period sprung from their inventors minds completely unprecedented. The roots spread back into the early Modern period from the abacus on. For example: ~~So it was not just the process of invention that was developing.~~ Perhaps more important was the use to which these devices might be put. There was enormous change taking place...... market, industrialisation, mass production, complexification of governance, solidification (temporarily) of the nation state, rapidly growing trade..... Mass education and the extension of childhood, two world wars, developments in materials, precision, design, mass production and use.

to:

As already suggersted, none of these devices that were created during this period sprung from their inventors minds completely unprecedented. The roots spread back into the early Modern period from the earliest forms of embodied calculation (for example, the use of calculi). The period following the inventions already mentioned of Schickard, Pascal, Moreland and Leibniz were followed by a multitude of devices which built on the same basic principles.

So it was not just the process of invention that was developing.

Perhaps more important was the use to which these devices might be put. There was enormous change taking place...... market, industrialisation, mass production, complexification of governance, solidification (temporarily) of the nation state, rapidly growing trade..... Mass education and the extension of childhood, two world wars, developments in materials, precision, design, mass production and use.

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Mechanisation can come in the most basic forms and still carry the allure of the new. It can also be a useful substitute for mental skill. Very simple deviceswhose basic mechanism using metal strips or cogs which can be used by means of a stylis can be moved linearly or circularly the distance displaced standing for added numbers. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe,4 later to be known as the Addiator (of which there is one in this collection). Other devices used variations of this principle start with the Webb Patent Adder (1869) and Stevens Adder (1890s), and then proceeding through the Golden Gem, Addiator, and Lightning (1940s) - just illustrations of course of the wide range of different types and shapes of such devices that were sold. All of these work by adding movements (of cogs, chains, or straps) imprinted on which are the equivalent numbers.

to:

Mechanisation can come in the most basic forms and still carry the allure of the new. It can also be a useful substitute for mental skill.

General revamp of the concept behind mechanical calculation. Displacement as an analog for addition and subtraction. Repeated additiondisplacement as multiplication or subtraction displacement for division (with tests for overflow). Combinations of these for powers or roots. Use of complementary numbers where reverse displacement was rendered mechanically impossible. Then - either do this faster and more effectively, or in some way incorporate multiplication tables (or logarithms in the case of slide rules).

Very simple deviceswhose basic mechanism using metal strips or cogs which can be used by means of a stylis can be moved linearly or circularly the distance displaced standing for added numbers. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe,4 later to be known as the Addiator (of which there is one in this collection). Other devices used variations of this principle start with the Webb Patent Adder (1869) and Stevens Adder (1890s), and then proceeding through the Golden Gem, Addiator, and Lightning (1940s) - just illustrations of course of the wide range of different types and shapes of such devices that were sold. All of these work by adding movements (of cogs, chains, or straps) imprinted on which are the equivalent numbers.

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Thomas de Colmar arithmometer (1884) ~~subsequent devices - TIM (“Time is Money” ) from 1909 which was by now designed as~~ a ~~more robust arithmometer, mounted now in an all steel frame. Burkhardt in Austria produced~~ the first Austrian version of the Thomas machine, and later improvements were marketed in association with Bunzel. In this collection there is a rare and probably unique Bunzel-Delton arithmometer (1913) - the only known one existing with a forward crank, and from this fact, and the expert way in which the modification has been made, almost certainly a prototype created in the Bunzel workshops to match a patent, also reproduced int his site.

to:

Thomas de Colmar arithmometer (1884) Each represents a different mechanical approach to digitally carrying out the four functions, with an easy input, and a digital readout. Each then was improved through a series of innovations, first by the original inventors, and then as more players across the world competed to produce and market better variants.%0a %0aThomas de Colmar was the first person to produce a commercially useable calculator based on Leibnitz’s stepped drum principle, and he named his machine the “arithmometer”. The Thomas design was copied and improved by a number of other engineers and marketed from different countries.

subsequent devices - TIM (“Time is Money” ) from 1909 which was by now designed as a more robust arithmometer, mounted now in an all steel frame. Burkhardt in Austria produced the first Austrian version of the Thomas machine, and later improvements were marketed in association with Bunzel.

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Each represents a different mechanical approach to digitally carrying out the four functions, with an easy input, and a digital readout. Each then was improved through a series of innovations, first by the original inventors, and then as more players across the world competed to produce and market better variants.%0a %0aThomas de Colmar was the first person to produce a commercially useable calculator based on Leibnitz’s stepped drum principle, and he named his machine the “arithmometer”. The Thomas design was copied and improved by a number of other engineers and marketed from different countries.

to:

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!"Arms races" and mechanical evolution
In this collection there is a rare and probably unique Bunzel-Delton arithmometer (1913) - the only known one existing with a forward crank, and from this fact, and the expert way in which the modification has been made, almost certainly a prototype created in the Bunzel workshops to match a patent, also reproduced int his site.

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!Thomas de Colmar - ~~the advent of the commercially useful calculating machine~~

to:

!Thomas de Colmar - a commercial calculator

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to:

Many variations. Eg Frieden's cam timed "Frieden wheel".

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Thomas de Colmar

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!Thomas de Colmar - the advent of the commercially useful calculating machine

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!~~Mechanical minituarisation at its best - the Curta Calculator~~ (1947–1970)

to:

!Curta: The peak of minituarisation (1947–1970)

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~~Building on Napier’s rods: the search to automate multiplication and division~~

to:

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Electricity could be utilised once there was a national grid....

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Centrally increasing role of science, engineering, mathematics in production, governance and civil society.

Transformation from the old aristocratic machines to those of mass production.

Style, tyle, "usability". Break into mechanism, role, .....

Refs: WIT. NSOT.

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to:

The late modern period, spanning roughly the mid-nineteenth century through to the two world wars of the twentieth century, was a time of enormous economic, technological, cultural and political change. The role of calculators, from one point of view, was a comparatively minor part of this panoramic and turbulent time, and yet, it also was profoundly shaped by it, and helped facilitate its development.

None of these devices that were created during this period sprung from their inventors minds completely unprecedented. The roots spread back into the early Modern period from the abacus on. For example: So it was not just the process of invention that was developing. Perhaps more important was the use to which these devices might be put. There was enormous change taking place...... market, industrialisation, mass production, complexification of governance, solidification (temporarily) of the nation state, rapidly growing trade..... Mass education and the extension of childhood, two world wars, developments in materials, precision, design, mass production and use.

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We should remind ouselves that none of these devices sprung from their inventors minds completely unprecedented. The roots spread back into the early Modern period from the abacus on. For example: So it was not just the process of invention that was developing. Perhaps more important was the use to which these devices might be put. There was enormous change taking place...... market, industrialisation, mass production, complexification of governance, solidification (temporarily) of the nation state, rapidly growing trade..... Mass education and the extension of childhood, two world wars....

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We should remind ouselves that none of these devices sprung from their inventors minds completely unprecedented. The roots spread back into the early Modern period from the abacus on. For example: So it was not just the process of invention that was developing. Perhaps more important was the use to which these devices might be put. There was enormous change taking place...... market, industrialisation, mass production, complexification of governance, solidification (temporarily) of the nation state, rapidly growing trade..... Mass education and the extension of childhood,

to:

We should remind ouselves that none of these devices sprung from their inventors minds completely unprecedented. The roots spread back into the early Modern period from the abacus on. For example: So it was not just the process of invention that was developing. Perhaps more important was the use to which these devices might be put. There was enormous change taking place...... market, industrialisation, mass production, complexification of governance, solidification (temporarily) of the nation state, rapidly growing trade..... Mass education and the extension of childhood, two world wars....

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!Reshaping style

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!!Vanishing point: electronics and the arrival of the HP35

to:

!The Vanishing point: electronics and the arrival of the HP35

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!!!~~The blind alley~~ - the search for true multiplication and division

to:

!!!Evolutionary cul-de-sac: the search for true multiplication and division

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Relationship between mechanisation of arithmetic and more general love of mechanisation. Most notably the huge reforms of the French revolution and the more steady but important innovations of England and elsewhere.

~~However, mechanisation can come in~~ the ~~most basic forms and still carry the allure of the new~~. Very simple deviceswhose basic mechanism using metal strips or cogs which can be used by means of a stylis can be moved linearly or circularly the distance displaced standing for added numbers. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe,4 later to be known as the Addiator (of which there is one in this collection). Other devices used variations of this principle start with the Webb Patent Adder (1869) and Stevens Adder (1890s), and then proceeding through the Golden Gem, Addiator, and Lightning (1940s) - just illustrations of course of the wide range of different types and shapes of such devices that were sold. All of these work by adding movements (of cogs, chains, or straps) imprinted on which are the equivalent numbers.

to:

Relationship between mechanisation of arithmetic and more general love of mechanisation. Most notably the huge reforms of the French revolution and the more steady but important innovations of England and elsewhere. The displacement of the ancienne regime changes the relationship of science (and calculation) to society. Most dramatic in France, but elsewhere too the secular but accelerating increase in the power of merchant and market over the last several centuries has a similar effect.

Mechanisation can come in the most basic forms and still carry the allure of the new. It can also be a useful substitute for mental skill. Very simple deviceswhose basic mechanism using metal strips or cogs which can be used by means of a stylis can be moved linearly or circularly the distance displaced standing for added numbers. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe,4 later to be known as the Addiator (of which there is one in this collection). Other devices used variations of this principle start with the Webb Patent Adder (1869) and Stevens Adder (1890s), and then proceeding through the Golden Gem, Addiator, and Lightning (1940s) - just illustrations of course of the wide range of different types and shapes of such devices that were sold. All of these work by adding movements (of cogs, chains, or straps) imprinted on which are the equivalent numbers.

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!!!The blind alley - the search for true multiplication and division

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However, mechanisation can come in the most basic forms and still carry the allure of the new. Very simple deviceswhose basic mechanism using metal strips or cogs which can be used by means of a stylis can be moved linearly or circularly the distance displaced standing for added numbers. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe,4 later to be known as the Addiator (of which there is one in this collection). Other devices used variations of this principle start with the Webb Patent Adder (1869) and Stevens Adder (1890s), and then proceeding through the Golden Gem, Addiator, and Lightning (1940s) - just illustrations of course of the wide range of different types and shapes of such devices that were sold. All of these work by adding movements (of cogs, chains, or straps) imprinted on which are the equivalent numbers. ~~One~~ using rods - a Comptator from 1910 is in this collection. In a sense the above devices are linear digital sliding rules. One of the key innovations achieved by most of these devices (but not by the ‘Troncets’) was to develop a mechanical means of ‘carrying’ (interestingly already solved by Shickard) when a sum of two numbers in the same ‘column’ was greater than 9. A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which simply used successive rotations of a wheel to wind on successive numbers whilst a ball bearing, moving in a spiral groove, tracked the successive rotations. Such adders, whilst simple in concept and cheap to manufacture, are slow and virtually useless for efficient multiplication and division. Early experiments with keyboards can be seen in the Adix adding machine of 1903, but as the one in this collection shows, it can only add and is very hard even to zero.

to:

However, mechanisation can come in the most basic forms and still carry the allure of the new. Very simple deviceswhose basic mechanism using metal strips or cogs which can be used by means of a stylis can be moved linearly or circularly the distance displaced standing for added numbers. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe,4 later to be known as the Addiator (of which there is one in this collection). Other devices used variations of this principle start with the Webb Patent Adder (1869) and Stevens Adder (1890s), and then proceeding through the Golden Gem, Addiator, and Lightning (1940s) - just illustrations of course of the wide range of different types and shapes of such devices that were sold. All of these work by adding movements (of cogs, chains, or straps) imprinted on which are the equivalent numbers.

One using rods - a Comptator from 1910 is in this collection. In a sense the above devices are linear digital sliding rules. One of the key innovations achieved by most of these devices (but not by the ‘Troncets’) was to develop a mechanical means of ‘carrying’ (interestingly already solved by Shickard) when a sum of two numbers in the same ‘column’ was greater than 9.

A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which simply used successive rotations of a wheel to wind on successive numbers whilst a ball bearing, moving in a spiral groove, tracked the successive rotations. Such adders, whilst simple in concept and cheap to manufacture, are slow and virtually useless for efficient multiplication and division. Early experiments with keyboards can be seen in the Adix adding machine of 1903, but as the one in this collection shows, it can only add and is very hard even to zero.

We should remind ouselves that none of these devices sprung from their inventors minds completely unprecedented. The roots spread back into the early Modern period from the abacus on. For example: So it was not just the process of invention that was developing. Perhaps more important was the use to which these devices might be put. There was enormous change taking place...... market, industrialisation, mass production, complexification of governance, solidification (temporarily) of the nation state, rapidly growing trade..... Mass education and the extension of childhood,

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~~More elaborate machines were developed in the nineteenth century each aiming~~ to ~~allow all four operations to be successfully carried out. Early examples in this collection include~~ a ~~Felt and Tarrant “woodie” Comptometer? (1896) - one of the first 40 known to still exist;~~ a ~~highly sought after - also in the first 180 of these known to still exist, and a very early Brunsviga-Schuster pinwheel (1896) calculator~~.

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!Felt and Tarrant - a "model T" for industrial calculation.
A further approach to the problem of the four functions is found in the American invention by Felt, of a device that he called the comptometer and patented in 1887. It performs the task of addition by a system of keys and levers. Notably no crank handle needs to be turned in order to perform the addition. Addition of a number automatically occurs whenever a corresponding key is pressed. This is fast. But the difficulty is that subtraction must be carried out by a process of addition of complementary numbers. Carrying of “tens” must be done by addition also. And the process of multiplication is done by multiple presses of the number. As already mentioned, in this collection we have one of the first models of the comptomoter - one from 1896 cased in wood? and one of the 40 oldest known to still be in existence, as well as a later demonstration machine from Bell Punch, and then its embodiment in a fully working Bell Punch Sumlock (from the 1950s).-

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!Ohdner's Pinwheels

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~~A further approach to the problem of~~ the four functions is found in the American invention by Felt, of a device that he called the comptometer and patented in 1887. It performs the task of addition by a system of keys and levers. Notably no crank handle needs to be turned in order to perform the addition. Addition of a number automatically occurs whenever a corresponding key is pressed. This is fast. But the difficulty is that subtraction must be carried out by a process of addition of complementary numbers. Carrying of “tens” must be done by addition also. And the process of multiplication is done by multiple presses of the number. As already mentioned, in this collection we have one of the first models of the comptomoter - one from 1896 cased in wood? and one of the 40 oldest known to still be in existence, as well as a later demonstration machine from Bell Punch, and then its embodiment in a fully working Bell Punch Sumlock (~~from the 1950s~~).
Mechanical minituarisation at its best - the Curta Calculator (1947–1970)

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!Mechanical minituarisation at its best - the Curta Calculator (1947–1970)

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!!Vanishing point: the arrival of the HP35

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!!Vanishing point: electronics and the arrival of the HP35

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!!To be continued....

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!To be continued....

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!!!Notes as I think about what I will write next!

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!!Notes as I think about what I will write next!

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The expansion of the market in the late Modern period.

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!!!The expansion of the market in the late Modern period.

!!!Simple devices

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~~devices whose~~ basic mechanism using metal strips or cogs which can be used by means of a stylis can be moved linearly or circularly the distance displaced standing for added numbers. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe,4 later to be known as the Addiator (of which there is one in this collection). Other devices used variations of this principle start with the Webb Patent Adder (1869) and Stevens Adder (1890s), and then proceeding through the Golden Gem, Addiator, and Lightning (1940s) - just illustrations of course of the wide range of different types and shapes of such devices that were sold. All of these work by adding movements (of cogs, chains, or straps) imprinted on which are the equivalent numbers. One using rods - a Comptator from 1910 is in this collection. In a sense the above devices are linear digital sliding rules. One of the key innovations achieved by most of these devices (but not by the ‘Troncets’) was to develop a mechanical means of ‘carrying’ (interestingly already solved by Shickard) when a sum of two numbers in the same ‘column’ was greater than 9. A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which simply used successive rotations of a wheel to wind on successive numbers whilst a ball bearing, moving in a spiral groove, tracked the successive rotations. Such adders, whilst simple in concept and cheap to manufacture, are slow and virtually useless for efficient multiplication and division. Early experiments with keyboards can be seen in the Adix adding machine of 1903, but as the one in this collection shows, it can only add and is very hard even to zero.

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However, mechanisation can come in the most basic forms and still carry the allure of the new. Very simple deviceswhose basic mechanism using metal strips or cogs which can be used by means of a stylis can be moved linearly or circularly the distance displaced standing for added numbers. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe,4 later to be known as the Addiator (of which there is one in this collection). Other devices used variations of this principle start with the Webb Patent Adder (1869) and Stevens Adder (1890s), and then proceeding through the Golden Gem, Addiator, and Lightning (1940s) - just illustrations of course of the wide range of different types and shapes of such devices that were sold. All of these work by adding movements (of cogs, chains, or straps) imprinted on which are the equivalent numbers. One using rods - a Comptator from 1910 is in this collection. In a sense the above devices are linear digital sliding rules. One of the key innovations achieved by most of these devices (but not by the ‘Troncets’) was to develop a mechanical means of ‘carrying’ (interestingly already solved by Shickard) when a sum of two numbers in the same ‘column’ was greater than 9. A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which simply used successive rotations of a wheel to wind on successive numbers whilst a ball bearing, moving in a spiral groove, tracked the successive rotations. Such adders, whilst simple in concept and cheap to manufacture, are slow and virtually useless for efficient multiplication and division. Early experiments with keyboards can be seen in the Adix adding machine of 1903, but as the one in this collection shows, it can only add and is very hard even to zero.

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!!!Harnessing electricity

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!!!To be continued....

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!!To be continued....

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Conversion devices
The bane of earlier centuries, and even still, is the fact that quantities were often measured in different incompatible units. ~~Special purpose devices, basically just forms of mechanical look-up tables were devised to deal~~ with ~~this sort of issue, since performing the calculation each time was time consuming, and many did not have the skills in any case to do it.~~ The need to be able to measure and compare occurred extensively in shipping and commerce rather early. In this collection we have a “Convertisseur” from (1780–1810) designed by Gabrielle Chaix in Paris, to ~~assist merchants and artisans to convert between~~ the ~~old measure of distance (the “Aune”)~~ and ~~the new measure introduced by~~ the ~~Revolutionary Government of the metre in 1791~~.

Other simple mechanisms for adding and subtracting were developed in a series of devices whose basic mechanism using metal strips or cogs which can be used by means of a stylis can be moved linearly or circularly the distance displaced standing for added numbers. This type of device, first developed in the 17th Century by ~~inventors such as Claude Perrot (1613–88) was popularised by J~~. ~~Louis Troncet, a French inventor who created his Arithmographe,4 later to be known as~~ the Addiator (of which there is one in this collection).

Other devices used variations of this principle start with the Webb Patent Adder (1869) and Stevens Adder (1890s), and then proceeding through the Golden Gem, Addiator, and Lightning (1940s) - just illustrations of course of the wide range of different types and shapes of such devices that were sold. All of these work by adding movements (of cogs, chains, or straps) imprinted on which are the equivalent numbers. One using rods - a Comptator from 1910 is in this collection. In a sense the above devices are linear digital sliding rules. One of ~~the key innovations achieved by most of these devices~~ (~~but not by the ‘Troncets’~~) ~~was to develop a mechanical means of ‘carrying’ (interestingly already solved by Shickard) when a sum~~ of two numbers in the same ‘column’ was greater than 9. A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which simply used successive rotations of a ~~wheel to wind on successive numbers whilst~~ a ball bearing, moving in a spiral groove, tracked the successive rotations. Such adders, whilst simple in concept and cheap to manufacture, are slow and virtually useless for efficient multiplication and division. Early experiments with keyboards can be seen in the Adix adding machine of 1903, but as the one in this collection shows, it can only add and is very hard even to zero.

The first commercial calculators (C19-C20)
More elaborate machines were developed in the nineteenth century each aiming to allow all four operations to be successfully carried out. Early examples in this collection include a Felt and Tarrant “woodie” Comptometer? (1896) - one of the first 40 known to still exist; a highly sought after Thomas de Colmar arithmometer (1884) - also in the first 180 of these known to still exist, and a very early Brunsviga-Schuster pinwheel (1896) calculator.

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!!!Notes as I think about what I will write next!

The expansion of the market in the late Modern period.

Comment - historical epochs do not come with nice clear boundaries. All transitions with interleaving and layering. Thus for example, we have the development from tables to simple mechanical devices which did the same thing. The bane of earlier centuries, and even still, is the fact that quantities were often measured in different incompatible units. Special purpose devices, basically just forms of mechanical look-up tables were devised to deal with this sort of issue, since performing the calculation each time was time consuming, and many did not have the skills in any case to do it. The need to be able to measure and compare occurred extensively in shipping and commerce rather early. In this collection we have a “Convertisseur” from (1780–1810) designed by Gabrielle Chaix in Paris, to assist merchants and artisans to convert between the old measure of distance (the “Aune”) and the new measure introduced by the Revolutionary Government of the metre in 1791.

Relationship between mechanisation of arithmetic and more general love of mechanisation. Most notably the huge reforms of the French revolution and the more steady but important innovations of England and elsewhere.

devices whose basic mechanism using metal strips or cogs which can be used by means of a stylis can be moved linearly or circularly the distance displaced standing for added numbers. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe,4 later to be known as the Addiator (of which there is one in this collection). Other devices used variations of this principle start with the Webb Patent Adder (1869) and Stevens Adder (1890s), and then proceeding through the Golden Gem, Addiator, and Lightning (1940s) - just illustrations of course of the wide range of different types and shapes of such devices that were sold. All of these work by adding movements (of cogs, chains, or straps) imprinted on which are the equivalent numbers. One using rods - a Comptator from 1910 is in this collection. In a sense the above devices are linear digital sliding rules. One of the key innovations achieved by most of these devices (but not by the ‘Troncets’) was to develop a mechanical means of ‘carrying’ (interestingly already solved by Shickard) when a sum of two numbers in the same ‘column’ was greater than 9. A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which simply used successive rotations of a wheel to wind on successive numbers whilst a ball bearing, moving in a spiral groove, tracked the successive rotations. Such adders, whilst simple in concept and cheap to manufacture, are slow and virtually useless for efficient multiplication and division. Early experiments with keyboards can be seen in the Adix adding machine of 1903, but as the one in this collection shows, it can only add and is very hard even to zero.

Thomas de Colmar

Thomas de Colmar arithmometer (1884) subsequent devices - TIM (“Time is Money” ) from 1909 which was by now designed as a more robust arithmometer, mounted now in an all steel frame. Burkhardt in Austria produced the first Austrian version of the Thomas machine, and later improvements were marketed in association with Bunzel. In this collection there is a rare and probably unique Bunzel-Delton arithmometer (1913) - the only known one existing with a forward crank, and from this fact, and the expert way in which the modification has been made, almost certainly a prototype created in the Bunzel workshops to match a patent, also reproduced int his site.

More elaborate machines were developed in the nineteenth century each aiming to allow all four operations to be successfully carried out. Early examples in this collection include a Felt and Tarrant “woodie” Comptometer? (1896) - one of the first 40 known to still exist; a highly sought after - also in the first 180 of these known to still exist, and a very early Brunsviga-Schuster pinwheel (1896) calculator.

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As well as an original Thomas de Colmar, this collection has a TIM (“Time is Money” ) from 1909 which was by now designed as a more robust arithmometer, mounted now in an all steel frame. Burkhardt in Austria produced the first Austrian version of the Thomas machine, and later improvements were marketed in association with Bunzel. In this collection there is a rare and probably unique Bunzel-Delton arithmometer (1913) - the only known one existing with a forward crank, and from this fact, and the expert way in which the modification has been made, almost certainly a prototype created in the Bunzel workshops to match a patent, also reproduced int his site.

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~~Late Modern 1800 - mid 2000~~

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Conversion devices
The bane of earlier centuries, and even still, is the fact that quantities were often measured in different incompatible units. Special purpose devices, basically just forms of mechanical look-up tables were devised to deal with this sort of issue, since performing the calculation each time was time consuming, and many did not have the skills in any case to do it. The need to be able to measure and compare occurred extensively in shipping and commerce rather early. In this collection we have a “Convertisseur” from (1780–1810) designed by Gabrielle Chaix in Paris, to assist merchants and artisans to convert between the old measure of distance (the “Aune”) and the new measure introduced by the Revolutionary Government of the metre in 1791.

Other simple mechanisms for adding and subtracting were developed in a series of devices whose basic mechanism using metal strips or cogs which can be used by means of a stylis can be moved linearly or circularly the distance displaced standing for added numbers. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe,4 later to be known as the Addiator (of which there is one in this collection).

Other devices used variations of this principle start with the Webb Patent Adder (1869) and Stevens Adder (1890s), and then proceeding through the Golden Gem, Addiator, and Lightning (1940s) - just illustrations of course of the wide range of different types and shapes of such devices that were sold. All of these work by adding movements (of cogs, chains, or straps) imprinted on which are the equivalent numbers. One using rods - a Comptator from 1910 is in this collection. In a sense the above devices are linear digital sliding rules. One of the key innovations achieved by most of these devices (but not by the ‘Troncets’) was to develop a mechanical means of ‘carrying’ (interestingly already solved by Shickard) when a sum of two numbers in the same ‘column’ was greater than 9. A particularly simple approach to the issue of carrying was addressed in the Addall from 1910, a circular proportional adder which simply used successive rotations of a wheel to wind on successive numbers whilst a ball bearing, moving in a spiral groove, tracked the successive rotations. Such adders, whilst simple in concept and cheap to manufacture, are slow and virtually useless for efficient multiplication and division. Early experiments with keyboards can be seen in the Adix adding machine of 1903, but as the one in this collection shows, it can only add and is very hard even to zero.

The first commercial calculators (C19-C20)
More elaborate machines were developed in the nineteenth century each aiming to allow all four operations to be successfully carried out. Early examples in this collection include a Felt and Tarrant “woodie” Comptometer? (1896) - one of the first 40 known to still exist; a highly sought after Thomas de Colmar arithmometer (1884) - also in the first 180 of these known to still exist, and a very early Brunsviga-Schuster pinwheel (1896) calculator.

Each represents a different mechanical approach to digitally carrying out the four functions, with an easy input, and a digital readout. Each then was improved through a series of innovations, first by the original inventors, and then as more players across the world competed to produce and market better variants.%0a %0aThomas de Colmar was the first person to produce a commercially useable calculator based on Leibnitz’s stepped drum principle, and he named his machine the “arithmometer”. The Thomas design was copied and improved by a number of other engineers and marketed from different countries.

As well as an original Thomas de Colmar, this collection has a TIM (“Time is Money” ) from 1909 which was by now designed as a more robust arithmometer, mounted now in an all steel frame. Burkhardt in Austria produced the first Austrian version of the Thomas machine, and later improvements were marketed in association with Bunzel. In this collection there is a rare and probably unique Bunzel-Delton arithmometer (1913) - the only known one existing with a forward crank, and from this fact, and the expert way in which the modification has been made, almost certainly a prototype created in the Bunzel workshops to match a patent, also reproduced int his site.

The pinwheel calculator was developed as an improvement on the arithmometer, utilising a clever ‘counting gear’ in which the number of teeth could be adjusted by sliders (and later a push-down keyboard). In this collection there is the already mentioned very early Brunsviga-Schuster pinwheel calculator from 1896 (an Ohdner Brunsviga which had been re-badged by Schuster who on-sold them). There is also a later Ohdner from 1938 and a Facit calculator from around 1945, and then from near the end of production of such machines, from the 1950s a very nice demonstration Walther 160 calculator, showing its mechanism, complemented by a complete and fully operational Walther of the same model.
A further approach to the problem of the four functions is found in the American invention by Felt, of a device that he called the comptometer and patented in 1887. It performs the task of addition by a system of keys and levers. Notably no crank handle needs to be turned in order to perform the addition. Addition of a number automatically occurs whenever a corresponding key is pressed. This is fast. But the difficulty is that subtraction must be carried out by a process of addition of complementary numbers. Carrying of “tens” must be done by addition also. And the process of multiplication is done by multiple presses of the number. As already mentioned, in this collection we have one of the first models of the comptomoter - one from 1896 cased in wood? and one of the 40 oldest known to still be in existence, as well as a later demonstration machine from Bell Punch, and then its embodiment in a fully working Bell Punch Sumlock (from the 1950s).
Mechanical minituarisation at its best - the Curta Calculator (1947–1970)

Finally there is the last and most beautifully mintuarised of the four function manual mechanical calculators buit by Curt Hertzstark, the son of Samuel Hertzstark (mentioned earlier) which he developed when a prisoner in Buchenwald concentration camp. The first model (the Model 1) began production in 1947. A (rare) example of the Model I Curta ( with pin sliders which were soon improved upon) in mint condition coming from the first 5500 made in ~July 1948, is in this collection along with another Model I (complete with its packing box and instructions) from 1967, and a Model II Curta from 1962 (with an ‘extra’ leather carrying case). These machines constitute the pinacle reached in the development of the personal hand-operated mechanical digital calculator - able to carry out all four functions by means of a crank operated machine of exquisite minituarised workmanship and design. Production ceased in November 1970 although sales continued through 1973.
Building on Napier’s rods: the search to automate multiplication and division

An entirely different evolutionary path which has already been mentioned was attempted to solving the problem of mechanising the four arithmetic operations (+, -, x, /), with emphasis on finding ways to directly perform the more difficult two operations of multiplication and division. This developed from the Napier’s rods - or “bones” (developed by John Napier (1550–1617) to which we have already referred. As already mentioned calculational approaches were designed around them by Wilhelm Schickard in 1623, Charles Cotterel in 1667, Gaspard Schott in 1668, and Samuel Morland between 1625 and 1695. A late and unique expression of these in this collection is Justin Bamberger’s Omega Calculating Machine (1903-6). It combines a stylus operated adding machine (complete with provision for automatic carry) with a sophisticated Napier bones based machine for discovering the partial products of two multiplied numbers (a bit like that in Schickard’s much earlier device), which can then be added in the adding machine to find corresponding products and quotients. I am working on an English language set of instructions for its use have been devised and are available. For that, watch this space.

One helpful development in design was the development of a proportional rack which moved cogs through a series of increments depending on the length of a toothed rack with which they engaged. Different lengths thus represented different numbers to be added. In 1906 Christel Haman founded the Mercedes-Euklid company who adopted this principle to create a machine that after a process of development eventually could automate the process of division. There is both a demonstration Mercedes-Euklid (model 29 from 1934) and then a fully working Mercedes-Euklid 29 in this collection.

An arithmometer, the MADAS (standing for “Multiplication, Addition, Division - Automatically, Substraction”) was developed by Erwin Janz and manufactured by Egli in Zurich, starting in 1913. As the acronym suggests, this machine achieved an entirely automatic division process - the first ever for an arithmometer style calculator. In this collection there is a MADAS IX Maxima calculator (produced in 1917) which could display 16 numbers in its results register.

A much heavier and complex mechanical approach was also explored. First it was embodied in Léon Bollée’s calculating machine which won a gold medal at the Paris Exposition of 1889. One surviving example of this bulky but beautiful machine can be seen at the Musée des Arts et Métiers in Paris. This collection has only an article on this “New Calculating Machine of very General Applicability” from the Manufacturer and Builder of 1890. Similar principles were however utilised by Otto Steiger who patented a rather more practical “Millionaire calculating machine” which had a simple enough mechanism to enable production on a commercial scale. The Millionaire calculating machine combines the idea of the physical embodiment of multiplication tables with that of the proportional rack. It is able to interrogate a multiplication table represented by metal rods, and in a single crank of the handle multiplies the multiplicand by a number set between 1 and 9 then advancing its internal carriage one place ready for the next multiplier to be set and applied. Manufactured by H.W. Egli, some 4,655 of these were sold. The Millionaire calculating machine in this collection is from 1912, and is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones.
One step backward, many steps forward: applying the electric motor (C20)

The electric motor marked the beginning of the end for all forms of mechanism more ingenious than those depending on the simple minded operation of addition and its inverse, subtraction. The greatest gains in efficiency could be obtained by simply increasing the speed with which these operations were repeated and controlled. Speed gains followed from simpler rather than more complex basic mechanisms. The control mechanisms that utilised these simple repeated basic operations, however did become more complex in the interests of using them to produce more complex and accurate outputs.

In this collection there is an arithmometer branded by Samuel Hertzstark from 1929, although by then he was not making machines. It is actually a Badenia (manufactured by the German Company Math. Bauerle in the Black Forest) which Hertzstark was by then re-badging (not long before he died). It features an electric motor, still in good working order, and with a keyboard instead of sliders for input. The features of it were not only that it had a keyboard for input, but also a control mechanism consisting of a column of keys which enabled a number to be entered and then added through 0 to 8 repeats representing multiplication by one to nine.

Whilst the above was an obvious innovation, the clumsiest approach in all the calculating devices - from the first arithmometer through to the Millionaire was division, which could only be done by a process along the lines of that done in long division. That is, the number to be divided (the dividend) is considered sequentially from the highest power of ten, and thus decomposed into a series of partial products of the successive parts of the dividend with the divisor. This required a process of guessing each partial product and then trying it out, the result being subtracted from the dividend to give a remainder, exactly as is done in pen and paper long division.

As well as Haman (and the Mercedes-Euklid) mentioned earlier, H.W. Egli also began the chain of innovation to mechanise this process, but only by abandonning the sophistication of the Millionaire and like Haman returning to the principles of the arithmometer. The result was the MADAS calculator, first produced in manual form, which could advance the carriage automatically one place at a time as division and multiplication were carried out. With progressive further modifications, including the insertion of an electric motor, the MADAS became the highly effective electric mechanical calculating machine whose use continued right into the 1960s. The late MADAS 20BTG calculator which is part of this collection represents a classic exemplar of the late stages of this evolutionary development. Its mechanism was also adopted in its essentials, then with many innovations (but with less of the Swiss robust construction of the Madas), in the US Frieden calculators. As it turned out, this final class of machines represented the pinacle of achievement in motorised mechanical calculation.

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!Part 3. The Advent of Commercial Mechanical Calculation.

(:toc:)

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Part 3. The Advent of Commercial Mechanical Calculation.

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~~Commercial mechanical calculation~~

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!!!To be continued....
This essay is under construction. If it is ever finished (:-) it is intended to utilise this collection to shape a continuing if idiosyncratic story of the development of embodied calculation up to the introduction of personal electronic calculation. So do visit again if you have got this far, and there may (should) be more.

Late Modern 1800 - mid 2000

!!Vanishing point: the arrival of the HP35

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Commercial mechanical calculation

Site.LateModern History