Site.LateModern History
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1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator125.jpg |
1910–20s | Comptator (9 col) | Schubert & Salzer | Rod | http://meta-studies.net/pmwiki/uploads/Comptator125.jpg |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator125.jpg |
1910–20s | Comptator (9 col) | Schubert & Salzer | Rod | http://meta-studies.net/pmwiki/uploads/Comptator125.jpg |
serial 1230A 79429, 1972|| December 1973
serial 1230A 79429|| December 1973
serial 1350A 36719, 1973|| August 1973
serial 1350A 36719|| August 1973
serial 1333A 06752, 1973||
serial 1333A 06752||
http://meta-studies.net/pmwiki/uploads/HP35H250.jpg | http://meta-studies.net/pmwiki/uploads/HP-45H250.jpg |
http://meta-studies.net/pmwiki/uploads/HP35H250.jpg | http://meta-studies.net/pmwiki/uploads/HP-45H250.jpg | http://meta-studies.net/pmwiki/uploads/HP-65-15pc.jpg |
serial 1350A 36719, 1973||
serial 1350A 36719, 1973|| August 1973
Hewlett Packard
HP 65 Calculator
serial 1333A 06752, 1973||
http://meta-studies.net/pmwiki/uploads/HP35H250.jpg | http://meta-studies.net/pmwiki/uploads/HP-45H250.jpg | http://meta-studies.net/pmwiki/uploads/HP-65-15pc.jpg |
http://meta-studies.net/pmwiki/uploads/HP35H250.jpg | http://meta-studies.net/pmwiki/uploads/HP-45H250.jpg | http://meta-studies.net/pmwiki/uploads/HP-65-15pc.jpg |
(collection Calculant) |
(collection Calculant) |
http://meta-studies.net/pmwiki/uploads/HP35H250.jpg | http://meta-studies.net/pmwiki/uploads/HP-45H250.jpg |
http://meta-studies.net/pmwiki/uploads/HP35H250.jpg | http://meta-studies.net/pmwiki/uploads/HP-45H250.jpg | http://meta-studies.net/pmwiki/uploads/HP-65-15pc.jpg |
serial 1350A 36719, 1973||
serial 1350A 36719, 1973|| August 1973
Hewlett Packard
HP 65 Calculator
serial 1333A 06752, 1973||
~1909 | Kuli Calculator | Addix Co. | Key input, lever & gears | http://meta-studies.net/pmwiki/uploads/Kuli50pcWeb.jpg |
~1909 | Kuli Calculator | Addix Co. | Key input, lever & gears | http://meta-studies.net/pmwiki/uploads/Kuli50pcWeb.jpg |
~1909 | Kuli Calculator | Addix Co. | Key input, lever & gears | http://meta-studies.net/pmwiki/uploads/Kuli50pcWeb.jpg |
Early experiments with keyboards also were evident in the late C19, some of which are shown (:if equal {Site.PrintBook$:PSW} "True":)in this table(:ifend:) below. (:if equal {Site.PrintBook$: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.
Early experiments with keyboards also were evident in the late C19, some of which are shown (:if equal {Site.PrintBook$:PSW} "True":)in this table(:ifend:) below. (:if equal {Site.PrintBook$: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.
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.
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,1 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.
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,2 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.
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.
tablend |
1903 | Adix Adding Machine | Manheim | Key input, lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
1903 | Adix Adding Machine | Adix Co. | Key input, lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
~1909 | Kuli Calculator | Addix Co. | Key input, lever & gears | http://meta-studies.net/pmwiki/uploads/Kuli50pcWeb.jpg |
tablend |
1908 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/CalcumeterH50.jpg |
~1912 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/CalcumeterH50.jpg |
1908 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/CalcumeterH50.jpg |
~1912 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/CalcumeterH50.jpg |
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 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.
1908 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg |
1908 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/CalcumeterH50.jpg |
1908 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg |
1908 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/CalcumeterH50.jpg |
1908 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg |
1908 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg |
1908 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg |
1908 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg |
1908 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg |
1908 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg |
1908 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg |
1908 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg |
1908 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg |
1908 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg |
1908 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg |
1908 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg |
1908 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg |
1908 | Standard Desk Calcumeter | James Walsh | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Calcumeter.jpg |
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.
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.
Early experiments with keyboards also were evident in the late C19, some of which are shown (:if equal {Site.PrintBook$:PSW} "True":)in this table(:ifend:) below. (:if equal {Site.PrintBook$: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).
Early experiments with keyboards also were evident in the late C19, some of which are shown (:if equal {Site.PrintBook$:PSW} "True":)in this table(:ifend:) below. (:if equal {Site.PrintBook$: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).
Early experiments with keyboards can be seen below (:if equal {Site.PrintBook$:PSW} "True":)in this table(:ifend:) below. (:if equal {Site.PrintBook$: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).
Early experiments with keyboards also were evident in the late C19, some of which are shown (:if equal {Site.PrintBook$:PSW} "True":)in this table(:ifend:) below. (:if equal {Site.PrintBook$: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).
Early experiments with keyboards can be seen below (:if equal {Site.PrintBook$:PSW} "True":)in this table(:ifend:) below. (:if equal {Site.PrintBook$: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).
Early experiments with keyboards can be seen below (:if equal {Site.PrintBook$:PSW} "True":)in this table(:ifend:) below. (:if equal {Site.PrintBook$: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).
Early experiments with keyboards can be seen below (:if equal {Site.PrintBook$:PSW} "True":)in this table(:ifend:) below. (:if equal {Site.PrintBook$: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).
Early experiments with keyboards can be seen below (:if equal {Site.PrintBook$:PSW} "True":)in this table(:ifend:) below. (:if equal {Site.PrintBook$: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).
1908 | Adder Adding Machine | A. J. Postans | Key input, lever & gears | http://meta-studies.net/pmwiki/uploads/AdderW.jpg |
1908 | Adder Adding Machine | A. J. Postans | Key input, lever & gears | http://meta-studies.net/pmwiki/uploads/AdderW.jpg |
Wilhelm Schickard’s machine | Calculating Machine |
Wilhelm Schickard’s machine | Calculating Machine |
Locke Adder 1905–10 |
(collection Calculant) |
Locke Adder 1905–10 (collection Calculant) |
Locke Adder 1905–10 |
(collection Calculant) |
Locke Adder 1905–10 |
(collection Calculant) |
Locke Adder 1905–10 |
(collection Calculant) |
Locke Adder 1905–10 |
(collection Calculant) |
1891 | Centigraph Adding Machine | Am. Add. Co. | Key input, lever & gear | http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg |
1891 | Centigraph Adding Machine | Am. Add. Co. | Key input, lever & gear | http://meta-studies.net/pmwiki/uploads/CentigraphW175.gif |
(:title The Late Modern Period (from 1800) :)
(:if equal {Site.PrintBook$:PSW} "False":) (:table class=pictures width=100% align=left class=border cwidth=7:)
(:tableend:) (:ifend:) (:ifend:)
(:title The Late Modern Period (from 1800) :)
http://meta-studies.net/pmwiki/uploads/SpaldingW200.jpg|1884: Spalding Adding Machine\
http://meta-studies.net/pmwiki/uploads/SpaldingW200.jpg|1884: Spalding Adding Machine
Early experiments with keyboards can be seen below (:if equal {Site.PrintBook$:PSW} "True":)in this table(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:) Each of them is very different in appearance yet all three - the Spalding Adding machine of 1884 (of which only a very few were produced, and fewer still survive), the Centigraph of 1891 (also extremely rare), and the more conventional looking layout of the Addix Adding Machine of 1905. In each case the depression of the different number keys actuates a lever to move a gear wheel a corresponding number of notches, thus adding the number. Different forms of visual output of the accumulated number - dials (for the Spalding), a two digit display and arrow pointing out the 100s (up to 500) for the Centigraph, and a more conventional set of windows for the Addix.
Early experiments with keyboards can be seen below (:if equal {Site.PrintBook$:PSW} "True":)in this table(: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).
Spalding Adding Machine1884
Spalding Adding Machine 1884
http://meta-studies.net/pmwiki/uploads/SpaldingW200.jpg|1884: Spalding Adding Machine\
http://meta-studies.net/pmwiki/uploads/SpaldingW200.jpg|1884: Spalding Adding Machine\
1891 | Centigraph Adding Machine | Am. Add. Co. | Key input, lever & gear | http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg |
1891 | Centigraph Adding Machine | Am. Add. Co. | Key input, lever & gear | http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg |
1891 | Centigraph Adding Machine | Am. Add. Co. | Key input, lever & gear | http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg |
1891 | Centigraph Adding Machine | Am. Add. Co. | Key input, lever & gear | http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg |
align=center cellpadding=6 border=0 id=EarlyKeyboards summary=“Early keyboards”
1891 | Centigraph Adding Machine | Am. Add. Co. | Key input | lever & gear | http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg |
1903 | Adix Adding Machine | Manheim | Key input | lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
align=center cellpadding=6 border=0 id=EarlyKeyboards summary=“Early keyboards”
1891 | Centigraph Adding Machine | Am. Add. Co. | Key input, lever & gear | http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg |
1903 | Adix Adding Machine | Manheim | Key input, lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
1891 | Centigraph Adding Machine | Am. Add. Co. | Key input | lever & gear | http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg |
1903 | Adix Adding Machine | Manheim | Key input | lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
1891 | Centigraph Adding Machine | Am. Add. Co. | Key input, lever & gear | http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg |
1903 | Adix Adding Machine | Manheim | Key input, lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
1903 | Adix Adding Machine | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
1903 | Adix Adding Machine | Manheim | Key input | lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
1891 | Centigraph Adding Machine | Am. Add. Co. | Key input, lever & gear | http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg |
1891 | Centigraph Adding Machine | Am. Add. Co. | Key input | lever & gear | http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg |
1891 | Centigraph Adding Machine | Am. Add. Co. | Key input, lever & gear | http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg |
1903 | Adix Adding Machine | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
1891 | Centigraph Adding Machine | Am. Add. Co. | Key input | lever & gear | http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg |
1903 | Adix Adding Machine | Manheim | Key input | lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
1891 | Centigraph Adder | Am. Add. Co. | Key input, lever & gear | http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
1891 | Centigraph Adding Machine | Am. Add. Co. | Key input, lever & gear | http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg |
1903 | Adix Adding Machine | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
1891 | Centigraph Adder | Am. Add. Co. | Key input, lever & gear | http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
1891 | Centigraph Adding Machine | Am. Add. Co. | Key input, lever & gear | http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg |
1903 | Adix Adding Machine | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
1884 | Spalding Adding Machine | C.G. Spalding | Key input, lever & dialsl | http://meta-studies.net/pmwiki/uploads/SpaldingW100.jpg |
1884 | Spalding Adding Machine | C.G. Spalding | Key input, lever & dialsl | http://meta-studies.net/pmwiki/uploads/SpaldingW100.jpg |
Early experiments with keyboards can be seen in the Adix adding machine of 1903.
Early experiments with keyboards can be seen below (:if equal {Site.PrintBook$:PSW} "True":)in Early keyboards(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:) Each of them is very different in appearance yet all three - the Spalding Adding machine of 1884 (of which only a very few were produced, and fewer still survive), the Centigraph of 1891 (also extremely rare), and the more conventional looking layout of the Addix Adding Machine of 1905. In each case the depression of the different number keys actuates a lever to move a gear wheel a corresponding number of notches, thus adding the number. Different forms of visual output of the accumulated number - dials (for the Spalding), a two digit display and arrow pointing out the 100s (up to 500) for the Centigraph, and a more conventional set of windows for the Addix.
(:cellnr:) http://meta-studies.net/pmwiki/uploads/WebbH200.jpg
Webb Patent Adder and Talley Board 1869
(:cellnr:) http://meta-studies.net/pmwiki/uploads/SpaldingW200.jpg.jpg
Spalding Adding Machine1884
http://meta-studies.net/pmwiki/uploads/WebbH200.jpg|1869:Webb Patent Adder and Talley Board
http://meta-studies.net/pmwiki/uploads/SpaldingW200.jpg|1884: Spalding Adding Machine\
Other simple rotational adding devices in this collection are shown (:if equal {Site.PrintBook$:PSW} "True":)in Simple Rotational Calculators(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)
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,3 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 1820.4 His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.5 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).6
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 this figure(:ifend:) below.
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.
(:if equal {Site.PrintBook$:PSW} "False":)
(:table align=center :)
(:cellnr:) http://meta-studies.net/pmwiki/uploads/WebbH200.jpg
Webb Patent Adder and Talley Board 1869
(collection Calculant)
(:tableend:)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
http://meta-studies.net/pmwiki/uploads/WebbH200.jpg|1869:Webb Patent Adder and Talley Board
(collection Calculant)
(:ifend:)
Other simple rotational adding devices in this collection are shown (:if equal {Site.PrintBook$:PSW} "True":)in Simple Rotational Calculators(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)
(:if equal {Site.PrintBook$:PSW} "False":)
1884 | Spalding Adding Machine | C.G. Spalding | Key input, lever & dialsl | http://meta-studies.net/pmwiki/uploads/SpaldingW100.jpg |
1891 | Centigraph Adder | Am. Add. Co. | Key input, lever & gear | http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
(collection Calculant - all above) (:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
Date | Description | Maker | Type | Device |
1884 | Spalding Adding Machine | C.G. Spalding | Key input, lever & dialsl | http://meta-studies.net/pmwiki/uploads/SpaldingW100.jpg |
1891 | Centigraph Adder | Am. Add. Co. | Key input, lever & gear | http://meta-studies.net/pmwiki/uploads/CentigraphW175.jpg |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
(collection Calculant - all above) |
(:ifend:)
http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491
(collection Calculant)
http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491 (collection Calculant)
http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491
http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491
http://meta-studies.net/pmwiki/uploads/Brunsviga1896H250.jpg|
~1896: Brunsviga Schuster Pinwheel Calculator
Serial 3406 (collection Calculant)
http://meta-studies.net/pmwiki/uploads/Brunsviga1896H250.jpg|~1896: Brunsviga Schuster Pinwheel Calculator
Serial 3406
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Serial 3406
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Serial 3406 (collection Calculant)
http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg]|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491
http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491
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http://meta-studies.net/pmwiki/uploads/Locke170.jpg|The Locke Adder
(collection Calculant)
http://meta-studies.net/pmwiki/uploads/Locke170.jpg|The Locke Adder
(collection Calculant)
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July1972 Hewlett Packard HP 35 Calculator serial 1230A 79429, 1972 | December 1973 Hewlett Packard HP 45 Calculator serial 1350A 36719, 1973 |
July1972 Hewlett Packard HP 35 Calculator serial 1230A 79429, 1972 | December 1973 Hewlett Packard HP 45 Calculator serial 1350A 36719, 1973 |
July1972 Hewlett Packard HP 35 Calculator serial 1230A 79429, 1972 | December 1973 Hewlett Packard HP 45 Calculator serial 1350A 36719, 1973 |
July1972 Hewlett Packard HP 35 Calculator serial 1230A 79429, 1972 | December 1973 Hewlett Packard HP 45 Calculator serial 1350A 36719, 1973 |
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp’s Commercial Calculator
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp’s Commercial Calculator
http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg|~1790: Conversion device
http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg|~1790: Conversion device
http://meta-studies.net/pmwiki/uploads/Locke170.jpg|The Locke Adder
(collection Calculant)
http://meta-studies.net/pmwiki/uploads/Locke170.jpg|The Locke Adder
(collection Calculant)
http://meta-studies.net/pmwiki/uploads/WebbH200.jpg|1869:Webb Patent Adder and Talley Board
http://meta-studies.net/pmwiki/uploads/WebbH200.jpg|1869:Webb Patent Adder and Talley Board
http://meta-studies.net/pmwiki/uploads/Misc/ThomasMechRelH200.jpg|1862: Thomas de Colmar arithmometer mechanism
http://meta-studies.net/pmwiki/uploads/Misc/ThomasMechRelH200.jpg|1862: Thomas de Colmar arithmometer mechanism
http://meta-studies.net/pmwiki/uploads/TIMDrumH200.jpg|Step drum (in a later ‘TIM’ arithmometer)
http://meta-studies.net/pmwiki/uploads/TIMDrumH200.jpg|Step drum (in a later ‘TIM’ arithmometer)
http://meta-studies.net/pmwiki/uploads/ThomasDeColmarH300.jpg|1884: Thomas de Colmar Arithmometer
http://meta-studies.net/pmwiki/uploads/ThomasDeColmarH300.jpg|1884: Thomas de Colmar Arithmometer
http://meta-studies.net/pmwiki/uploads/Brunsviga1896H250.jpg|
http://meta-studies.net/pmwiki/uploads/Brunsviga1896H250.jpg|
http://meta-studies.net/pmwiki/uploads/Misc/RackMechH200.jpg|Rack mechanism
http://meta-studies.net/pmwiki/uploads/Misc/RackMechH200.jpg|Rack mechanism
(:table align=center id=Woodie"Woodie" :) http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491
http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg]|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491
http://meta-studies.net/pmwiki/uploads/Schickard1W300_1.jpg|1623: Recreation of Wilhelm Schickard’s calculating machine
http://meta-studies.net/pmwiki/uploads/Schickard1W300_1.jpg|1623: Recreation of Wilhelm Schickard’s calculating machine
http://meta-studies.net/pmwiki/uploads/BambergerOmegaH250.jpg|1904–1905: Bamberger's Omega calculating machine
http://meta-studies.net/pmwiki/uploads/BambergerOmegaH250.jpg|1904–1905: Bamberger's Omega calculating machine
http://meta-studies.net/pmwiki/uploads/BolleeMAB1890H250.jpg|Leon Bollée Calculating Machine
http://meta-studies.net/pmwiki/uploads/BolleeMAB1890H250.jpg|Leon Bollée Calculating Machine
http://meta-studies.net/pmwiki/uploads/MillionairH300.jpg|1912: Millionaire Calculating Machine, serial 2015 (10×10×20)
http://meta-studies.net/pmwiki/uploads/MillionairH300.jpg|1912: Millionaire Calculating Machine, serial 2015 (10×10×20)
http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometerH250.jpg|~1929: "Herzstark" electric Calculating Machine serial 6549
http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometerH250.jpg|~1929: "Herzstark" electric Calculating Machine serial 6549
http://meta-studies.net/pmwiki/uploads/HerzstarkMechH250.jpg|1950s-1960s: Underneath view of the Herzstark mechanism (note the stepped drums)
http://meta-studies.net/pmwiki/uploads/HerzstarkMechH250.jpg|1950s-1960s: Underneath view of the Herzstark mechanism (note the stepped drums)
http://meta-studies.net/pmwiki/uploads/MADAS_SmallerH250.jpg|1950s-1960s: MADAS
http://meta-studies.net/pmwiki/uploads/MADAS_SmallerH250.jpg|1950s-1960s: MADAS
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.
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.
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.7 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.)
The three arithmometers (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.8 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.)
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.9
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.10
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.11. 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$:PSW} "True":)in Demonstration Pinwheel Calculator(:ifend:) below.
The pinwheel calculator was developed as an improvement on the arithmometer more or less simultaneously in Russia in 1878 by Swedish engineer Willgodt Theophil Odhner (1845–1905) and in the US in 1874, by Frank Stephen Baldwin (1838–1925). Although they worked independently of each other their machines were so similar that the ‘Ohdner’ or ‘Baldwin’ machine became more or less interchangeable terms.12. The designs utilised a clever 'counting gear' in which the number of teeth protruding could be adjusted by sliders (and later a push-down keyboard). A pinwheel and the internal mechanism (with some pinwheels removed) from a Walther pinwheel calculator in this collection is shown (:if equal {Site.PrintBook$:PSW} "True":)in Demonstration Pinwheel Calculator(:ifend:) below.
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.13. 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.14 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.15
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.16. 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.17 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.18
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.
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$:PSW} "True":)in Comptometers(:ifend:) is the remaining comptometer in this collection, this time made of plastic in the 1950s by the British Bell Punch company. Also shown is a demonstration model showing the keys and lever system used in the Bell Punch machine.
The comptometer was a highly successful innovation and was sufficiently cheap and useful to reach a broad market. Characterised by extremely effective marketing and capable of being mass produced the device continued to be marketed for some 80 years. Unusually for such innovations it left its inventor extremely wealthy. By then its essential mechanism was being utilised by more than one company. Shown below (:if equal {Site.PrintBook$:PSW} "True":)in 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.
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).
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).
The first model (the Model 1) began production in 1947. Below left (:if equal {Site.PrintBook$:PSW} "True":)in Curta Calculators(:ifend:) is a (rare) example of the Model I Curta ( with pin sliders which were soon improved upon) in mint condition coming from the first 5500 made in ~July 1948, the year after production began and in the first 5,500 made. As can be seen the sliders are pins which were used by Curta before he introduced bakelite handles on them. Centre is a later Curta from 1967 complete with the original box in which it was sold and its instructions, all in mint condition. On the right is a Curta Model II from 1962. The Model II was a larger machine capable of a number input to 11 significant figures, compared with the more compact Model I which could accept a number accurate to 8 significant figures. Note the very ‘modern’ anodised aluminium sliders on the Model II which comes also with an optional leather carry case (not shown).
The first model (the Model 1) began production in 1947. Below left (:if equal {Site.PrintBook$:PSW} "True":)in Curta Calculators(: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).
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.
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.
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.
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.
The earliest of these machines had been that of Schickard (immediately below in Schickard’s Calculator). 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.
The earliest of these machines had been that of Schickard (Schickard’s Calculator) 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
A late and unique expression of the same principle in this collection is Justin Bamberger's Omega Calculating Machine (1903–6), shown in Bamberger Omega 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.
A later and unique expression of the same principles can be found in this collection (shown in Bamberger Omega ). 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.
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.
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.
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.
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.
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.
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.
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.
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.
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$:PSW} "True":)in Hewlett Packard Pocket Scientific Calculators(:ifend:) below). It was an extraordinary leap forward, equipped not only with a red lit showing smooth performance of the arithmetic functions but also reciprocals, powers, square roots, logarithms and anti-logarithms (base e and 10), the trigonometric functions, pi, and a system of registers which enabled chain operations without having to write down intermediate results. For those of a technical orientation who could afford it, all else was now as obsolete as gaslight. Hewlett Packard followed quickly with the HP-45 appearing in the following year with a configurable display, more functions and registers, a variety of constants, and a more compact shape, more suited for the male shirt top pocket. A year later in 1974 the HP-65 was launched with all that could be done by the HP-45 but with the added feature of being user-programmable through a small built in magnetic strip reader. With that the diminutive HP calculator had taken a huge step towards the first mass-marketed personal computers (the TRS-80 - the author wrote his second book on one of these in 1981 - launched by Tandy, and the Apple-II by Apple, both launched in 1977).
It was in July 1972, that the old ways for scientists and citizen alike were definitively undermined. In that month, to some astonishment, the Hewlett Packard company produced the HP-35 electronic ‘pocket’ calculator (see (:if equal {Site.PrintBook$:PSW} "True":)in Hewlett Packard Pocket Scientific Calculators(: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).
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.
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.
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 Gauvin19 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:
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 Gauvin20 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:
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.
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.
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.
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.21 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'.22 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.23 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.”24 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.”25 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).26
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.27 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'.28 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.29 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.”30 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.”31 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).32
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”.33 Nevertheless, it formed the standard against which improvements were sought and new designs contemplated.
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”.34 Nevertheless, it formed the standard against which improvements were sought and new designs contemplated.
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917W250.jpg |
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917W250.jpg |
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.35 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.
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.36 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.
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.37 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.
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.38 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.
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.
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.
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.
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.
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.39 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 Ropp’s Calculator(:ifend:), is the 1892 World’s Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.
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 .40 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$:PSW} "True":) in Ropp’s Calculator(:ifend:), is the 1892 World’s Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.
The dominant role of ready reckoners at this period is indicated by M. Norton Wise’s comment in relation to Victorian England that:
The dominant role of ready reckoners in this period is indicated by M. Norton Wise’s comment in relation to Victorian England that:
Subtraction could be achieved by units of motion in the opposite direction, or where that was not possible, the addition of complementary numbers.
Subtraction could be achieved by units of motion in the opposite direction, or where that was not possible, the addition of (:if equal {Site.PrintBook$:PSW} "False":)complementary numbers(:ifend:)(:if equal {Site.PrintBook$:PSW} "True":)complementary numbers(:ifend:).
One such line of development was based on the possibility of adding linear displacements of strips of metal. This type of device, first developed in the 17th Century by inventors such as Claude Perrot (1613–88) was popularised by J. Louis Troncet, a French inventor who created his Arithmographe, later to be known as the Addiator (of which there is one in this collection), of which a bewildering number of different designs appeared in the late C19 and early C20. Some used strips or rods, and some used chains which were more versatile. A rather beautiful Locke Adder which uses strips moved by knobs, from 1905–10, sold by Clarence Locke, is shown (:if equal {Site.PrintBook$:PSW} "True":)in The Locke Adder(:ifend:) below.
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 The Locke Adder(:ifend:) below.
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.
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.
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 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.
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,41 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.
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,42 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.
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 1820.43. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.44 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 invention45).
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 1820.46 His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.47 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).48
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 Step drum(: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.
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 Step drum(: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.
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.49 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.
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.50 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.
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.51 Below (:if equal {Site.PrintBook$:PSW} "True":)in this figure(: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.
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.52 Below (:if equal {Site.PrintBook$:PSW} "True":)in this figure(: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.
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.55 For more on the Curta see the marvellous collection of documents and simulations at The Curta Caclulator Page.56
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.57
Leon Bollée Calculating Machine “A New Calculating Machine of very General Applicability"
/’The Manufacturer and Builder 1890/’58
Leon Bollée Calculating Machine “A New Calculating Machine of very General Applicability"
The Manufacturer and Builder 189059
/’The Manufacturer and Builder 1890/’60
The Manufacturer and Builder 189061
Manufactured by H.W. Egli, some 4,655 Millionaires were sold between 1895 and 193562 at a 1912 price of about US$48063 (about $11,700 in 2013 US dollars64). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,65 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.
Manufactured by H.W. Egli, some 4,655 Millionaires were sold between 1895 and 193566 at a 1912 price of about US$48067 (about $11,700 in 2013 US dollars68). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,69 and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones. The machine still operates reliably after more than 100 years.
Samuel Herzstark (1867–1937), the father of Curt Herzstark who built the Curta, also was a pioneer in calculator construction and together with Gustav Perger established the Austria Calculator Machines Manufacturing Company in Vienna in 1905–6. In an interview in 1987 Curt Herzstark reports that in 1907 Samuel became the first to attach an electric motor to an arithmometer, which he equipped also with a keyboard. Curt also notes that this machine was equipped with automatic division.70 However after the 1914–18 War Herzstark returned to a demolished business. He restarted with a combination of importing and selling calculators from other manufacturers, assembling old stock of his own design, and then as the business built up designing new machines. Below (:if equal {Site.PrintBook$:PSW} "True":)in Herzstark arithmometer(: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.
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.71 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 Herzstark arithmometer(: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.
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.74 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.)
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.75 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.)
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.76 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.
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.77 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.
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.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 Ropp’s Calculator(:ifend:), is the 1892 World’s Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.
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.81 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 Ropp’s Calculator(:ifend:), is the 1892 World’s Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.
- something else that can be moved (for example, although it was barely used,84 the height of columns of water).
- something else that can be moved (for example, although it was barely used,85 the height of columns of water).
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,86 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.
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,87 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.
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 1820.88. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.89 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 invention90).
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 1820.91. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.92 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 invention93).
1862: Diagram of the Thomas de Colmar arithmometer mechanism.94
(Click on the image for an enlargement.)
(Source: Museum of the History of Science, University of Oxford.)
1862: Diagram of the Thomas de Colmar arithmometer mechanism.95
(Click on the image for an enlargement.)
(Source: Museum of the History of Science, University of Oxford.)
diagram.96
(Source: Museum of the History of Science, University of Oxford.)
diagram.97
(Source: Museum of the History of Science, University of Oxford.)
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.98 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.99 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'.100 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.101 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.”102 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.
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.103 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.104 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'.105 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.106 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.”107 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.
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.108 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.)
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.109 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.)
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.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.111
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.112. 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 Demonstration Pinwheel Calculator(:ifend:) below.
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.113. 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$:PSW} "True":)in Demonstration Pinwheel Calculator(:ifend:) below.
Ohdner began manufacture of his machines in 1886 under the name “Original Ohdner” but sold his rights also to Grimme, Natalis and Co., Braunsweig, who began marketing the machines under the name Brunsviga.114 In turn they also licenced agents such as Schuster to sell them. Reflecting a later start these machines were made from a wider range of materials than the arithmometers, including iron and nickel alloys as well as brass and steel. The Brunsviga was a quick success selling 20,000 units between 1892 and 1912.[115 Below (:if equal {Site.PrintBook$:PSW} "True":)in Brunsviga Calculator(:ifend:) is the very early Brunsviga-Schuster pinwheel calculator from 1896, followed (:if equal {Site.PrintBook$:PSW} "True":)in Pinwheel Calculators(:ifend:) by the other pinwheel calculators in this collection.
Ohdner began manufacture of his machines in 1886 under the name “Original Ohdner” but sold his rights also to Grimme, Natalis and Co., Braunsweig, who began marketing the machines under the name Brunsviga.116 In turn they also licenced agents such as Schuster to sell them. Reflecting a later start these machines were made from a wider range of materials than the arithmometers, including iron and nickel alloys as well as brass and steel. The Brunsviga was a quick success selling 20,000 units between 1892 and 1912.[117 Below (:if equal {Site.PrintBook$:PSW} "True":)in Brunsviga Calculator(:ifend:) is the very early Brunsviga-Schuster pinwheel calculator from 1896, followed (:if equal {Site.PrintBook$:PSW} "True":)in Pinwheel Calculators(:ifend:) by the other pinwheel calculators in this collection.
There were of course many variations on this theme. These included the “Frieden Wheel” which managed to achieve the same effect as the pinwheel but through simply a nicely timed use of a cam. More of that sort of mechanical detail for all the machines referred to here can be found in the classic book by Martin,118 and the marvellous websites of Rechnerlexikon119 and John Wolff120.
There were of course many variations on this theme. These included the “Frieden Wheel” which managed to achieve the same effect as the pinwheel but through simply a nicely timed use of a cam. More of that sort of mechanical detail for all the machines referred to here can be found in the classic book by Martin,121 and the marvellous websites of Rechnerlexikon122 and John Wolff123.
Felt first demonstrated this famously with a model constructed in a wooden macaroni box in 1885. He patented his design in 1887 and began selling it from his manufacturing company in Chicago. In 1890 he gave it the name “the Comptometer” and energetically promoted it.124 Below (:if equal {Site.PrintBook$:PSW} "True":)in this figure(: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.
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.125 Below (:if equal {Site.PrintBook$:PSW} "True":)in this figure(: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.
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.128 For more on the Curta see the marvellous collection of documents and simulations at The Curta Caclulator Page.129
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.130 For more on the Curta see the marvellous collection of documents and simulations at The Curta Caclulator Page.131
Leon Bollée Calculating Machine “A New Calculating Machine of very General Applicability"
The Manufacturer and Builder 1890132
Leon Bollée Calculating Machine “A New Calculating Machine of very General Applicability"
/’The Manufacturer and Builder 1890/’133
The Manufacturer and Builder 1890134
/’The Manufacturer and Builder 1890/’135
Manufactured by H.W. Egli, some 4,655 Millionaires were sold between 1895 and 1935136 at a 1912 price of about US$480137 (about $11,700 in 2013 US dollars138). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,139 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.
Manufactured by H.W. Egli, some 4,655 Millionaires were sold between 1895 and 1935140 at a 1912 price of about US$480141 (about $11,700 in 2013 US dollars142). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,143 and was until 1954 held by the B. B. Company in New York, NY. It is rather rare since it is capable of greater accuracy - 10 column - than the more common 8 column ones. The machine still operates reliably after more than 100 years.
Samuel Herzstark (1867–1937), the father of Curt Herzstark who built the Curta, also was a pioneer in calculator construction and together with Gustav Perger established the Austria Calculator Machines Manufacturing Company in Vienna in 1905–6. In an interview in 1987 Curt Herzstark reports that in 1907 Samuel became the first to attach an electric motor to an arithmometer, which he equipped also with a keyboard. Curt also notes that this machine was equipped with automatic division.144 However after the 1914–18 War Herzstark returned to a demolished business. He restarted with a combination of importing and selling calculators from other manufacturers, assembling old stock of his own design, and then as the business built up designing new machines. Below (:if equal {Site.PrintBook$:PSW} "True":)in Herzstark arithmometer(: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.
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.145 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 Herzstark arithmometer(: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.
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:
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:
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 operation148) and Moreland (allowing addition and subtraction “without charging the memory or disturbing the mind149). 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.
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 operation150) and Moreland (allowing addition and subtraction “without charging the memory or disturbing the mind151). 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.
http://meta-studies.net/pmwiki/uploads/Schickard1H250.jpg|1623: Recreation of Wilhelm Schickard’s calculating machine
http://meta-studies.net/pmwiki/uploads/Schickard1W300_1.jpg|1623: Recreation of Wilhelm Schickard’s calculating machine
http://meta-studies.net/pmwiki/uploads/Schickard1H250.jpg | http://meta-studies.net/pmwiki/uploads/BambergerOmegaH250.jpg |
http://meta-studies.net/pmwiki/uploads/Schickard1W300_1.jpg | http://meta-studies.net/pmwiki/uploads/BambergerOmegaH250.jpg |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/LightningH125.jpg |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/LightningH125.jpg |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/LightningH125.jpg |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/LightningH125.jpg |
1922 | Conto Mod C Adding Machine | Carl Landolt | Rotating Knob | http://meta-studies.net/pmwiki/uploads/ContoW175.jpg |
1922 | Conto Mod C Adding Machine | Carl Landolt | Rotating Knob | http://meta-studies.net/pmwiki/uploads/ContoW175.jpg |
1920 | Addo adder | Aktiebolaget Addo | Rod | http://meta-studies.net/pmwiki/uploads/AddoW150.jpg? |
1920 | Addo adder | Aktiebolaget Addo | Rod | http://meta-studies.net/pmwiki/uploads/AddoW150.jpg |
1922 | Conto Mod C Adding Machine | Carl Landolt | Rotating Knob | http://meta-studies.net/pmwiki/uploads/ContoW175.jpg |
1922 | Conto Mod C Adding Machine | Carl Landolt | Rotating Knob | http://meta-studies.net/pmwiki/uploads/ContoW175.jpg |
1920 | Addo adder | Aktiebolaget Addo | Rod | http://meta-studies.net/pmwiki/uploads/AddoW150.jpg |
1920 | Addo adder | Aktiebolaget Addo | Rod | http://meta-studies.net/pmwiki/uploads/AddoW150.jpg |
1920 | Addo adder | Aktiebolaget Addo | Rod | http://meta-studies.net/pmwiki/uploads/AddoW150.jpg? |
1920 | Addo adder | Aktiebolaget Addo | Rod | http://meta-studies.net/pmwiki/uploads/AddoW150.jpg |
1922 | Scribola 10 column printing adding machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg |
1922 | Scribola 10 column printing adding machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg |
1920 | Addo adder | Aktiebolaget Addo | Rod | http://meta-studies.net/pmwiki/uploads/AddoW150.png? |
1920 | Addo adder | Aktiebolaget Addo | Rod | http://meta-studies.net/pmwiki/uploads/AddoW150.jpg? |
1920 | Addo adder | Aktiebolaget Addo | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg? |
1920 | Addo adder | Aktiebolaget Addo | Rod | http://meta-studies.net/pmwiki/uploads/AddoW150.jpg? |
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.
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.
In short, the use of a calculating technology is not just intellectual. It is what Jean-François Gauvin152 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:
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 Gauvin153 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:
1920 | Addo adder | Aktiebolaget Addo | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg? |
1922 | Scribola 10 column printing adding machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/AddoW150.png |
1920 | Addo adder | Aktiebolaget Addo | Rod | http://meta-studies.net/pmwiki/uploads/AddoW150.png? |
1922 | Scribola 10 column printing adding machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg |
1920 | Addo adder | Aktiebolaget Addo | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg? |
1920 | Addo adder | Aktiebolaget Addo | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg? |
1920 | Addo adder | Aktiebolaget Addo | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg? |
1920 | Addo adder | Aktiebolaget Addo | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg? |
1920 | Addo adder | Aktiebolaget Addo | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg? |
1922 | Scribola 10 column printing adding machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg |
1920 | Addo adder | Aktiebolaget Addo | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg? |
1922 | Scribola 10 column printing adding machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/AddoW150.png |
http://meta-studies.net/pmwiki/uploads/Mercedes.png | http://meta-studies.net/pmwiki/uploads/MercedesDemoH200.jpg |
http://meta-studies.net/pmwiki/uploads/MercedesH200.jpg | http://meta-studies.net/pmwiki/uploads/MercedesDemoH200.jpg |
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. 154 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.
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.155 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.
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. 156 For more on the Curta see the marvellous collection of documents and simulations at The Curta Caclulator Page.157
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.158 For more on the Curta see the marvellous collection of documents and simulations at The Curta Caclulator Page.159
1910 | Adall Adding Machine | Dreyfus and Levy | Key input Concentric toothed disk and groove | http://meta-studies.net/pmwiki/uploads/AdallH125.jpg |
1910 | Adall Adding Machine | Dreyfus and Levy | Concentric toothed disk and groove | http://meta-studies.net/pmwiki/uploads/AdallH125.jpg |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
1910 | Adall Adding Machine | Dreyfus and Levy | Key input Concentric toothed disk and groove | http://meta-studies.net/pmwiki/uploads/AdallH125.jpg |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/LightningH125.jpg |
1968 | SEE Demonstration Adding Machine | Selective Educational Equipment Corporation | 4 Wheels | http://meta-studies.net/pmwiki/uploads/SEE-1H75.jpg |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
1910 | Adall Adding Machine | Dreyfus and Levy | Concentric toothed disk and groove | http://meta-studies.net/pmwiki/uploads/AdallH125.jpg |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/LightningH125.jpg |
1968 | SEE Demonstration Adding Machine | Selective Educational Equipment Corporation | 4 Wheels | http://meta-studies.net/pmwiki/uploads/SEE-1H75.jpg |
1937 | Add-O-Matic Adding Machine | Allied MFG. Co. | Chain | http://meta-studies.net/pmwiki/uploads/AddOMatic1_125.jpg |
1937 | Add-O-Matic Adding Machine | Allied MFG. Co. | Chain | http://meta-studies.net/pmwiki/uploads/AddOMatic1_125.jpg |
1922 | Scribola 10 column printing adding machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg |
1922 | Scribola 10 column printing adding machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg |
1890–1900 | A. M. Stevenson Adder | Joliet, Ill. | 2 Wheel | http://meta-studies.net/pmwiki/uploads/StevensonH75.jpg |
1890–1900 | A. M. Stevenson Adder | Joliet, Ill. | 2 Wheel | http://meta-studies.net/pmwiki/uploads/StevensonH75.jpg |
~1913 | Bunzel-Denton Arithmometer | Bunzel | Prototype Front Crank | http://meta-studies.net/pmwiki/uploads/BunzelH150.jpg |
~1913 | Bunzel-Denton Arithmometer | Bunzel | Prototype Front Crank | http://meta-studies.net/pmwiki/uploads/BunzelH150.jpg |
1945 | Facit Model S Calculator serial 210652 | Facit | Pinwheel | http://meta-studies.net/pmwiki/uploads/FacitH150.jpg |
~1951 | Original Ohdner Model 39 serial 39–288965 | Ohdner | Pinwheel | http://meta-studies.net/pmwiki/uploads/Ohdner1951H150.jpg |
1945 | Facit Model S Calculator serial 210652 | Facit | Pinwheel | http://meta-studies.net/pmwiki/uploads/FacitH150.jpg |
~1951 | Original Ohdner Model 39 serial 39–288965 | Ohdner | Pinwheel | http://meta-studies.net/pmwiki/uploads/Ohdner1951H150.jpg |
~1915 | Golden Gem Automatic Adding Machine | H. & H. Goldmann | Chain | http://meta-studies.net/pmwiki/uploads/GoldenGem100.jpg |
~1915 | Golden Gem Automatic Adding Machine | H. & H. Goldmann | Chain | http://meta-studies.net/pmwiki/uploads/GoldenGem100.jpg |
1922 | Scribola 10 column printing Adding Machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg |
1922 | Scribola 10 column printing adding machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator125.jpg |
~1915 | Golden Gem Automatic Adding Machine | H. & H. Goldmann | Chain | http://meta-studies.net/pmwiki/uploads/GoldenGem100.jpg |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator125.jpg |
~1915 | Golden Gem Automatic Adding Machine | H. & H. Goldmann | Chain | http://meta-studies.net/pmwiki/uploads/GoldenGem100.jpg |
1922 | Scribola 10 column printing Adding Machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg |
1937 | Add-O-Matic Adding Machine | Allied MFG. Co. | Chain | http://meta-studies.net/pmwiki/uploads/AddOMatic1_125.jpg |
1922 | Scribola 10 column printing Adding Machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg |
1937 | Add-O-Matic Adding Machine | Allied MFG. Co. | Chain | http://meta-studies.net/pmwiki/uploads/AddOMatic1_125.jpg |
1890–1900 | A. M. Stevenson Adder | Joliet, Ill. | 2 Wheel | http://meta-studies.net/pmwiki/uploads/StevensonH75.jpg |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
1910 | Adall Adding Machine | Dreyfus and Levy | Key input Concentric toothed disk and groove | http://meta-studies.net/pmwiki/uploads/AdallH125.jpg |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/LightningH125.jpg |
1968 | SEE Demonstration Adding Machine | Selective Educational Equipment Corporation | 4 Wheels | http://meta-studies.net/pmwiki/uploads/SEE-1H75.jpg |
1890–1900 | A. M. Stevenson Adder | Joliet, Ill. | 2 Wheel | http://meta-studies.net/pmwiki/uploads/StevensonH75.jpg |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
1910 | Adall Adding Machine | Dreyfus and Levy | Key input Concentric toothed disk and groove | http://meta-studies.net/pmwiki/uploads/AdallH125.jpg |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/LightningH125.jpg |
1968 | SEE Demonstration Adding Machine | Selective Educational Equipment Corporation | 4 Wheels | http://meta-studies.net/pmwiki/uploads/SEE-1H75.jpg |
1909 | TIM (Time is Money) Arithmometer | Ludwig Spitz & Co | Arithmometer | http://meta-studies.net/pmwiki/uploads/TIMH150.jpg |
1909 | TIM (Time is Money) Arithmometer | Ludwig Spitz & Co | Arithmometer | http://meta-studies.net/pmwiki/uploads/TIMH150.jpg |
A single pinwheel | Mechanism of the Walther pinwheel calculator (parts removed for demonstration) |
A single pinwheel | Mechanism of the Walther pinwheel calculator (parts removed for demonstration) |
1945 | Facit Model S Calculator serial 210652 | Facit | Pinwheel | http://meta-studies.net/pmwiki/uploads/FacitH150.jpg |
~1951 | Original Ohdner Model 39 serial 39–288965 | Ohdner | Pinwheel | http://meta-studies.net/pmwiki/uploads/Ohdner1951H150.jpg] |
~1957 | Walther WSR160 Pinwheel Calculator | Walther | Pinwheel | http://meta-studies.net/pmwiki/uploads/WaltherH150.jpg |
~1957 | Walther WSR160 Demonstration Pinwheel Calculator | Walther | Demonstration Pinwheel | http://meta-studies.net/pmwiki/uploads/WaltherDemoH150.jpg |
1945 | Facit Model S Calculator serial 210652 | Facit | Pinwheel | http://meta-studies.net/pmwiki/uploads/FacitH150.jpg |
~1951 | Original Ohdner Model 39 serial 39–288965 | Ohdner | Pinwheel | http://meta-studies.net/pmwiki/uploads/Ohdner1951H150.jpg] |
~1957 | Walther WSR160 Pinwheel Calculator | Walther | Pinwheel | http://meta-studies.net/pmwiki/uploads/WaltherH150.jpg |
~1957 | Walther WSR160 Demonstration Pinwheel Calculator | Walther | Demonstration Pinwheel | http://meta-studies.net/pmwiki/uploads/WaltherDemoH150.jpg |
1923: Mercedes-Euklid Model 29 calculator | 1923: Mercedes-Euklid Model 29 Demonstration calculator |
1923: Mercedes-Euklid Model 29 calculator | 1923: Mercedes-Euklid Model 29 Demonstration calculator |
http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491
http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491
~1955 | Bell Punch Sumlock | Bell Punch | Demonstration Comptometer | http://meta-studies.net/pmwiki/uploads/BellPunchDemoH250.jpg |
~1955 | Bell Punch Sumlock | Bell Punch | Demonstration Comptometer | http://meta-studies.net/pmwiki/uploads/BellPunchDemoH250.jpg |
~1955 | Bell Punch Sumlock | Bell Punch | Demonstration Comptometer | http://meta-studies.net/pmwiki/uploads/BellPunchDemoH250.jpg |
~1955 | Bell Punch Sumlock | Bell Punch | Demonstration Comptometer | http://meta-studies.net/pmwiki/uploads/BellPunchDemoH250.jpg |
~July 1948: CURTA Type 1 (pin sliders) earliest model calculator serial 5424 | 1967: CURTA Type I calculator serial 76436 & cardboard box | 1963: CURTA Type II calculator |
~July 1948: CURTA Type 1 (pin sliders) earliest model calculator serial 5424 | 1967: CURTA Type I calculator serial 76436 & cardboard box | 1963: CURTA Type II calculator |
1623: Recreation of | 1904–1905: Bamberger's Omega |
1623: Re-creation of | 1904–1905: Bamberger's Omega |
Other simple linear devices in this collection are shown in Simple Linear Calculators below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)
Other simple linear devices in this collection are shown (:if equal {Site.PrintBook$:PSW} "True":)in Simple Linear Calculators (:ifend:)below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator125.jpg |
~1915 | Golden Gem Automatic Adding Machine | H. & H. Goldmann | Chain | http://meta-studies.net/pmwiki/uploads/GoldenGem100.jpg |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator125.jpg |
~1915 | Golden Gem Automatic Adding Machine | H. & H. Goldmann | Chain | http://meta-studies.net/pmwiki/uploads/GoldenGem100.jpg |
1922 | Scribola 10 column printing Adding Machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg |
1937 | Add-O-Matic Adding Machine | Allied MFG. Co. | Chain | http://meta-studies.net/pmwiki/uploads/AddOMatic1_125.jpg |
1922 | Scribola 10 column printing Adding Machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg |
1937 | Add-O-Matic Adding Machine | Allied MFG. Co. | Chain | http://meta-studies.net/pmwiki/uploads/AddOMatic1_125.jpg |
Other simple rotational adding devices in this collection are shown in (:if equal {Site.PrintBook$:PSW} "True":)Simple Rotational Calculators(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)
Other simple rotational adding devices in this collection are shown (:if equal {Site.PrintBook$:PSW} "True":)in Simple Rotational Calculators(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)
Other simple rotational adding devices in this collection are shown in Simple Rotational Calculators below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)
Other simple rotational adding devices in this collection are shown in (:if equal {Site.PrintBook$:PSW} "True":)Simple Rotational Calculators(:ifend:) below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)
Ready reckoners were in widespread use by shopkeepers and many others from the C17 on. They presented tables of precalculated results of many kinds of multiplication. These included the much needed calculations of the price for multiples of an item for sale, or per unit of weight. They could also be used to look up the calculations needed for wages and interest.160 One such, from 1892 is “Ropp’s Commercial Calculator: a practical arithmetic for practical purposes, containing a complete system of useful, accurate, and convenient tables, together with simple, short, and practical methods for rapid calculation”, published in the US and used widely into the early C20. This one, shown below (:if equal {Site.PrintBook$:PSW} "True":)in Thomas Arithmometeras Ropp’s Calculator(:ifend:), is the 1892 World’s Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.
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.161 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$:PSW} "True":) in Ropp’s Calculator(:ifend:), is the 1892 World’s Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.
Ready reckoners were in widespread use by shopkeepers and many others from the C17 on. They presented tables of precalculated results of many kinds of multiplication. These included the much needed calculations of the price for multiples of an item for sale, or per unit of weight. They could also be used to look up the calculations needed for wages and interest.162 One such, from 1892 is “Ropp’s Commercial Calculator: a practical arithmetic for practical purposes, containing a complete system of useful, accurate, and convenient tables, together with simple, short, and practical methods for rapid calculation”, published in the US and used widely into the early C20. This one, shown below as Ropp’s Calculator, is the 1892 World’s Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.
Ready reckoners were in widespread use by shopkeepers and many others from the C17 on. They presented tables of precalculated results of many kinds of multiplication. These included the much needed calculations of the price for multiples of an item for sale, or per unit of weight. They could also be used to look up the calculations needed for wages and interest.163 One such, from 1892 is “Ropp’s Commercial Calculator: a practical arithmetic for practical purposes, containing a complete system of useful, accurate, and convenient tables, together with simple, short, and practical methods for rapid calculation”, published in the US and used widely into the early C20. This one, shown below (:if equal {Site.PrintBook$:PSW} "True":)in Thomas Arithmometeras Ropp’s Calculator(:ifend:), is the 1892 World’s Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.
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 Conversion device below.
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 Conversion device(:ifend:) below.
http://meta-studies.net/pmwiki/uploads/TIMDrumH200.jpg|Step drum (in a later ‘TIM’ arithmometer)
http://meta-studies.net/pmwiki/uploads/TIMDrumH200.jpg|Step drum (in a later ‘TIM’ arithmometer)
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.
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.
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.164 One such, from 1892, shown below in Ropp’s Calculator 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.
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.165 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 Ropp’s Calculator, is the 1892 World’s Fair Edition containing 128 pages of useful mathematical facts, formulas and tables.
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp’s Commercial Calculator
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp’s Commercial Calculator
http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg|~1790: Conversion device
http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg|~1790: Conversion device
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.
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 Thomas mechanism(:ifend:) below.
1862: Diagram of the Thomas de Colmar arithmometer mechanism.166
(:if equal {Site.PrintBook$:PSW} "False":)(Click on the image for an enlargement.)(:ifend:)
(Source: Museum of the History of Science, University of Oxford.)
1862: Diagram of the Thomas de Colmar arithmometer mechanism.167
(Click on the image for an enlargement.)
(Source: Museum of the History of Science, University of Oxford.)
http://meta-studies.net/pmwiki/uploads/Misc/ThomasMechRelH200.jpg|1862: Thomas de Colmar arithmometer mechanism
diagram.168 (:if equal {Site.PrintBook$:PSW} "False":)(Click on the image for an enlargement.)(:ifend:)
(Source: Museum of the History of Science, University of Oxford.)
http://meta-studies.net/pmwiki/uploads/Misc/ThomasMechRelH200.jpg|1862: Thomas de Colmar arithmometer mechanism
diagram.169
(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 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.
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$:PSW} "True":)in Step drum(:ifend:) is a picture of a step drum from a later arithmometer, but based on the Thomas mechanism, showing the slider, drum with its ‘counting gear’ positioned for the input of ‘5’. In this arithmometer the input number selected shows in the immediately adjacent window. Note the square section axle on which the counting gear moves.
http://meta-studies.net/pmwiki/uploads/TIMDrumH200.jpg|Step drum (in a later ‘TIM’ arithmometer)
http://meta-studies.net/pmwiki/uploads/TIMDrumH200.jpg|Step drum (in a later ‘TIM’ arithmometer)
By the time Thomas died, in May 1870, some 800 arithmometers had been made. His son, Thomas de Bojano then took over manufacturing. Thomas de Bojano died in 1881 and Thomas’s grandson, the Compte de Ronseray, continued manufacturing arithmometers under the management of Payen. By 1878 some 1500 Thomas arithmometers had been constructed. Some 180 Thomas arithmometers are known to have survived to the present, of which 110 are in public collections and 50 in private collections. Below is the Thomas Arithmometer in this collection, which is from 1884.
By the time Thomas died, in May 1870, some 800 arithmometers had been made. His son, Thomas de Bojano then took over manufacturing. Thomas de Bojano died in 1881 and Thomas’s grandson, the Compte de Ronseray, continued manufacturing arithmometers under the management of Payen. By 1878 some 1500 Thomas arithmometers had been constructed. Some 180 Thomas arithmometers are known to have survived to the present, of which 110 are in public collections and 50 in private collections. Below (:if equal {Site.PrintBook$:PSW} "True":)in Thomas Arithmometer(:ifend:) is the Thomas Arithmometer in this collection, which is from 1884.
http://meta-studies.net/pmwiki/uploads/ThomasDeColmarH300.jpg|1884: Thomas de Colmar Arithmometer
http://meta-studies.net/pmwiki/uploads/ThomasDeColmarH300.jpg|1884: Thomas de Colmar Arithmometer
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.170 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.
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.171 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$:PSW} "True":)in Arithmometers(:ifend:), are products of this now enlarging set of competing manufacturers and designers.
The pinwheel calculator was developed as an improvement on the arithmometer more or less simultaneously in Russia in 1878 by Swedish engineer Willgodt Theophil Odhner (1845–1905) and in the US in 1874, by Frank Stephen Baldwin (1838–1925). Although they worked independently of each there machines were so similar that the ‘Ohdner’ or ‘Baldwin’ machine became more or less interchangeable terms.172. The designs utilised a clever 'counting gear' in which the number of teeth protruding could be adjusted by sliders (and later a push-down keyboard). A pinwheel and the internal mechanism (with some pinwheels removed) from a Walther pinwheel calculator in this collection is shown below.
The pinwheel calculator was developed as an improvement on the arithmometer more or less simultaneously in Russia in 1878 by Swedish engineer Willgodt Theophil Odhner (1845–1905) and in the US in 1874, by Frank Stephen Baldwin (1838–1925). Although they worked independently of each there machines were so similar that the ‘Ohdner’ or ‘Baldwin’ machine became more or less interchangeable terms.173. The designs utilised a clever 'counting gear' in which the number of teeth protruding could be adjusted by sliders (and later a push-down keyboard). A pinwheel and the internal mechanism (with some pinwheels removed) from a Walther pinwheel calculator in this collection is shown (:if equal {Site.PrintBook$:PSW} "True":)in Demonstration Pinwheel Calculator(:ifend:) below.
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$:PSW} "False":)(Click on the image to enlarge.)(:ifend:)
As can be seen above, the pinwheel (left, above) is a thin disk with the slider shown protruding in the top right corner. It is in the ‘3’ position, with the cam slot rotated pushing 3 teeth out (seen between and behind the fixed teeth at the bottom). These then are the teeth that are added by the counting wheel. (:if equal {Site.PrintBook$:PSW} "False":)(Click on the image to enlarge.)(:ifend:)
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.174 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.[175 Below is the very early Brunsviga-Schuster pinwheel calculator from 1896 in this collection.
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.176 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.[177 Below (:if equal {Site.PrintBook$:PSW} "True":)in Brunsviga Calculator(:ifend:) is the very early Brunsviga-Schuster pinwheel calculator from 1896, followed (:if equal {Site.PrintBook$:PSW} "True":)in Pinwheel Calculators(:ifend:) by the other pinwheel calculators in this collection.
http://meta-studies.net/pmwiki/uploads/Brunsviga1896H250.jpg|
http://meta-studies.net/pmwiki/uploads/Brunsviga1896H250.jpg|
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.
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$:PSW} "True":)in Rack mechanism(:ifend:) is the rack mechanism of such a calculator. Note how successive racks have moved increasing distances as the crank handle is turned (creating the diagonal pattern). The loose cogs seen on the square section axle are an example of the nine such cogs under each column of keys. Normally lying between the racks when a key is depressed it moves the corresponding cog sideways on the axle to engage with the appropriate rack for the number of the key depressed.
http://meta-studies.net/pmwiki/uploads/Misc/RackMechH200.jpg|Rack mechanism
http://meta-studies.net/pmwiki/uploads/Misc/RackMechH200.jpg|Rack mechanism
In 1906 Christel Haman founded the Mercedes-Euklid company who adopted the rack mechanism. In 1910 he incorporated the mechanism patented by Alexander Rechnitzer, referred to earlier, which enabled his machine to automatically perform the process of division, thus becoming the first mass produced machine with this capacity. The fully working Mercedes-Euklid 29 can be seen below (left) and a demonstration Mercedes-Euklid (model 29 from 1934) can be seen below (right).
In 1906 Christel Haman founded the Mercedes-Euklid company who adopted the rack mechanism. In 1910 he incorporated the mechanism patented by Alexander Rechnitzer, referred to earlier, which enabled his machine to automatically perform the process of division, thus becoming the first mass produced machine with this capacity. The fully working Mercedes-Euklid 29 can be seen below (left) and a demonstration Mercedes-Euklid (model 29 from 1934) can be seen below (right)(:if equal {Site.PrintBook$:PSW} "True":) in Proportional Rack Calculators(:ifend:).
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.178 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.
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.179 Below (:if equal {Site.PrintBook$:PSW} "True":)in this figure(:ifend:) is the Comptometer in this collection - an example from 1896 of the first model, cased in wood, and one of the 40 oldest known to still be in existence. Remarkably with a drop of oil on the springs it still works perfectly.
http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491
http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491
The comptometer was a highly successful innovation and was sufficiently cheap and useful to reach a broad market. Characterised by extremely effective marketing and capable of being mass produced the device continued to be marketed for some 80 years unusually for such innovations leaving its inventor extremely wealthy. By then its essential mechanism was being utilised by more than one company. Shown below is the remaining comptometer in this collection, this time made of plastic in the 1950s by the British Bell Punch company. Also shown is a demonstration model showing the keys and lever system used in the Bell Punch machine.
The comptometer was a highly successful innovation and was sufficiently cheap and useful to reach a broad market. Characterised by extremely effective marketing and capable of being mass produced the device continued to be marketed for some 80 years unusually for such innovations leaving its inventor extremely wealthy. By then its essential mechanism was being utilised by more than one company. Shown below (:if equal {Site.PrintBook$:PSW} "True":)in 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.
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).
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).
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).
The first model (the Model 1) began production in 1947. Below left (:if equal {Site.PrintBook$:PSW} "True":)in Curta Calculators(: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).
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.
http://meta-studies.net/pmwiki/uploads/Schickard1H250.jpg|1623: Recreation of Wilhelm Schickard’s calculating machine
The earliest of these machines had been that of Schickard (immediately below in Schickard’s Calculator). 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.
http://meta-studies.net/pmwiki/uploads/Schickard1H250.jpg|1623: Recreation of Wilhelm Schickard’s calculating machine
http://meta-studies.net/pmwiki/uploads/BambergerOmegaH250.jpg|1904–1905: Bamberger's Omega calculating machine
A late and unique expression of the same principle in this collection is Justin Bamberger's Omega Calculating Machine (1903–6), shown in Bamberger Omega 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.
http://meta-studies.net/pmwiki/uploads/BambergerOmegaH250.jpg|1904–1905: Bamberger's Omega calculating machine
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.
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":) Bollée calculator(:ifend:) below.
http://meta-studies.net/pmwiki/uploads/BolleeMAB1890H250.jpg|Leon Bollée Calculating Machine
http://meta-studies.net/pmwiki/uploads/BolleeMAB1890H250.jpg|Leon Bollée Calculating Machine
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.
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$:PSW} "True":) Millionaire calculator(:ifend:)below).
http://meta-studies.net/pmwiki/uploads/MillionairH300.jpg|1912: Millionaire Calculating Machine, serial 2015 (10×10×20)
http://meta-studies.net/pmwiki/uploads/MillionairH300.jpg|1912: Millionaire Calculating Machine, serial 2015 (10×10×20)
The deck of the Millionaire in this collection is shown below with the selector on the left which picks the multiplying factor, and the selector on the right which sets it for addition, subtraction, multiplication and division (AMDS). The ten sliders for setting the number to be operated on are obvious, as are the result windows, and on the far right, the crank handle.
The deck of the Millionaire in this collection is shown below (:if equal {Site.PrintBook$:PSW} "True":)in this figure(: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.
http://meta-studies.net/pmwiki/uploads/MillionaireDeckH230.jpg|Deck of the Millionaire Calculating Machine
http://meta-studies.net/pmwiki/uploads/MillionaireDeckH230.jpg|Deck of the Millionaire Calculating Machine
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.180 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.
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.181 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$:PSW} "True":)in Herzstark arithmometer(:ifend:) is an arithmometer in this collection branded by Samuel Herzstark from 1929. It is actually a Badenia (manufactured by the German Company Math. Bauerle in the Black Forest) which Herzstark was at that time re-badging and selling.
http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometerH250.jpg|~1929: "Herzstark" electric Calculating Machine serial 6549
http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometerH250.jpg|~1929: "Herzstark" electric Calculating Machine serial 6549
This calculator features its original electric motor, still in good working order, and with a keyboard instead of sliders for input. The features of it were not only that it had a keyboard for input, but also a control mechanism consisting of a column of keys which enabled a number to be entered and then added through 0 to 8 repeats representing multiplication by one to nine. A view of the mechanism of this machine is shown below.
This calculator features its original electric motor, still in good working order, and with a keyboard instead of sliders for input. The features of it were not only that it had a keyboard for input, but also a control mechanism consisting of a column of keys which enabled a number to be entered and then added through 0 to 8 repeats representing multiplication by one to nine. A view of the mechanism of this machine is shown below (:if equal {Site.PrintBook$:PSW} "True":)in Herzstark mechanism(:ifend:).
http://meta-studies.net/pmwiki/uploads/HerzstarkMechH250.jpg|1950s-1960s: Underneath view of the Herzstark mechanism (note the stepped drums)
http://meta-studies.net/pmwiki/uploads/HerzstarkMechH250.jpg|1950s-1960s: Underneath view of the Herzstark mechanism (note the stepped drums)
http://meta-studies.net/pmwiki/uploads/MADAS_SmallerH250.jpg|1950s-1960s: MADAS
http://meta-studies.net/pmwiki/uploads/MADAS_SmallerH250.jpg|1950s-1960s: MADAS
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.
The late MADAS 20BTG calculator, seen above (:if equal {Site.PrintBook$:PSW} "True":)in MADAS 20BTG(: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.
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).
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 Hewlett Packard Pocket Scientific Calculators(: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).
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.182 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.
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp’s Commercial Calculator
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.183 One such, from 1892, shown below in 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.
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp’s Commercial Calculator
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.
http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg|~1790: Conversion device
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 Convertiseur below.
http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg|~1790: Conversion device
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.
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$:PSW} "True":)in The Locke Adder(:ifend:) below.
http://meta-studies.net/pmwiki/uploads/Locke170.jpg|The Locke Adder
(collection Calculant)
http://meta-studies.net/pmwiki/uploads/Locke170.jpg|The Locke Adder
(collection Calculant)
Other simple linear devices in this collection are shown below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)
Other simple linear devices in this collection are shown in Simple Linear Calculators below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)
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.
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.
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.
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 Webb Adder(: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.
Web Patent Adder and Talley Board 1869
Webb Patent Adder and Talley Board 1869
http://meta-studies.net/pmwiki/uploads/WebbH200.jpg|1869:Web Patent Adder and Talley Board
http://meta-studies.net/pmwiki/uploads/WebbH200.jpg|1869:Webb Patent Adder and Talley Board
Other simple rotational adding devices in this collection are shown below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)
Other simple rotational adding devices in this collection are shown in Simple Rotational Calculators below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)
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 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.
~1951 | Original Ohdner Model 39 serial 39–288965 | Ohdner | Pinwheel | Add Picture |
~1951 | Original Ohdner Model 39 serial 39–288965 | Ohdner | Pinwheel | http://meta-studies.net/pmwiki/uploads/Ohdner1951H150.jpg |
~1951 | Original Ohdner Model 39 serial 39–288965 | Ohdner | Pinwheel | Add Picture |
~1951 | Original Ohdner Model 39 serial 39–288965 | Ohdner | Pinwheel | http://meta-studies.net/pmwiki/uploads/Ohdner1951H150.jpg] |
(:ifend:)
(:ifend:)
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917H125.jpg |
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917W250.jpg |
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917H125.jpg |
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917W250.jpg |
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917H125.jpg |
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917H125.jpg |
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917H125.jpg |
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917H125.jpg |
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.
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.
- something else that can be moved (for example, although it was barely used,186 the height of columns of water).
- something else that can be moved (for example, although it was barely used,187 the height of columns of water).
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.
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.
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,188 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.
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,189 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.
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 1820.190. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.191 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 invention192).
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 1820.193. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.194 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 invention195).
1862: Diagram of the Thomas de Colmar arithmometer mechanism.196
(:if equal {Site.PrintBook$:PSW} "False":)(Click on the image for an enlargement.)(:ifend:)
(Source: Museum of the History of Science, University of Oxford.)
1862: Diagram of the Thomas de Colmar arithmometer mechanism.197
(:if equal {Site.PrintBook$:PSW} "False":)(Click on the image for an enlargement.)(:ifend:)
(Source: Museum of the History of Science, University of Oxford.)
diagram.198 (:if equal {Site.PrintBook$:PSW} "False":)(Click on the image for an enlargement.)(:ifend:)
(Source: Museum of the History of Science, University of Oxford.)
diagram.199 (:if equal {Site.PrintBook$:PSW} "False":)(Click on the image for an enlargement.)(:ifend:)
(Source: Museum of the History of Science, University of Oxford.)
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.200 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’.201 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.202 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.”203 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.”204 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).205
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.206 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'.207 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.208 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.”209 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.”210 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).211
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.212 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.)
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.213 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.)
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.214
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.215
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.216. 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.
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.217. 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.
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.
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.
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.
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.
1623: Recreation of | 1904–1905: Bamberger’s Omega |
1623: Recreation of | 1904–1905: Bamberger's Omega |
http://meta-studies.net/pmwiki/uploads/BambergerOmegaH250.jpg|1904–1905: Bamberger’s Omega calculating machine
http://meta-studies.net/pmwiki/uploads/BambergerOmegaH250.jpg|1904–1905: Bamberger's Omega calculating machine
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.
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.
Leon Bollée Calculating Machine “A New Calculating Machine of very General Applicability”
The Manufacturer and Builder 1890218
Leon Bollée Calculating Machine “A New Calculating Machine of very General Applicability"
The Manufacturer and Builder 1890219
http://meta-studies.net/pmwiki/uploads/BolleeMAB1890H250.jpg|Leon Bollée Calculating Machine
”A New Calculating Machine of very General Applicability”
The Manufacturer and Builder 1890220
http://meta-studies.net/pmwiki/uploads/BolleeMAB1890H250.jpg|Leon Bollée Calculating Machine
”A New Calculating Machine of very General Applicability"
The Manufacturer and Builder 1890221
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.
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.
Manufactured by H.W. Egli, some 4,655 Millionaires were sold between 1895 and 1935222 at a 1912 price of about US$480223 (about $11,700 in 2013 US dollars224). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,225 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.
Manufactured by H.W. Egli, some 4,655 Millionaires were sold between 1895 and 1935226 at a 1912 price of about US$480227 (about $11,700 in 2013 US dollars228). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,229 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.
~1929: “Herzstark” electric Calculating Machine serial 6549
badged by Herzstark, Vienna
(essentially a Badenia Model TE 13 Duplex)
~1929: "Herzstark" electric Calculating Machine serial 6549
badged by Herzstark, Vienna
(essentially a Badenia Model TE 13 Duplex)
http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometerH250.jpg|~1929: “Herzstark” electric Calculating Machine serial 6549
http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometerH250.jpg|~1929: "Herzstark" electric Calculating Machine serial 6549
In short, the use of a calculating technology is not just intellectual. It is what Jean-François Gauvin230 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:
In short, the use of a calculating technology is not just intellectual. It is what Jean-François Gauvin231 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:
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 operation232) and Moreland (allowing addition and subtraction “without charging the memory or disturbing the mind233). 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.
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 operation234) and Moreland (allowing addition and subtraction “without charging the memory or disturbing the mind235). 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.
(:ifend:)
(:ifend:)
http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer
earliest wood-cased model, serial 2491
http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer: earliest wood-cased model, serial 2491
http://meta-studies.net/pmwiki/uploads/Schickard1H250.jpg|1623: Recreation of Wilhelm Schickard’s
calculating machine
http://meta-studies.net/pmwiki/uploads/Schickard1H250.jpg|1623: Recreation of Wilhelm Schickard’s calculating machine
http://meta-studies.net/pmwiki/uploads/BambergerOmegaH250.jpg|1904–1905: Bamberger’s Omega
calculating machine
http://meta-studies.net/pmwiki/uploads/BambergerOmegaH250.jpg|1904–1905: Bamberger’s Omega calculating machine
Leon Bollée Calculating Machine
”A New Calculating Machine of very General Applicability”
The Manufacturer and Builder 1890236
Leon Bollée Calculating Machine “A New Calculating Machine of very General Applicability”
The Manufacturer and Builder 1890237
http://meta-studies.net/pmwiki/uploads/MillionairH300.jpg|1912: Millionaire Calculating Machine
serial 2015 (10×10×20)
http://meta-studies.net/pmwiki/uploads/MillionairH300.jpg|1912: Millionaire Calculating Machine, serial 2015 (10×10×20)
http://meta-studies.net/pmwiki/uploads/HerzstarkMechH250.jpg|1950s-1960s: Underneath view
the Herzstark mechanism - note the stepped drums
http://meta-studies.net/pmwiki/uploads/HerzstarkMechH250.jpg|1950s-1960s: Underneath view of the Herzstark mechanism (note the stepped drums)
Model 20BTG serial 94046
electric calculator with true automatic division
Model 20BTG serial 94046 electric calculator with true automatic division
http://meta-studies.net/pmwiki/uploads/Misc/ThomasMechRelH200.jpg|1862: Diagram of the Thomas de Colmar arithmometer mechanism.238 (:if equal {Site.PrintBook$:PSW} "False":)(Click on the image for an enlargement.)(:ifend:)
(Source: Museum of the History of Science, University of Oxford.)
http://meta-studies.net/pmwiki/uploads/Misc/ThomasMechRelH200.jpg|1862: Thomas de Colmar arithmometer mechanism
diagram.239 (:if equal {Site.PrintBook$:PSW} "False":)(Click on the image for an enlargement.)(:ifend:)
(Source: Museum of the History of Science, University of Oxford.)
Earliest - wood-cased model, serial 2491
earliest wood-cased model, serial 2491
http://meta-studies.net/pmwiki/uploads/Schickard1H250.jpg||1623: Recreation of Wilhelm Schickard’s
http://meta-studies.net/pmwiki/uploads/Schickard1H250.jpg|1623: Recreation of Wilhelm Schickard’s
calculating machine|
calculating machine
- if equal False “True”
- )
(:if equal {Site.PrintBook$:PSW} "True":)
http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometer250.jpg|~1929: “Herzstark” electric Calculating Machine serial 6549
http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometerH250.jpg|~1929: “Herzstark” electric Calculating Machine serial 6549
http://meta-studies.net/pmwiki/uploads/Curta1-1948H200.jpg | http://meta-studies.net/pmwiki/uploads/Curta1-1967H200.jpg]] | http://meta-studies.net/pmwiki/uploads/Curta2H200.jpg |
http://meta-studies.net/pmwiki/uploads/Curta1-1948H200.jpg | http://meta-studies.net/pmwiki/uploads/Curta1-1967H200.jpg | http://meta-studies.net/pmwiki/uploads/Curta2H200.jpg |
http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometer250.jpg|~1929: “Herzstark” electric Calculating Machine serial 6549
badged by Herzstark, Vienna
http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometer250.jpg|~1929: “Herzstark” electric Calculating Machine serial 6549
badged by Herzstark, Vienna
(:if equal {Site.PrintBook$:PSW} "False":)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
http://meta-studies.net/pmwiki/uploads/PinWheelSingleH200.jpg | http://meta-studies.net/pmwiki/uploads/PinwheelDemoH200.jpg |
A single pinwheel | Mechanism of the Walther pinwheel calculator (parts removed for demonstration) |
(collection Calculant) | (collection Calculant) |
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "False":)
Brunsviga Schuster Pinwheel Calculator ~1896
~1896: Brunsviga Schuster Pinwheel Calculator
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
http://meta-studies.net/pmwiki/uploads/Brunsviga1896H250.jpg|
~1896: Brunsviga Schuster Pinwheel Calculator
Serial 3406
(collection Calculant)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "False":)
(collection Calculant - all above) |
(collection Calculant | - all above) |
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
Date | Description | Maker | Type | Device (click for greater detail) |
1945 | Facit Model S Calculator serial 210652 | Facit | Pinwheel | http://meta-studies.net/pmwiki/uploads/FacitH150.jpg |
~1951 | Original Ohdner Model 39 serial 39–288965 | Ohdner | Pinwheel | Add Picture |
~1957 | Walther WSR160 Pinwheel Calculator | Walther | Pinwheel | http://meta-studies.net/pmwiki/uploads/WaltherH150.jpg |
~1957 | Walther WSR160 Demonstration Pinwheel Calculator | Walther | Demonstration Pinwheel | http://meta-studies.net/pmwiki/uploads/WaltherDemoH150.jpg |
(collection Calculant | - all above) |
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "False":)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
http://meta-studies.net/pmwiki/uploads/Misc/RackMechH200.jpg|Rack mechanism
of a Mercedes-Euklid 29 calculator.
(collection Calculant)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "False":)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
http://meta-studies.net/pmwiki/uploads/Mercedes.png | http://meta-studies.net/pmwiki/uploads/MercedesDemoH200.jpg |
1923: Mercedes-Euklid Model 29 calculator | 1923: Mercedes-Euklid Model 29 Demonstration calculator |
(collection Calculant) | (collection Calculant) |
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "False":)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
(:table align=center :)
http://meta-studies.net/pmwiki/uploads/ComptometerWoodieH250.jpg|1896: Felt and Tarrant Comptometer
Earliest - wood-cased model, serial 2491
(collection Calculant)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "False":)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
Date | Description | Maker | Type | Device |
1950s | Bell Sumlock Comptometer | Bell Sumlock | Model 909/S/117.878 | http://meta-studies.net/pmwiki/uploads/SumlockH250.jpg |
~1955 | Bell Punch Sumlock | Bell Punch | Demonstration Comptometer | http://meta-studies.net/pmwiki/uploads/BellPunchDemoH250.jpg |
(collection Calculant | - all above) |
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "False":)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
http://meta-studies.net/pmwiki/uploads/Curta1-1948H200.jpg | http://meta-studies.net/pmwiki/uploads/Curta1-1967H200.jpg]] | http://meta-studies.net/pmwiki/uploads/Curta2H200.jpg |
~July 1948: CURTA Type 1 (pin sliders) earliest model calculator serial 5424 | 1967: CURTA Type I calculator serial 76436 & cardboard box | 1963: CURTA Type II calculator |
(collection Calculant) | (collection Calculant) | (collection Calculant) |
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "False":)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
http://meta-studies.net/pmwiki/uploads/Schickard1H250.jpg||1623: Recreation of Wilhelm Schickard’s
calculating machine
(collection Calculant)
http://meta-studies.net/pmwiki/uploads/BambergerOmegaH250.jpg|1904–1905: Bamberger’s Omega
calculating machine|
(collection Calculant)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "False":)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
http://meta-studies.net/pmwiki/uploads/BolleeMAB1890H250.jpg|Leon Bollée Calculating Machine
”A New Calculating Machine of very General Applicability”
The Manufacturer and Builder 1890240
(collection Calculant)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "False":)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
http://meta-studies.net/pmwiki/uploads/MillionairH300.jpg|1912: Millionaire Calculating Machine
serial 2015 (10×10×20)
(collection Calculant)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "False":)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
http://meta-studies.net/pmwiki/uploads/MillionaireDeckH230.jpg|Deck of the Millionaire Calculating Machine
(collection Calculant)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "False":)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
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:)
(:if equal {Site.PrintBook$:PSW} "False":)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
http://meta-studies.net/pmwiki/uploads/HerzstarkMechH250.jpg|1950s-1960s: Underneath view
the Herzstark mechanism - note the stepped drums
(collection Calculant)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "False":)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
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:)
(:if equal {Site.PrintBook$:PSW} "False":)
(:ifend:)
- if equal False “True”
- )
http://meta-studies.net/pmwiki/uploads/HP35H250.jpg | http://meta-studies.net/pmwiki/uploads/HP-45H250.jpg |
July1972 Hewlett Packard HP 35 Calculator serial 1230A 79429, 1972 | December 1973 Hewlett Packard HP 45 Calculator serial 1350A 36719, 1973 |
(collection Calculant) |
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "False":)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
http://meta-studies.net/pmwiki/uploads/TIMDrumH200.jpg|Step drum (in a later ‘TIM’ arithmometer)
(collection Calculant)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "False":)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
http://meta-studies.net/pmwiki/uploads/ThomasDeColmarH300.jpg|1884: Thomas de Colmar Arithmometer
Serial 2083 Model T1878 B
(collection Calculant)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "False":)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
Date | Description | Maker | Type | Device |
1909 | TIM (Time is Money) Arithmometer | Ludwig Spitz & Co | Arithmometer | http://meta-studies.net/pmwiki/uploads/TIMH150.jpg |
~1913 | Bunzel-Denton Arithmometer | Bunzel | Prototype Front Crank | http://meta-studies.net/pmwiki/uploads/BunzelH150.jpg |
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917H125.jpg |
(collection Calculant - all above) |
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "False":)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
http://meta-studies.net/pmwiki/uploads/Misc/ThomasMechRelH200.jpg|1862: Diagram of the Thomas de Colmar arithmometer mechanism.241 (:if equal {Site.PrintBook$:PSW} "False":)(Click on the image for an enlargement.)(:ifend:)
(Source: Museum of the History of Science, University of Oxford.)
(:ifend:)
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.)
Other simple linear devices in this collection are shown below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)
Date | Description | Maker | Type | Device (click for greater detail) |
Date | Description | Maker | Type | Device (click for greater detail) |
Date | Description | Maker | Type | Device (click for greater detail) |
Date | Description | Maker | Type | Device |
(:if equal {Site.PrintBook$:PSW} "False":)
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.)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
http://meta-studies.net/pmwiki/uploads/WebbH200.jpg|1869:Web Patent Adder and Talley Board
(collection Calculant)
(:ifend:)
Other simple rotational adding devices in this collection are shown below. (:if equal {Site.PrintBook$:PSW} "False":)(Clicking on the image will take you to a larger image on the description page.)(:ifend:)
(:if equal {Site.PrintBook$:PSW} "False":)
Date | Description | Maker | Type | Device (click for greater detail) |
Date | Description | Maker | Type | Device (click for greater detail) |
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
Date | Description | Maker | Type | Device |
1890–1900 | A. M. Stevenson Adder | Joliet, Ill. | 2 Wheel | http://meta-studies.net/pmwiki/uploads/StevensonH75.jpg |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
1910 | Adall Adding Machine | Dreyfus and Levy | Key input Concentric toothed disk and groove | http://meta-studies.net/pmwiki/uploads/AdallH125.jpg |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/LightningH125.jpg |
1968 | SEE Demonstration Adding Machine | Selective Educational Equipment Corporation | 4 Wheels | http://meta-studies.net/pmwiki/uploads/SEE-1H75.jpg |
(collection Calculant - all above) |
(:ifend:)
1862: Diagram of the Thomas de Colmar arithmometer mechanism.242
(click on the image for an enlargement)
(Source: Museum of the History of Science, University of Oxford.)
1862: Diagram of the Thomas de Colmar arithmometer mechanism.243
(:if equal {Site.PrintBook$:PSW} "False":)(Click on the image for an enlargement.)(:ifend:)
(Source: Museum of the History of Science, University of Oxford.)
As can be seen above, the pinwheel (left, above) is a thin disk with the slider shown protruding in the top right corner. It is in the ‘3’ position, with the cam slot rotated pushing 3 teeth out (seen between and behind the fixed teeth at the bottom). These then are the teeth that are added by the counting wheel. (Click on the image to enlarge.)
As can be seen above, the pinwheel (left, above) is a thin disk with the slider shown protruding in the top right corner. It is in the ‘3’ position, with the cam slot rotated pushing 3 teeth out (seen between and behind the fixed teeth at the bottom). These then are the teeth that are added by the counting wheel. (:if equal {Site.PrintBook$:PSW} "False":)(Click on the image to enlarge.)(:ifend:)
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|~1790: Conversion device
http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg|~1790: Conversion device
(:if equal {Site.PrintBook$:PSW} "False":)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
Date | Description | Maker | Type | Device (click for greater detail) |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator125.jpg |
~1915 | Golden Gem Automatic Adding Machine | H. & H. Goldmann | Chain | http://meta-studies.net/pmwiki/uploads/GoldenGem100.jpg |
1920 | Addiator Troncet adder | Ruthard & Co | Chain | http://meta-studies.net/pmwiki/uploads/Addiator125.jpg |
1922 | Scribola 10 column printing Adding Machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg |
1937 | Add-O-Matic Adding Machine | Allied MFG. Co. | Chain | http://meta-studies.net/pmwiki/uploads/AddOMatic1_125.jpg |
(collection Calculant - all above) |
(:ifend:)
http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg |
~1790: Conversion device |
(from Aunes to Metres) |
(collection Calculant) |
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|~1790: Conversion device
(collection Calculant)
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp’s Commercial Calculator
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp’s Commercial Calculator
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp’s Commercial Calculator//
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp’s Commercial Calculator
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg |
1892: Ropp’s Commercial Calculator |
(collection Calculant) |
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp’s Commercial Calculator// (collection Calculant)
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp’s Commercial Calculator)
(collect. Calculant)
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg |
(collection Calculant) |
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp’s Commercial Calc.//(collection Calculant)
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp’s Commercial Calculator)
(collect. Calculant)
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp’s Commercial Calc. (collection Calculant)
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp’s Commercial Calc.//(collection Calculant)
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|Ropp’s Commercial Calculator, 1892
(collection Calculant)
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|1892: Ropp’s Commercial Calc. (collection Calculant)
(:if equal {Site.PrintBook$:PSW} "False":)
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg
Ropp’s Commercial Calculator, 1892
(collection Calculant)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "False":)
(:ifend:)
(:if equal {Site.PrintBook$:PSW} "True":)
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg|Ropp’s Commercial Calculator, 1892
(collection Calculant)
(:ifend:)
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.
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.
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 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 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 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 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.
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.
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.244 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.)
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.245 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.)
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.)
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.)
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.
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.
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.
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.
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.
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.
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).
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).
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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http://meta-studies.net/pmwiki/uploads/Locke170.jpg|The Locke Adder
(collection Calculant)
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(:table align=center id=Convertiseur"Convertiseur:) (:cellnr:) http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg%% (:cellnr:) ~1790: Conversion device (:cellnr:) (from Aunes to Metres) (:cellnr:) (collection Calculant) (:tableend:)
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~1790: Conversion device |
(from Aunes to Metres) |
(collection Calculant) |
http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg |
~1790: Conversion device |
(from Aunes to Metres) |
(collection Calculant) |
http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg |
~1790: Conversion device |
(from Aunes to Metres) |
(collection Calculant) |
~1790: Conversion device |
(from Aunes to Metres) |
(collection Calculant) |
http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg |
~1790: Conversion device |
(from Aunes to Metres) |
(collection Calculant) |
tableend |
(:table align=center :) (:cellnr:) http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg%% (:cellnr:) ~1790: Conversion device (:cellnr:) (from Aunes to Metres) (:cellnr:) (collection Calculant)
(:table align=center id=Convertiseur"Convertiseur:) (:cellnr:) http://meta-studies.net/pmwiki/uploads/Convertiseur200.jpg%% (:cellnr:) ~1790: Conversion device (:cellnr:) (from Aunes to Metres) (:cellnr:) (collection Calculant)
(:cell:) ~1790: Conversion device (:cell:) (from Aunes to Metres) (:cell:) (collection Calculant)
(:cellnr:) ~1790: Conversion device (:cellnr:) (from Aunes to Metres) (:cellnr:) (collection Calculant)
~1790: Conversion device (from Aunes to Metres) (collection Calculant)
(:cell:) ~1790: Conversion device (:cell:) (from Aunes to Metres) (:cell:) (collection Calculant)
~1790: Conversion device
(from Aunes to Metres)
(collection Calculant)
~1790: Conversion device (from Aunes to Metres) (collection Calculant)
Brunsviga Schuster Pinwheel Calculator ~1896
Serial 3406
Brunsviga Schuster Pinwheel Calculator ~1896 Serial 3406
1909 | TIM (Time is Money) Arithmometer | Ludwig Spitz & Co | Arithmometer | http://meta-studies.net/pmwiki/uploads/TIMH150.JPG |
1909 | TIM (Time is Money) Arithmometer | Ludwig Spitz & Co | Arithmometer | http://meta-studies.net/pmwiki/uploads/TIMH150.jpg |
1890–1900 | A. M. Stevenson Adder | Joliet, Ill. | 2 Wheel | http://meta-studies.net/pmwiki/uploads/Stevenson.png |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/Adix.png |
1910 | Adall Adding Machine | Dreyfus and Levy | Key input Concentric toothed disk and groove | http://meta-studies.net/pmwiki/uploads/Adall.jpg |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Lightning.png |
1968 | SEE Demonstration Adding Machine | Selective Educational Equipment Corporation | 4 Wheels | http://meta-studies.net/pmwiki/uploads/SEE-1.jpg |
1890–1900 | A. M. Stevenson Adder | Joliet, Ill. | 2 Wheel | http://meta-studies.net/pmwiki/uploads/StevensonH75.jpg |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/AdixH175.jpg |
1910 | Adall Adding Machine | Dreyfus and Levy | Key input Concentric toothed disk and groove | http://meta-studies.net/pmwiki/uploads/AdallH125.jpg |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/LightningH125.jpg |
1968 | SEE Demonstration Adding Machine | Selective Educational Equipment Corporation | 4 Wheels | http://meta-studies.net/pmwiki/uploads/SEE-1H75.jpg |
1909 | TIM (Time is Money) Arithmometer | Ludwig Spitz & Co | Arithmometer | http://meta-studies.net/pmwiki/uploads/TIM.JPG |
~1913 | Bunzel-Denton Arithmometer | Bunzel | Prototype Front Crank | http://meta-studies.net/pmwiki/uploads/Bunzel.JPG |
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917.jpg |
1909 | TIM (Time is Money) Arithmometer | Ludwig Spitz & Co | Arithmometer | http://meta-studies.net/pmwiki/uploads/TIMH150.JPG |
~1913 | Bunzel-Denton Arithmometer | Bunzel | Prototype Front Crank | http://meta-studies.net/pmwiki/uploads/BunzelH150.jpg |
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917H125.jpg |
http://meta-studies.net/pmwiki/uploads/PinWheelSingle.jpg | http://meta-studies.net/pmwiki/uploads/PinwheelDemo.jpg |
http://meta-studies.net/pmwiki/uploads/PinWheelSingleH200.jpg | http://meta-studies.net/pmwiki/uploads/PinwheelDemoH200.jpg |
1945 | Facit Model S Calculator serial 210652 | Facit | Pinwheel | http://meta-studies.net/pmwiki/uploads/Facit.png |
1945 | Facit Model S Calculator serial 210652 | Facit | Pinwheel | http://meta-studies.net/pmwiki/uploads/FacitH150.jpg |
~1957 | Walther WSR160 Pinwheel Calculator | Walther | Pinwheel | http://meta-studies.net/pmwiki/uploads/Walther.png |
~1957 | Walther WSR160 Demonstration Pinwheel Calculator | Walther | Demonstration Pinwheel | http://meta-studies.net/pmwiki/uploads/WaltherDemo.png |
~1957 | Walther WSR160 Pinwheel Calculator | Walther | Pinwheel | http://meta-studies.net/pmwiki/uploads/WaltherH150.jpg |
~1957 | Walther WSR160 Demonstration Pinwheel Calculator | Walther | Demonstration Pinwheel | http://meta-studies.net/pmwiki/uploads/WaltherDemoH150.jpg |
http://meta-studies.net/pmwiki/uploads/Mercedes.png | http://meta-studies.net/pmwiki/uploads/MercedesDemo.png |
http://meta-studies.net/pmwiki/uploads/Mercedes.png | http://meta-studies.net/pmwiki/uploads/MercedesDemoH200.jpg |
1950s | Bell Sumlock Comptometer | Bell Sumlock | Model 909/S/117.878 | http://meta-studies.net/pmwiki/uploads/Sumlock.png |
~1955 | Bell Punch Sumlock | Bell Punch | Demonstration Comptometer | http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png |
1950s | Bell Sumlock Comptometer | Bell Sumlock | Model 909/S/117.878 | http://meta-studies.net/pmwiki/uploads/SumlockH250.jpg |
~1955 | Bell Punch Sumlock | Bell Punch | Demonstration Comptometer | http://meta-studies.net/pmwiki/uploads/BellPunchDemoH250.jpg |
http://meta-studies.net/pmwiki/uploads/Curta1-1948.png | http://meta-studies.net/pmwiki/uploads/Curta1-1967.png | http://meta-studies.net/pmwiki/uploads/Curta2.png |
http://meta-studies.net/pmwiki/uploads/Curta1-1948H200.jpg | http://meta-studies.net/pmwiki/uploads/Curta1-1967H200.jpg | http://meta-studies.net/pmwiki/uploads/Curta2H200.jpg |
http://meta-studies.net/pmwiki/uploads/Schickard1.jpg | http://meta-studies.net/pmwiki/uploads/BambergerOmega.png |
http://meta-studies.net/pmwiki/uploads/Schickard1H250.jpg | http://meta-studies.net/pmwiki/uploads/BambergerOmegaH250.jpg |
(collection Calculant - all above)
(collection Calculant - all above) |
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.
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.
1623: Recreation of Wilhelm Schickard’s machine (collection Calculant) | 1904–1905: Bamberger’s Omega Calculating Machine (collection Calculant) |
1623: Recreation of | 1904–1905: Bamberger’s Omega |
Wilhelm Schickard’s machine | Calculating Machine |
(collection Calculant) | (collection Calculant) |
(collection Calculant - all above)
(collection Calculant - all above) |
(collection Calculant - all above)
(collection Calculant - all above) |
(collection Calculant - all above)
(collection Calculant - all above) |
(collection Calculant - all above)
(collection Calculant - all above) |
(:table align=center :)
(:cellnr:) http://meta-studies.net/pmwiki/uploads/Locke170.jpg
1905–10: Locke Adder
(collection Calculant)
(:tableend:)
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)
http://meta-studies.net/pmwiki/uploads/Locke170.jpg |
(collection Calculant) |
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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« Part 2 The Modern Era | | »
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« Part 2 The Modern Era | | »
« Part 2 The Modern Era | | »
« Part 2 The Modern Era | | »
http://meta-studies.net/pmwiki/uploads/Ropp.jpg
http://meta-studies.net/pmwiki/uploads/Ropp200.jpg
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1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator.png |
~1915 | Golden Gem Automatic Adding Machine | H. & H. Goldmann | Chain | http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg |
1920 | Addiator Troncet adder | Ruthard & Co | Chain | http://meta-studies.net/pmwiki/uploads/Addiator.png |
1922 | Scribola 10 column printing Adding Machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/Scribola.jpg |
1937 | Add-O-Matic Adding Machine | Allied MFG. Co. | Chain | http://meta-studies.net/pmwiki/uploads/AddOMatic1.jpg |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator125.jpg |
~1915 | Golden Gem Automatic Adding Machine | H. & H. Goldmann | Chain | http://meta-studies.net/pmwiki/uploads/GoldenGem100.jpg |
1920 | Addiator Troncet adder | Ruthard & Co | Chain | http://meta-studies.net/pmwiki/uploads/Addiator125.jpg |
1922 | Scribola 10 column printing Adding Machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/Scribola150.jpg |
1937 | Add-O-Matic Adding Machine | Allied MFG. Co. | Chain | http://meta-studies.net/pmwiki/uploads/AddOMatic1_125.jpg |
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.
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.
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.
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.
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.
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.
Curta: The peak of minituarisation (1947–1970)
Curta: The peak of miniaturisation (1947–1970)
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. 246 For more on the Curta see the marvellous collection of documents and simulations at The Curta Caclulator Page.247
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. 248 For more on the Curta see the marvellous collection of documents and simulations at The Curta Caclulator Page.249
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:
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:
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.
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.
Curta: The peak of minituarisation (1947–1970)
Curta: The peak of minituarisation (1947–1970)
(:table align=center :) (:cellnr:) http://meta-studies.net/pmwiki/uploads/HerzstarkMech.jpg
(:tableend:)
http://meta-studies.net/pmwiki/uploads/Misc/ThomasMechRel.jpg
1862: Diagram of the Thomas de Colmar arithmometer mechanism.250
(click on the image for an enlargement)
(Source: Museum of the History of Science, University of Oxford.)
(:table align=center :) (:cellnr:) http://meta-studies.net/pmwiki/uploads/TIMDrum.jpg
(:tableend:)
(:table align=center :) (:cellnr:) http://meta-studies.net/pmwiki/uploads/ThomasDeColmar.jpg
(:tableend:)
(:table align=center :) (:cellnr:) http://meta-studies.net/pmwiki/uploads/Brunsviga1896.png
(:tableend:)
(:table align=center :) (:cellnr:) http://meta-studies.net/pmwiki/uploads/Misc/RackMech.jpg
(:tableend:)
(:table align=center :) (:cellnr:) http://meta-studies.net/pmwiki/uploads/ComptometerWoodie.png
(:tableend:)
(:table align=center :) (:cellnr:) http://meta-studies.net/pmwiki/uploads/BolleeMAB1890.jpg
(:tableend:)
(:table align=center :) (:cellnr:) http://meta-studies.net/pmwiki/uploads/Millionair.png
(:tableend:)
(:table align=center :) (:cellnr:) http://meta-studies.net/pmwiki/uploads/MillionaireDeck.jpg
(:tableend:)
(:table align=center :) (:cellnr:) http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometer.png
(:tableend:)
(:table align=center :) (:cellnr:) http://meta-studies.net/pmwiki/uploads/MADAS_Smaller.png
(:tableend:)
(:table align=center :)
(:cellnr:) http://meta-studies.net/pmwiki/uploads/Misc/ThomasMechRel.jpg
1862: Diagram of the Thomas de Colmar arithmometer mechanism.251
(click on the image for an enlargement)
(Source: Museum of the History of Science, University of Oxford.)
(:tableend:)
(:table align=center :) (:cellnr:) http://meta-studies.net/pmwiki/uploads/Webb.jpg
(:table align=center :)
(:cellnr:) http://meta-studies.net/pmwiki/uploads/Locke.gif%%
Locke Adder 1905–10
(collection Calculant)
(:cellnr:) http://meta-studies.net/pmwiki/uploads/Locke.gif%%
(:cellnr:) http://meta-studies.net/pmwiki/uploads/Locke.gif%%
Locke Adder 1905–10
(:cellnr:) http://meta-studies.net/pmwiki/uploads/Locke.gif%%
1905–10: Locke Adder
(:table align=center :)
(:cellnr:) http://meta-studies.net/pmwiki/uploads/Locke.gif%%
Locke Adder 1905–10
(collection Calculant)
(:tableend:)
Conversion device (from Aunes to Metres) ~1790
(collection Calculant)
~1790: Conversion device
(from Aunes to Metres)
(collection Calculant)
(:cellnr:) http://meta-studies.net/pmwiki/uploads/Convertiseur.png%%
Conversion device (from Aunes to Metres) ~1790
(collection Calculant)
(:cellnr:) http://meta-studies.net/pmwiki/uploads/Convertiseur.png%%
Conversion device (from Aunes to Metres) ~1790
(collection Calculant)
(:cellnr:) http://meta-studies.net/pmwiki/uploads/Convertiseur.png
(:cellnr:) http://meta-studies.net/pmwiki/uploads/Convertiseur.png%%
(:cellnr:) ||http://meta-studies.net/pmwiki/uploads/Locke.gif||
(:cellnr:) http://meta-studies.net/pmwiki/uploads/Locke.gif%%
(:cellnr:) http://meta-studies.net/pmwiki/uploads/Locke.gif
(:cellnr:) ||http://meta-studies.net/pmwiki/uploads/Locke.gif||
(:cellnr:) http://meta-studies.net/pmwiki/uploads/Locke.gif
(:cellnr:) http://meta-studies.net/pmwiki/uploads/Locke.gif
(:cellnr:) http://meta-studies.net/pmwiki/uploads/Locke.gif
Locke Adder 1905–10
(:cellnr:) http://meta-studies.net/pmwiki/uploads/Locke.gif
Locke Adder 1905–10
http://meta-studies.net/pmwiki/uploads/Locke.gif |
Locke Adder 1905–10 (collection Calculant) |
(:table align=center :)
(:cellnr:) http://meta-studies.net/pmwiki/uploads/Locke.gif
Locke Adder 1905–10
(collection Calculant)
(:tableend:)
http://meta-studies.net/pmwiki/uploads/Convertiseur.png |
Conversion device (from Aunes to Metres) ~1790 (collection Calculant) |
(:cellnr:) http://meta-studies.net/pmwiki/uploads/Convertiseur.png
Conversion device (from Aunes to Metres) ~1790
(collection Calculant)
||http://meta-studies.net/pmwiki/uploads/Convertiseur.png||
||Conversion device (from Aunes to Metres) ~1790
(collection Calculant)||
http://meta-studies.net/pmwiki/uploads/Convertiseur.png |
Conversion device (from Aunes to Metres) ~1790 (collection Calculant) |
http://meta-studies.net/pmwiki/uploads/Locke.gif
Conversion device (from Aunes to Metres) ~1790
(collection Calculant)
||http://meta-studies.net/pmwiki/uploads/Convertiseur.png||
||Conversion device (from Aunes to Metres) ~1790
(collection Calculant)||
http://meta-studies.net/pmwiki/uploads/Convertiseur.png
http://meta-studies.net/pmwiki/uploads/Locke.gif
http://meta-studies.net/pmwiki/uploads/Locke.gif
Locke Adder 1905–10
(collection Calculant)
http://meta-studies.net/pmwiki/uploads/Locke.gif |
Locke Adder 1905–10 (collection Calculant) |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator.png |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator.png |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator.png |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator.png |
http://meta-studies.net/pmwiki/uploads/Locke.gif
http://meta-studies.net/pmwiki/uploads/Locke.gif
http://meta-studies.net/pmwiki/uploads/Locke.gif
http://meta-studies.net/pmwiki/uploads/Locke.gif
http://meta-studies.net/pmwiki/uploads/Locke.gif
http://meta-studies.net/pmwiki/uploads/Locke.gif
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 operation252 and Moreland (allowing addition and subtraction “without charging the memory or disturbing the mind253). 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.
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 operation254) and Moreland (allowing addition and subtraction “without charging the memory or disturbing the mind255). 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 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).
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).
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.
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.
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.
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.
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. 256 For more on the Curta see the marvellous collection of documents and simulations at The Curta Caclulator Page.257 The three Curta calculators in this collection are shown below.
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).
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).
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. 258 For more on the Curta see the marvellous collection of documents and simulations at The Curta Caclulator Page.259
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.
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.
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.
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.
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. 260
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. 261 For more on the Curta see the marvellous collection of documents and simulations at The Curta Caclulator Page.262 The three Curta calculators in this collection are shown below.
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.
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.
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.
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.
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:
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. 267
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.268 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).
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.269 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.
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.
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.
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.271 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).
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.272 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).
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).
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.273 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).
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.
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.
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 Gauvin274 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:
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 Gauvin275 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:
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.276
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.277
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.
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.
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. 278
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.279
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.
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).
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.280
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. 281
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.282
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.
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.
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 1902283 and had made its appearance first in the Mercedes-Euklid in 1910.284
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.
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.
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 1910.285
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 1902286 and had made its appearance first in the Mercedes-Euklid in 1910.287
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.
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.288 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.
- something else that can be moved (for example, although it was barely used,289 the height of columns of water).
- something else that can be moved (for example, although it was barely used,290 the height of columns of water).
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.
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.
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.
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.
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.
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.
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).
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).
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.
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.
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.
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.
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.
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.
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.
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).
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.
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.
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
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.
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.
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.
The Vanishing point: electronics and the arrival of the HP35
The Vanishing point: solid state electronics and the arrival of the HP35
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.
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.
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.
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
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.
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 1910.291
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.
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.
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.
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.
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.
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.
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.
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).
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).
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.
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.
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.
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.
~1929 “Herzstark” electric Calculating Machine serial 6549
badged by Herzstark, Vienna
(essentially a Badenia Model TE 13 Duplex)
~1929: “Herzstark” electric Calculating Machine serial 6549
badged by Herzstark, Vienna
(essentially a Badenia Model TE 13 Duplex)
http://meta-studies.net/pmwiki/uploads/HerzstarkMech.jpg
1950s-1960s: Underneath view of the Herzstark mechanism
- note the stepped drums
(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. 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 1935292 at a 1912 price of about US$480293 (about $11,700 in 2013 US dollars294). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,295 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 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.
Manufactured by H.W. Egli, some 4,655 Millionaires were sold between 1895 and 1935296 at a 1912 price of about US$480297 (about $11,700 in 2013 US dollars298). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,299 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.
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.
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.
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
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.
Electricity could be utilised once there was a national grid….
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.
Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480300 (about $11,700 in 2013 US dollars301). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,302 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.
Manufactured by H.W. Egli, some 4,655 of these were sold between 1895 and 1935303 at a 1912 price of about US$480304 (about $11,700 in 2013 US dollars305). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,306 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.
Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480307 (about $11,700 in 2013 US dollars308).309 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.
Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480310 (about $11,700 in 2013 US dollars311). The Millionaire calculating machine in this collection was manufactured on 16 October 1912,312 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.
Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480313314 (about $11,700 in 2013 US dollars315).316 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.
Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480317 (about $11,700 in 2013 US dollars318).319 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.
Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480 (about $11,700 in 2013 US$ 320).321 The Millionaire calculating machine in this collection was manufactured on 16 October 1912,322323 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.
Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480324325 (about $11,700 in 2013 US dollars326).327 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.
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^]).328 The Millionaire calculating machine in this collection was manufactured on 16 October 1912,329330 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.
Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480 (about $11,700 in 2013 US$ 331).332 The Millionaire calculating machine in this collection was manufactured on 16 October 1912,333334 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.
Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480.335 The Millionaire calculating machine in this collection was manufactured on 16 October 1912,336337 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.
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^]).338 The Millionaire calculating machine in this collection was manufactured on 16 October 1912,339340 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.
Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480.341 The Millionaire calculating machine in this collection was manufactured on 16 October 1912,342343 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.
Manufactured by H.W. Egli, some 4,655 of these were sold at a 1912 price of about US$480.344 The Millionaire calculating machine in this collection was manufactured on 16 October 1912,345346 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.
Scheutz and Babbage - difference engines
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,
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.
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.
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.
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 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$480.347 The Millionaire calculating machine in this collection was manufactured on 16 October 1912,348349 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 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.
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.
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.
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.
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.
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.
http://meta-studies.net/pmwiki/uploads/Millionair.png?
Deck of the Millionaire Calculating Machine
(collection Calculant)
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.
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,350 and the marvellous websites of Rechnerlexikon351 and John Wolff352.
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,353 and the marvellous websites of Rechnerlexikon354 and John Wolff355.
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,356 and the marvellous websites of Rechnerlexikon357 and John Wolff358.
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,359 and the marvellous websites of Rechnerlexikon360 and John Wolff361.
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
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,362 and the marvellous websites of Rechnerlexikon363 and John Wolff364.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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 Gauvin365 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:
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 Gauvin366 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:
As mentioned earlier (in 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:
As mentioned earlier (in 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:
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 operation367 and Moreland (allowing addition and subtraction “without charging the memory or disturbing the mind368). 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).
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 operation369 and Moreland (allowing addition and subtraction “without charging the memory or disturbing the mind370). 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.
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 operation371 and Moreland (allowing addition and subtraction “without charging the memory or disturbing the mind372) 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).
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 operation373 and Moreland (allowing addition and subtraction “without charging the memory or disturbing the mind374). 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
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.
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.
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 operation375 and Moreland (allowing addition and subtraction “without charging the memory or disturbing the mind376) 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).
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 operation377 and Moreland (allowing addition and subtraction “without charging the memory or disturbing the mind378) 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.
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).
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 operation379 and Moreland (allowing addition and subtraction “without charging the memory or disturbing the mind380) 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).
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.381 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.
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.382 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.[383 Below is the very early Brunsviga-Schuster pinwheel calculator from 1896 in this collection.
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
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:
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
As mentioned earlier (in 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.
As mentioned earlier (in 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.
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.
As mentioned earlier (in 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.
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
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
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
The point here is that the use of a calculating technology is not just intellectual. It is what Jean-François Gauvin390 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.
The point here is that the use of a calculating technology is not just intellectual. It is what Jean-François Gauvin391 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:
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 Gauvin392 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.
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.393 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.394
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.395. 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.396 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.397
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.398 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.399
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.400 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.401
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.402 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.
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.403 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.404
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1623: Recreation of Wilhelm Schickard’s machine (collection Calculant) | 1904–1905: Bamberger’s Omega Calculating Machine (collection Calculant) |
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1623: Recreation of Wilhelm Schickard’s machine (collection Calculant) | 1904–1905: Bamberger’s Omega Calculating Machine (collection Calculant) |
http://meta-studies.net/pmwiki/uploads/Schickard1.jpg | http://meta-studies.net/pmwiki/uploads/BambergerOmega.png |
1623: Recreation of Wilhelm Schickard’s machine (collection Calculant) | 1904–1905: Bamberger’s Omega Calculating Machine (collection Calculant) |
http://meta-studies.net/pmwiki/uploads/Schickard1.jpg | http://meta-studies.net/pmwiki/uploads/BambergerOmega.png |
1623: Recreation of Wilhelm Schickard’s machine (collection Calculant) | 1904–1905: Bamberger’s Omega Calculating Machine (collection Calculant) |
http://meta-studies.net/pmwiki/uploads/Schickard1.jpg | http://meta-studies.net/pmwiki/uploads/BambergerOmega.png |
1623: Recreation of Wilhelm Schickard’s machine (collection Calculant) | 1904–1905: Bamberger’s Omega Calculating Machine (collection Calculant) |
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1623: Recreation of Wilhelm Schickard’s machine (collection Calculant) | 1904–1905: Bamberger’s Omega Calculating Machine (collection Calculant) |
The quest for true multiplication and division
The quest for direct multiplication and division
Evolutionary cul-de-sac: the search for true multiplication and division
The quest for true multiplication and division
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.
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.
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.
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.
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.
1623: Recreation of Wilhelm Schickard’s machine (collection Calculant) | 1904–1905: Bamberger’s Omega Calculating Machine (collection Calculant) |
1623: Recreation of Wilhelm Schickard’s machine (collection Calculant) | 1904–1905: Bamberger’s Omega Calculating Machine (collection Calculant) |
1623: Recreation of Wilhelm Schickard’s machine//(collection Calculant) | 1904–1905: Bamberger’s Omega Calculating Machine |
1623: Recreation of Wilhelm Schickard’s machine (collection Calculant) | 1904–1905: Bamberger’s Omega Calculating Machine |
http://meta-studies.net/pmwiki/uploads/Schickard1.jpg 1623: Recreation of Wilhelm Schickard’s machine//(collection Calculant)
http://meta-studies.net/pmwiki/uploads/BambergerOmega.png
1904–1905: Bamberger’s Omega Calculating Machine
(collection Calculant)
http://meta-studies.net/pmwiki/uploads/Schickard1.jpg | http://meta-studies.net/pmwiki/uploads/BambergerOmega.png |
1623: Recreation of Wilhelm Schickard’s machine//(collection Calculant) | 1904–1905: Bamberger’s Omega Calculating Machine (collection Calculant) |
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.
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.
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.
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.
http://meta-studies.net/pmwiki/uploads/Schickard1.jpg 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.
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.405 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.
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.406 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.
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.
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.407 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.
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.
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.408 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.)
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.409 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.)
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.
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.
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.410 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 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.411 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.)
~1915 | Golden Gem Automatic Adding Machine | H. & H. Goldmann | Chain | http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg |
~1915 | Golden Gem Automatic Adding Machine | H. & H. Goldmann | Chain | http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/Adix.png |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/Adix.png |
1950s | Bell Sumlock Comptometer | Bell Sumlock | Model 909/S/117.878 | http://meta-studies.net/pmwiki/uploads/Sumlock.png |
~1955 | Bell Punch Sumlock | Bell Punch | Demonstration Comptometer | http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png |
1950s | Bell Sumlock Comptometer | Bell Sumlock | Model 909/S/117.878 | http://meta-studies.net/pmwiki/uploads/Sumlock.png |
~1955 | Bell Punch Sumlock | Bell Punch | Demonstration Comptometer | http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png |
1909 | TIM (Time is Money) Arithmometer | Ludwig Spitz & Co | Arithmometer | http://meta-studies.net/pmwiki/uploads/TIM.JPG |
~1913 | Bunzel-Denton Arithmometer | Bunzel | Prototype Front Crank | http://meta-studies.net/pmwiki/uploads/Bunzel.JPG |
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917.jpg |
1909 | TIM (Time is Money) Arithmometer | Ludwig Spitz & Co | Arithmometer | http://meta-studies.net/pmwiki/uploads/TIM.JPG |
~1913 | Bunzel-Denton Arithmometer | Bunzel | Prototype Front Crank | http://meta-studies.net/pmwiki/uploads/Bunzel.JPG |
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917.jpg |
1945 | Facit Model S Calculator serial 210652 | Facit | Pinwheel | http://meta-studies.net/pmwiki/uploads/Facit.png |
1945 | Facit Model S Calculator serial 210652 | Facit | Pinwheel | http://meta-studies.net/pmwiki/uploads/Facit.png |
~1957 | Walther WSR160 Pinwheel Calculator | Walther | Pinwheel | http://meta-studies.net/pmwiki/uploads/Walther.png |
~1957 | Walther WSR160 Demonstration Pinwheel Calculator | Walther | Demonstration Pinwheel | http://meta-studies.net/pmwiki/uploads/WaltherDemo.png |
~1957 | Walther WSR160 Pinwheel Calculator | Walther | Pinwheel | http://meta-studies.net/pmwiki/uploads/Walther.png |
~1957 | Walther WSR160 Demonstration Pinwheel Calculator | Walther | Demonstration Pinwheel | http://meta-studies.net/pmwiki/uploads/WaltherDemo.png |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Lightning.png |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Lightning.png |
1890–1900 | A. M. Stevenson Adder | Joliet, Ill. | 2 Wheel | http://meta-studies.net/pmwiki/uploads/Stevenson.png |
1890–1900 | A. M. Stevenson Adder | Joliet, Ill. | 2 Wheel | http://meta-studies.net/pmwiki/uploads/Stevenson.png |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Lightning.png |
1968 | SEE Demonstration Adding Machine | Selective Educational Equipment Corporation | 4 Wheels | http://meta-studies.net/pmwiki/uploads/SEE-1.jpg |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Lightning.png |
1968 | SEE Demonstration Adding Machine | Selective Educational Equipment Corporation | 4 Wheels | http://meta-studies.net/pmwiki/uploads/SEE-1.jpg |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator.png |
~1915 | Golden Gem Automatic Adding Machine | H. & H. Goldmann | Chain | http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg |
1920 | Addiator Troncet adder | Ruthard & Co | Chain | http://meta-studies.net/pmwiki/uploads/Addiator.png |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator.png |
~1915 | Golden Gem Automatic Adding Machine | H. & H. Goldmann | Chain | http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg |
1920 | Addiator Troncet adder | Ruthard & Co | Chain | http://meta-studies.net/pmwiki/uploads/Addiator.png |
1937 | Add-O-Matic Adding Machine | Allied MFG. Co. | Chain | http://meta-studies.net/pmwiki/uploads/AddOMatic1.jpg |
1937 | Add-O-Matic Adding Machine | Allied MFG. Co. | Chain | http://meta-studies.net/pmwiki/uploads/AddOMatic1.jpg |
1890–1900 | A. M. Stevenson Adder | Joliet, Ill. | 2 Wheel | http://meta-studies.net/pmwiki/uploads/Stevenson.png |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/Adix.png |
1910 | Adall Adding Machine | Dreyfus and Levy | Key input Concentric toothed disk and groove | http://meta-studies.net/pmwiki/uploads/Adall.jpg |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Lightning.png |
1968 | SEE Demonstration Adding Machine | Selective Educational Equipment Corporation | 4 Wheels | http://meta-studies.net/pmwiki/uploads/SEE-1.jpg |
1890–1900 | A. M. Stevenson Adder | Joliet, Ill. | 2 Wheel | http://meta-studies.net/pmwiki/uploads/Stevenson.png |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/Adix.png |
1910 | Adall Adding Machine | Dreyfus and Levy | Key input Concentric toothed disk and groove | http://meta-studies.net/pmwiki/uploads/Adall.jpg |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Lightning.png |
1968 | SEE Demonstration Adding Machine | Selective Educational Equipment Corporation | 4 Wheels | http://meta-studies.net/pmwiki/uploads/SEE-1.jpg |
1890–1900 | A. M. Stevenson Adder | Joliet, Ill. | 2 Wheel | http://meta-studies.net/pmwiki/uploads/Stevenson.png |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/Adix.png |
1910 | Adall Adding Machine | Dreyfus and Levy | Key input Concentric toothed disk and groove | http://meta-studies.net/pmwiki/uploads/Adall.jpg |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Lightning.png |
1968 | SEE Demonstration Adding Machine | Selective Educational Equipment Corporation | 4 Wheels | http://meta-studies.net/pmwiki/uploads/SEE-1.jpg |
1890–1900 | A. M. Stevenson Adder | Joliet, Ill. | 2 Wheel | http://meta-studies.net/pmwiki/uploads/Stevenson.png |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/Adix.png |
1910 | Adall Adding Machine | Dreyfus and Levy | Key input Concentric toothed disk and groove | http://meta-studies.net/pmwiki/uploads/Adall.jpg |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Lightning.png |
1968 | SEE Demonstration Adding Machine | Selective Educational Equipment Corporation | 4 Wheels | http://meta-studies.net/pmwiki/uploads/SEE-1.jpg |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator.png |
~1915 | Golden Gem Automatic Adding Machine | H. & H. Goldmann | Chain | http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator.png |
~1915 | Golden Gem Automatic Adding Machine | H. & H. Goldmann | Chain | http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg |
1922 | Scribola 10 column printing Adding Machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/Scribola.jpg |
1937 | Add-O-Matic Adding Machine | Allied MFG. Co. | Chain | http://meta-studies.net/pmwiki/uploads/AddOMatic1.jpg |
1922 | Scribola 10 column printing Adding Machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/Scribola.jpg |
1937 | Add-O-Matic Adding Machine | Allied MFG. Co. | Chain | http://meta-studies.net/pmwiki/uploads/AddOMatic1.jpg |
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.
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.
Notes
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.
http://meta-studies.net/pmwiki/uploads/PinWheelSingle.jpg | http://meta-studies.net/pmwiki/uploads/PinwheelDemo.jpg |
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).
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.412 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.
1923: Mercedes-Euklid Model 29 calculator | 1923: Mercedes-Euklid Model 29 Demonstration calculator |
1923: Mercedes-Euklid Model 29 calculator | 1923: Mercedes-Euklid Model 29 Demonstration calculator |
1923: Mercedes-Euklid Model 29 calculator (collection Calculant) | 1923: Mercedes-Euklid Model 29 Demonstration calculator |
1923: Mercedes-Euklid Model 29 calculator | 1923: Mercedes-Euklid Model 29 Demonstration calculator |
(collection Calculant) | (collection Calculant) |
(collection Calculant) | (collection Calculant) |
(collection Calculant) | (collection Calculant) | (collection Calculant) |
(collection Calculant) |
(collection Calculant) | (collection Calculant) |
(collection Calculant) |
(collection Calculant) | (collection Calculant) |
A single pinwheel | Mechanism of the Walther pinwheel calculator |
A single pinwheel | Mechanism of the Walther pinwheel calculator (parts removed for demonstration) |
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.
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.413. 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.
A single pinwheel | Mechanism of the Walther pinwheel calculator |
A single pinwheel | Mechanism of the Walther pinwheel calculator |
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.
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.
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.
http://meta-studies.net/pmwiki/uploads/TIMDrum.jpg
Step drum (in a later ‘TIM’ arithmometer)
(collection Calculant)
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.
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.
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.
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.
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).
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).
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).
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.
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).
http://meta-studies.net/pmwiki/uploads/PinWheelSingle.jpg | http://meta-studies.net/pmwiki/uploads/PinwheelDemo.jpg |
Site.DemonstrationPinwheel Site.DemonstrationPinwheelMechanism
http://meta-studies.net/pmwiki/uploads/PinWheelSingle.jpg | http://meta-studies.net/pmwiki/uploads/PinwheelDemo.jpg |
http://meta-studies.net/pmwiki/uploads/HP35.jpg | http://meta-studies.net/pmwiki/uploads/HP-45.jpg |
July1972 Hewlett Packard HP 35 Calculator serial 1230A 79429, 1972 | December 1973 Hewlett Packard HP 45 Calculator serial 1350A 36719, 1973 |
http://meta-studies.net/pmwiki/uploads/PinWheelSingle.jpg | http://meta-studies.net/pmwiki/uploads/PinwheelDemo.jpg |
A single pinwheel | Mechanism of the Walther pinwheel calculator |
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).
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
http://meta-studies.net/pmwiki/uploads/HP35.jpg | http://meta-studies.net/pmwiki/uploads/HP-45.jpg |
July1972 Hewlett Packard HP 35 Calculator serial 1230A 79429, 1972 | December 1973 Hewlett Packard HP 45 Calculator serial 1350A 36719, 1973 |
(collection Calculant) |
Notes
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
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.414 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’.415 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.416 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.”417 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.
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.418 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’.419 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.420 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.”421 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.
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.
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.
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.
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.
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.422
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.423
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.424
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.425
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.
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.426
1890–1900 | A. M. Stevenson Adder | Joliet, Ill. | 2 Wheel | http://meta-studies.net/pmwiki/uploads/Stevenson.png |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/Adix.png |
1910 | Adall Adding Machine | Dreyfus and Levy | Key input Concentric toothed disk and groove | http://meta-studies.net/pmwiki/uploads/Adall.jpg |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Lightning.png |
1968 | SEE Demonstration Adding Machine | Selective Educational Equipment Corporation | 4 Wheels | http://meta-studies.net/pmwiki/uploads/SEE-1.jpg |
1890–1900 | A. M. Stevenson Adder | Joliet, Ill. | 2 Wheel | http://meta-studies.net/pmwiki/uploads/Stevenson.png |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/Adix.png |
1910 | Adall Adding Machine | Dreyfus and Levy | Key input Concentric toothed disk and groove | http://meta-studies.net/pmwiki/uploads/Adall.jpg |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Lightning.png |
1968 | SEE Demonstration Adding Machine | Selective Educational Equipment Corporation | 4 Wheels | http://meta-studies.net/pmwiki/uploads/SEE-1.jpg |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator.png |
~1915 | Golden Gem Automatic Adding Machine | H. & H. Goldmann | Chain | http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg |
1920 | Addiator Troncet adder | Ruthard & Co | Chain | http://meta-studies.net/pmwiki/uploads/Addiator.png |
1922 | Scribola 10 column printing Adding Machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/Scribola.jpg |
1937 | Add-O-Matic Adding Machine | Allied MFG. Co. | Chain | http://meta-studies.net/pmwiki/uploads/AddOMatic1.jpg |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator.png |
~1915 | Golden Gem Automatic Adding Machine | H. & H. Goldmann | Chain | http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg |
1920 | Addiator Troncet adder | Ruthard & Co | Chain | http://meta-studies.net/pmwiki/uploads/Addiator.png |
1922 | Scribola 10 column printing Adding Machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/Scribola.jpg |
1937 | Add-O-Matic Adding Machine | Allied MFG. Co. | Chain | http://meta-studies.net/pmwiki/uploads/AddOMatic1.jpg |
~1957 | Walther WSR160 Pinwheel Calculator | Walther | Pinwheel | http://meta-studies.net/pmwiki/uploads/Walther.png |
~1957 | Walther WSR160 Demonstration Pinwheel Calculator | Walther | Demonstration Pinwheel | http://meta-studies.net/pmwiki/uploads/WaltherDemo.png |
~1957 | Walther WSR160 Pinwheel Calculator | Walther | Pinwheel | http://meta-studies.net/pmwiki/uploads/Walther.png |
~1957 | Walther WSR160 Demonstration Pinwheel Calculator | Walther | Demonstration Pinwheel | http://meta-studies.net/pmwiki/uploads/WaltherDemo.png |
1909 | TIM (Time is Money) Arithmometer | Ludwig Spitz & Co | Arithmometer | http://meta-studies.net/pmwiki/uploads/TIM.JPG |
~1913 | Bunzel-Denton Arithmometer | Bunzel | Prototype Front Crank | http://meta-studies.net/pmwiki/uploads/Bunzel.JPG |
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917.jpg |
1909 | TIM (Time is Money) Arithmometer | Ludwig Spitz & Co | Arithmometer | http://meta-studies.net/pmwiki/uploads/TIM.JPG |
~1913 | Bunzel-Denton Arithmometer | Bunzel | Prototype Front Crank | http://meta-studies.net/pmwiki/uploads/Bunzel.JPG |
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917.jpg |
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 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.
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.427 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.
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.428 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.429 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 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.
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 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.
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,
http://meta-studies.net/pmwiki/uploads/ComptometerWoodie.png
1896: Felt and Tarrant Comptometer
Earliest - wood-cased model, serial 2491
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).
http://meta-studies.net/pmwiki/uploads/Brunsviga1896.png
Brunsviga Schuster Pinwheel Calculator ~1896
Serial 3406
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.
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.
1950s | Bell Sumlock Comptometer | Bell Sumlock | Model 909/S/117.878 | http://meta-studies.net/pmwiki/uploads/Sumlock.png |
~1955 | Bell Punch Sumlock | Bell Punch | Demonstration Comptometer | http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png |
1945 | Facit Model S Calculator serial 210652 | Facit | Pinwheel | http://meta-studies.net/pmwiki/uploads/Facit.png |
~1951 | Original Ohdner Model 39 serial 39–288965 | Ohdner | Pinwheel | Add Picture |
~1957 | Walther WSR160 Pinwheel Calculator | Walther | Pinwheel | http://meta-studies.net/pmwiki/uploads/Walther.png |
~1957 | Walther WSR160 Demonstration Pinwheel Calculator | Walther | Demonstration Pinwheel | http://meta-studies.net/pmwiki/uploads/WaltherDemo.png |
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).
http://meta-studies.net/pmwiki/uploads/Brunsviga1896.png
Brunsviga Schuster Pinwheel Calculator ~1896
Serial 3406
(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 | http://meta-studies.net/pmwiki/uploads/Facit.png |
~1951 | Original Ohdner Model 39 serial 39–288965 | Ohdner | Pinwheel | Add Picture |
~1957 | Walther WSR160 Pinwheel Calculator | Walther | Pinwheel | http://meta-studies.net/pmwiki/uploads/Walther.png |
~1957 | Walther WSR160 Demonstration Pinwheel Calculator | Walther | Demonstration Pinwheel | http://meta-studies.net/pmwiki/uploads/WaltherDemo.png |
(collection Calculant - all above)
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,
http://meta-studies.net/pmwiki/uploads/ComptometerWoodie.png
1896: Felt and Tarrant Comptometer
Earliest - wood-cased model, serial 2491
(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 | http://meta-studies.net/pmwiki/uploads/Sumlock.png |
~1955 | Bell Punch Sumlock | Bell Punch | Demonstration Comptometer | http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png |
(collection Calculant - all above)
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.
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.430 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.
Date | Description | Maker | Type | Device (click for description) |
Date | Description | Maker | Type | Device (click for greater detail) |
Date | Description | Maker | Type | Device (click for description) |
Date | Description | Maker | Type | Device (click for greater detail) |
Date | Description | Maker | Type | Device (click for description) |
Date | Description | Maker | Type | Device (click for greater detail) |
Date | Description | Maker | Type | Device (click for description) |
Date | Description | Maker | Type | Device (click for greater detail) |
Date | Description | Maker | Type | Device (click for description) |
Date | Description | Maker | Type | Device (click for greater detail) |
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.431 From 1880, other manufacturers - Burkhardt, Layton, Saxonia, Bunzel, etc entered the market. Some later arithmometers in this collection are shown below.
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.432 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.
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.
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.
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.”433 In terms of today’s purchasing power, £12 from 1872
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.”434 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).435
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).
The Thomas design was copied and improved by a number of other engineers and marketed from different countries.436 From 1880, other manufacturers - Burkhardt, Layton, Saxonia, Bunzel, etc entered the market. Some later arithmometers in this collection are shown below.
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”.437 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.438 From 1880, other manufacturers - Burkhardt, Layton, Saxonia, Bunzel, etc entered the market. Some later arithmometers in this collection are shown below.
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.439 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’.440 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.441 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.”442 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.
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.443 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’.444 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.445 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.”446 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.”447 In terms of today’s purchasing power, £12 from 1872
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’.448 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.449 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.”450 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.
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.451 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’.452 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.453 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.”454 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.
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’.455 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.456 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.
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’.457 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.458 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.”459 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.
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 1820.460. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.461 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 invention462).
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 1820.463. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.464 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 invention465).
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. 466 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.467
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. 468 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’.469 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.470 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.
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. 471 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.472
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. 473 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.474
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. 475
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. 476 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.477
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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 1820.478. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.479 The somewhat circuitous route to that later success is described by Stephen Johnston. 480 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 invention481).
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 1820.482. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.483 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 invention484).
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.
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. 485
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.
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.
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.
1862: Diagram of the Thomas de Colmar arithmometer mechanism.486
(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.487
1862: Diagram of the Thomas de Colmar arithmometer mechanism.488
(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.
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.
The Thomas design was copied and improved by a number of other engineers and marketed from different countries.489 From 1880, other manufacturers - Burkhardt, Layton, Saxonia, Bunzel, etc entered the market. Some later arithmometers in this collection are shown below.
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.
1862: Diagram of the Thomas de Colmar arithmometer mechanism.490
Source: Museum of the History of Science, University of Oxford
1862: Diagram of the Thomas de Colmar arithmometer mechanism.491
(Source: Museum of the History of Science, University of Oxford.)
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.
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.
1862: Diagram of the Thomas de Colmar arithmometer mechanism.492
Source: Museum of the History of Science, University of Oxford
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 1820.493. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.494 The somewhat circuitous route to that later success is described by Stephen Johnston. 495
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.496
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 1820.497. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.498 The somewhat circuitous route to that later success is described by Stephen Johnston. 499 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 invention500).
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.501
July1972: Hewlett Packard HP 35 Calculator serial 1230A 79429, 1972 (second version) (collection Calculant) | December 1973: Hewlett Packard HP 45 Calculator serial 1350A 36719, 1973 |
July1972 Hewlett Packard HP 35 Calculator serial 1230A 79429, 1972 | December 1973 Hewlett Packard HP 45 Calculator serial 1350A 36719, 1973 |
(collection Calculant) |
- 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.
- 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.
~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.
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.
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.
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.
|| http://meta-studies.net/pmwiki/uploads/HP35.jpg|| http://meta-studies.net/pmwiki/uploads/HP-45.jpg||
|| July1972: Hewlett Packard
HP 35 Calculator
serial 1230A 79429, 1972
(second version)
(collection Calculant)|| December 1973: Hewlett Packard
HP 45 Calculator
serial 1350A 36719, 1973||
http://meta-studies.net/pmwiki/uploads/HP35.jpg | http://meta-studies.net/pmwiki/uploads/HP-45.jpg |
July1972: Hewlett Packard HP 35 Calculator serial 1230A 79429, 1972 (second version) (collection Calculant) | December 1973: Hewlett Packard HP 45 Calculator serial 1350A 36719, 1973 |
http://meta-studies.net/pmwiki/uploads/HP35.jpg | http://meta-studies.net/pmwiki/uploads/HP-45.jpg |
July1972: Hewlett Packard HP 35 Calculator serial 1230A 79429, 1972 (second version) (collection Calculant) | December 1973: Hewlett Packard HP 45 Calculator serial 1350A 36719, 1973 |
|| http://meta-studies.net/pmwiki/uploads/HP35.jpg|| http://meta-studies.net/pmwiki/uploads/HP-45.jpg||
|| July1972: Hewlett Packard
HP 35 Calculator
serial 1230A 79429, 1972
(second version)
(collection Calculant)|| December 1973: Hewlett Packard
HP 45 Calculator
serial 1350A 36719, 1973||
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 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 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 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 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.
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 1820.502. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.503 The somewhat circuitous route to that later success is described by Stephen Johnston 504
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 1820.505. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.506 The somewhat circuitous route to that later success is described by Stephen Johnston. 507
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 1820.508. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.509 The somewhat circuitous route to that later success is described by Stephen Johnston 510
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.511
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 1820.512. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.513 The somewhat circuitous route to that later success is described by Stephen Johnston 514
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.515
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.516
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 1820.517. His initial design was very different from the machines that would ultimately become the first successfully commercialised four function calculators, half a century later.518 The somewhat circuitous route to that later success is described by Stephen Johnston 519
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.520
July1972: Hewlett Packard HP 35 Calculator serial 1230A 79429, 1972 (second version)
December 1973: Hewlett Packard HP 45 Calculator serial 1350A 36719, 1973
http://meta-studies.net/pmwiki/uploads/HP35.jpg | http://meta-studies.net/pmwiki/uploads/HP-45.jpg |
July1972: Hewlett Packard HP 35 Calculator serial 1230A 79429, 1972 (second version) (collection Calculant) | December 1973: Hewlett Packard HP 45 Calculator serial 1350A 36719, 1973 |
http://meta-studies.net/pmwiki/uploads/HerzstarkArithmometer.png
~1929 “Herzstark” electric Calculating Machine serial 6549
badged by Herzstark, Vienna
(essentially a Badenia Model TE 13 Duplex)
(collection Calculant)
1950s-1960s: MADAS Model 20BTG serial 94046 electric calculator with true automatic division
http://meta-studies.net/pmwiki/uploads/MADAS_Smaller.png
1950s-1960s: MADAS Model 20BTG serial 94046
electric calculator with true automatic division
(collection Calculant)
http://meta-studies.net/pmwiki/uploads/BolleeMAB1890.jpg
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.
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.
http://meta-studies.net/pmwiki/uploads/Millionair.png
1912: Millionaire Calculating Machine
serial 2015 (10×10×20)
http://meta-studies.net/pmwiki/uploads/BolleeMAB1890.jpg
Leon Bollée Calculating Machine
”A New Calculating Machine of very General Applicability”
The Manufacturer and Builder 1890521
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.
http://meta-studies.net/pmwiki/uploads/Millionair.png
1912: Millionaire Calculating Machine
serial 2015 (10×10×20)
(collection Calculant)
Scheutz and Babbage - difference engines
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.
~ 1955 1950s: (made in Great Britain by Bell Punch Company Ltd)
Many variations. Eg Frieden’s cam timed “Frieden wheel”.
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.
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.
http://meta-studies.net/pmwiki/uploads/BambergerOmega.pngg
1904–1905: Bamberger’s Omega Calculating Machine
(collection Calculant)
1904–1905: Bamberger’s Omega Calculating Machine
1912: Millionaire Calculating Machine serial 2015 (10×10×20)
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)
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.
http://meta-studies.net/pmwiki/uploads/Millionair.png
1912: Millionaire Calculating Machine
serial 2015 (10×10×20)
(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.
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.
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.
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
In Lieu of a Conclusion
~July 1948: CURTA Type 1 (pin sliders) earliest model calculator serial 5424 | 1967: CURTA Type I calculator serial 76436 & cardboard box | 1963: CURTA Type II calculator with Leather Case |
~July 1948: CURTA Type 1 (pin sliders) earliest model calculator serial 5424 | 1967: CURTA Type I calculator serial 76436 & cardboard box | 1963: CURTA Type II calculator |
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
~July 1948: CURTA Type 1 (pin sliders) earliest model calculator serial 5424
http://meta-studies.net/pmwiki/uploads/Curta1-1948.png | http://meta-studies.net/pmwiki/uploads/Curta1-1967.png | http://meta-studies.net/pmwiki/uploads/Curta2.png |
~July 1948: CURTA Type 1 (pin sliders) earliest model calculator serial 5424 | 1967: CURTA Type I calculator serial 76436 & cardboard box | 1963: CURTA Type II calculator with Leather Case |
(collection Calculant) |
1923: Mercedes-Euklid Model 29 calculator | 1923: Mercedes-Euklid Model 29 Demonstration calculator |
(collection Calculant) |
1923: Mercedes-Euklid Model 29 calculator (collection Calculant) | 1923: Mercedes-Euklid Model 29 Demonstration calculator |
1923: Mercedes-Euklid Model 29 calculator | 1923: Mercedes-Euklid Model 29 Demonstration calculator |
1923: Mercedes-Euklid Model 29 calculator | 1923: Mercedes-Euklid Model 29 Demonstration calculator |
http://meta-studies.net/pmwiki/uploads/Mercedes.png | http://meta-studies.net/pmwiki/uploads/MercedesDemo.png | |
1923: Mercedes-Euklid Model 29 calculator | 1923: Mercedes-Euklid Model 29 Demonstration calculator | (collection Calculant) |
http://meta-studies.net/pmwiki/uploads/Mercedes.png | http://meta-studies.net/pmwiki/uploads/MercedesDemo.png |
1923: Mercedes-Euklid Model 29 calculator | 1923: Mercedes-Euklid Model 29 Demonstration calculator |
(collection Calculant) |
|| http://meta-studies.net/pmwiki/uploads/Mercedes.png|| http://meta-studies.net/pmwiki/uploads/MercedesDemo.png|| || 1923: Mercedes-Euklid Model 29 calculator|| 1923: Mercedes-Euklid Model 29 Demonstration calculator||
http://meta-studies.net/pmwiki/uploads/Mercedes.png | http://meta-studies.net/pmwiki/uploads/MercedesDemo.png | |
1923: Mercedes-Euklid Model 29 calculator | 1923: Mercedes-Euklid Model 29 Demonstration calculator |
~1951 | Original Ohdner Model 39 serial 39–288965 | Ohdner | Pinwheel | [[Site.OriginalOhdner39–1951|Add Picture |
~1951 | Original Ohdner Model 39 serial 39–288965 | Ohdner | Pinwheel | Add Picture |
1957: Walther Demonstration WSR160 Pinwheel Calculator ~1957: Walther WSR160 Pinwheel Calculator
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
1923: Mercedes-Euklid Model 29 Demonstration calculator
1923: Mercedes-Euklid Model 29 calculator
|| http://meta-studies.net/pmwiki/uploads/Mercedes.png|| http://meta-studies.net/pmwiki/uploads/MercedesDemo.png|| || 1923: Mercedes-Euklid Model 29 calculator|| 1923: Mercedes-Euklid Model 29 Demonstration calculator|| (collection Calculant)
~1951 | Original Ohdner Model 39 serial 39–288965 | Ohdner | Pinwheel | http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png |
~1951 | Original Ohdner Model 39 serial 39–288965 | Ohdner | Pinwheel | [[Site.OriginalOhdner39–1951|Add Picture |
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
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).
http://meta-studies.net/pmwiki/uploads/ComptometerWoodie.png
Brunsviga Schuster Pinwheel Calculator ~1896
Serial 3406
(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 | http://meta-studies.net/pmwiki/uploads/Facit.png |
~1951 | Original Ohdner Model 39 serial 39–288965 | Ohdner | Pinwheel | http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png |
~1957 | Walther WSR160 Pinwheel Calculator | Walther | Pinwheel | http://meta-studies.net/pmwiki/uploads/Walther.png |
~1957 | Walther WSR160 Demonstration Pinwheel Calculator | Walther | Demonstration Pinwheel | http://meta-studies.net/pmwiki/uploads/WaltherDemo.png |
(collection Calculant - all above)
“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.
1950s | Bell Sumlock Comptometer | Bell Sumlock | Model 909/S/117.878 | http://meta-studies.net/pmwiki/uploads/Sumlock.png? |
1950s | Bell Sumlock Comptometer | Bell Sumlock | Model 909/S/117.878 | http://meta-studies.net/pmwiki/uploads/Sumlock.png |
1950s | Bell Sumlock Comptometer | Bell Sumlock | Model 909/S/117.878 | http://meta-studies.net/pmwiki/uploads/Sumlock.png? |
1950s | Bell Sumlock Comptometer | Bell Sumlock | Model 909/S/117.878 | http://meta-studies.net/pmwiki/uploads/Sumlock.png? |
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).-
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,
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.
~1955 | Bell Punch Sumlock | Bell Punch | Demonstration Comptometer | http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png |
~1955 | Bell Punch Sumlock | Bell Punch | Demonstration Comptometer | http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png |
~1955 | Bell Punch Sumlock | Demonstration Comptometer | http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png |
1950s | Bell Sumlock Comptometer | Model 909/S/117.878 | http://meta-studies.net/pmwiki/uploads/Sumlock.png? |
~1955 | Bell Punch Sumlock | Bell Punch | Demonstration Comptometer | http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png |
1950s | Bell Sumlock Comptometer | Bell Sumlock | Model 909/S/117.878 | http://meta-studies.net/pmwiki/uploads/Sumlock.png? |
Date | Maker | Type | Device (click for description) |
Date | Description | Maker | Type | Device (click for description) |
Date | Maker | Type | Device (click for description) |
Date | Description | Maker | Type | Device (click for description) |
Date | Maker | Type | Device (click for description) |
Date | Description | Maker | Type | Device (click for description) |
Date | Maker | Type | Device (click for description) |
~ 1955 | Bell Punch Sumlock | Demonstration Comptometer | http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png |
1950s | Bell Sumlock Comptometer | Model 909/S/117.878 | http://meta-studies.net/pmwiki/uploads/Sumlock.png? |
Date | Description | Maker | Type | Device (click for description) |
~1955 | Bell Punch Sumlock | Demonstration Comptometer | http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png | |
1950s | Bell Sumlock Comptometer | Model 909/S/117.878 | http://meta-studies.net/pmwiki/uploads/Sumlock.png? |
Note | Date | Maker | Type | Device (click for description) |
Date | Maker | Type | Device (click for description) |
Note | Date | Maker | Type | Device (click for description) |
Date | Maker | Type | Device (click for description) |
Note | Date | Maker | Type | Device (click for description) |
Date | Maker | Type | Device (click for description) |
~ 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)
Date | Maker | Type | Device (click for description) |
~ 1955 | Bell Punch Sumlock | Demonstration Comptometer | http://meta-studies.net/pmwiki/uploads/BellPunchDemo.png |
1950s | Bell Sumlock Comptometer | Model 909/S/117.878 | http://meta-studies.net/pmwiki/uploads/Sumlock.png? |
(collection Calculant - all above)
~ 1955 1950s: (made in Great Britain by Bell Punch Company Ltd)
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.)
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.
Web Patent Adder and Talley Board 1869
(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.)
1869 | Web Patent Adder and Talley Board | C.H. Webb NY | 2 Wheel | http://meta-studies.net/pmwiki/uploads/Webb.jpg |
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.)
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.
Locke Adder 1905–10 (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.)
1905–11 | Locke Adder | Clarence Locke | Rod | http://meta-studies.net/pmwiki/uploads/Locke.gif |
Sept 1896: Felt and Tarrant Comptometer: Earliest - wood-cased “Woodie” model, serial 2491 - a “model T” for industrial calculation.
1896: Felt and Tarrant Comptometer
Earliest - wood-cased model, serial 2491
(collection Calculant)
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,522 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.
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,523 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.
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.
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,524 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.
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.
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.525
1909 | TIM (Time is Money) Arithmometer | Ludwig Spitz & Co | Arithmometer | http://meta-studies.net/pmwiki/uploads/TIM.JPG |
~1913 | Bunzel-Denton Arithmometer | Bunzel | Prototype Front Crank | http://meta-studies.net/pmwiki/uploads/Bunzel.JPG |
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917.jpg |
1909 | TIM (Time is Money) Arithmometer | Ludwig Spitz & Co | Arithmometer | http://meta-studies.net/pmwiki/uploads/TIM.JPG |
~1913 | Bunzel-Denton Arithmometer | Bunzel | Prototype Front Crank | http://meta-studies.net/pmwiki/uploads/Bunzel.JPG |
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917.jpg |
Note | Date | Maker | Type | Device (click for description) |
1909 | TIM (Time is Money) Arithmometer | Ludwig Spitz & Co | Arithmometer | http://meta-studies.net/pmwiki/uploads/TIM.JPG |
~1913 | Bunzel-Denton Arithmometer | Bunzel | Prototype Front Crank | http://meta-studies.net/pmwiki/uploads/Bunzel.JPG |
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917.jpg |
Note | Date | Maker | Type | Device (click for description) |
1909 | TIM (Time is Money) Arithmometer | Ludwig Spitz & Co | Arithmometer | http://meta-studies.net/pmwiki/uploads/TIM.JPG |
~1913 | Bunzel-Denton Arithmometer | Bunzel | Prototype Front Crank | http://meta-studies.net/pmwiki/uploads/Bunzel.JPG |
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917.jpg |
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
Note | Date | Maker | Type | Device (click for description) |
1909 | TIM (Time is Money) Arithmometer | Ludwig Spitz & Co | Arithmometer | http://meta-studies.net/pmwiki/uploads/TIM.JPG |
~1913 | Bunzel-Denton Arithmometer | Bunzel | Prototype Front Crank | http://meta-studies.net/pmwiki/uploads/Bunzel.JPG |
~1917 | Madas IX Maxima | Madas | Auto Division | http://meta-studies.net/pmwiki/uploads/MADAS-1917.jpg |
(collection Calculant - all above)
http://meta-studies.net/pmwiki/uploads/ThomasDeColmar.jpg
http://meta-studies.net/pmwiki/uploads/ThomasDeColmar.jpg 1884: Thomas de Colmar Arithmometer Serial 2083 Model T1878 B
http://meta-studies.net/pmwiki/uploads/ThomasDeColmar.jpg
1884: Thomas de Colmar Arithmometer
Serial 2083 Model T1878 B
(collection Calculant - all above)
(collection Calculant - all above)
http://meta-studies.net/pmwiki/uploads/ThomasDeColmar.jpg 1884: Thomas de Colmar Arithmometer Serial 2083 Model T1878 B (collection Calculant)
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
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
1910 | Adall Adding Machine | Dreyfus and Levy | Key input Concentric toothed disk and groove | http://meta-studies.net/pmwiki/uploads/Adall.jpg |
1910 | Adall Adding Machine | Dreyfus and Levy | Key input Concentric toothed disk and groove | http://meta-studies.net/pmwiki/uploads/Adall.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 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
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.
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
1890–1900 | A. M. Stevenson Adder | Joliet, Ill. | 2 Wheel | http://meta-studies.net/pmwiki/uploads/Stevenson.png |
1890–1900 | A. M. Stevenson Adder | Joliet, Ill. | 2 Wheel | http://meta-studies.net/pmwiki/uploads/Stevenson.png |
1910 | Adall Adding Machine | Dreyfus and Levy | Key input Concentric toothed disk and groove | http://meta-studies.net/pmwiki/uploads/Adall.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.
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.
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.
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.
1890–1900 | A. M. Stevenson Adder | Joliet, Ill. | 2 Wheel | http://meta-studies.net/pmwiki/uploads/Stevenson.png| |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/Adix.png| |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Lightning.png| |
1968 | SEE Demonstration Adding Machine | Selective Educational Equipment Corporation | 4 Wheels | 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.
1890–1900 | A. M. Stevenson Adder | Joliet, Ill. | 2 Wheel | http://meta-studies.net/pmwiki/uploads/Stevenson.png |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/Adix.png |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Lightning.png |
1968 | SEE Demonstration Adding Machine | Selective Educational Equipment Corporation | 4 Wheels | 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.
1968 | SEE Demonstration Adding Machine | Selective Educational Equipment Corporation | 4 Wheels | http://meta-studies.net/pmwiki/uploads/Locke.gif| |
1968 | SEE Demonstration Adding Machine | Selective Educational Equipment Corporation | 4 Wheels | http://meta-studies.net/pmwiki/uploads/SEE-1.jpg| |
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
Note | Date | Maker | Type | Device (click for description) |
1869 | Web Patent Adder and Talley Board | C.H. Webb NY | 2 Wheel | http://meta-studies.net/pmwiki/uploads/Webb.jpg |
1890–1900 | A. M. Stevenson Adder | Joliet, Ill. | 2 Wheel | http://meta-studies.net/pmwiki/uploads/Stevenson.png| |
1903 | Adix Adding Machine Original model | Manheim | Key input lever & gears | http://meta-studies.net/pmwiki/uploads/Adix.png| |
~1946 | Lightning Portable Adding Machine | Lightning Adding Machine Co. L.A. | 7 Wheels | http://meta-studies.net/pmwiki/uploads/Lightning.png| |
1968 | SEE Demonstration Adding Machine | Selective Educational Equipment Corporation | 4 Wheels | http://meta-studies.net/pmwiki/uploads/Locke.gif| |
Note | Date | Type | Maker | Device (click for description) |
Note | Date | Maker | Type | Device (click for description) |
1905–11 | Locke Adder | Clarence Lock | Rod | http://meta-studies.net/pmwiki/uploads/Locke.gif |
1905–11 | Locke Adder | Clarence Locke | Rod | http://meta-studies.net/pmwiki/uploads/Locke.gif |
~1915 | Golden Gem Automatic Adding Machine | H. & H. Goldmann | Chain | http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg |
~1915 | Golden Gem Automatic Adding Machine | H. & H. Goldmann | Chain | http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg |
1937 | Add-O-Matic Adding Machine | Allied MFG. Co. | Chain | http://meta-studies.net/pmwiki/uploads/AddOMatic1.jpg |
1937 | Add-O-Matic Adding Machine | Allied MFG. Co. | Chain | http://meta-studies.net/pmwiki/uploads/AddOMatic1.jpg |
~1915 | Golden Gem Automatic Adding Machine | Chain | H. & H. Goldmann | http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg |
~1915 | Golden Gem Automatic Adding Machine | H. & H. Goldmann | Chain | http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg |
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.
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.
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
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.
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.
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.)
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.)
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.)
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
Note | Date | Type | Maker |
Note | Date | Type | Maker | Device (click for description) |
1937 | Add-O-Matic Adding Machine | Allied MFG. Co. | Chain | http://meta-studies.net/pmwiki/uploads/AddOMatic2.jpg |
1937 | Add-O-Matic Adding Machine | Allied MFG. Co. | Chain | http://meta-studies.net/pmwiki/uploads/AddOMatic1.jpg |
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.
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.)
: , serial 73158
1920: Addiator Troncet adder
1922: Scribola 10 column printing Adding Machine
1937: Add-O-Matic Adding Machine
1920 | Addiator Troncet adder | Ruthard & Co | Chain | http://meta-studies.net/pmwiki/uploads/Addiator.png |
1922 | Scribola 10 column printing Adding Machine | Addiator Gesellschaft | Rod | http://meta-studies.net/pmwiki/uploads/Scribola.jpg |
1937 | Add-O-Matic Adding Machine | Allied MFG. Co. | Chain | http://meta-studies.net/pmwiki/uploads/AddOMatic2.jpg |
1905–11 | Locke Adder | Clarence Lock | Rod | http://meta-studies.net/pmwiki/uploads/Locke.gif |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator.png |
~1915 | Golden Gem Automatic Adding Machine | Chain | H. & H. Goldmann | http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg |
1905–11 | Locke Adder | Clarence Lock | Rod | http://meta-studies.net/pmwiki/uploads/Locke.gif |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator.png |
~1915 | Golden Gem Automatic Adding Machine | Chain | H. & H. Goldmann | http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg |
1905–11 | Locke Adder | Clarence Lock | Rod | http://meta-studies.net/pmwiki/uploads/Locke.gif |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator.png |
~1915 | Golden Gem Automatic Adding Machine | Chain | H. & H. Goldmann | http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg |
1905–11 | Locke Adder | Clarence Lock | Rod | http://meta-studies.net/pmwiki/uploads/Locke.gif |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator.png |
~1915 | Golden Gem Automatic Adding Machine | Chain | H. & H. Goldmann | http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg |
Note | Date | Maker | |
1905–11 | Locke Adder | Clarence Lock | http://meta-studies.net/pmwiki/uploads/Locke.gif |
(ii) | 1759–69 | Edward Roberts Everard pattern gauger’s rule | 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
Note | Date | Type | Maker | |
1905–11 | Locke Adder | Clarence Lock | Rod | http://meta-studies.net/pmwiki/uploads/Locke.gif |
1910–20s | Comptator (9 col) | Schubert & Salzer | Chain | http://meta-studies.net/pmwiki/uploads/Comptator.png |
~1915 | Golden Gem Automatic Adding Machine | Chain | H. & H. Goldmann | http://meta-studies.net/pmwiki/uploads/GoldenGem.jpg |
: , serial 73158
Note | Date | Maker | |
1905–11 | Locke Adder | Clarence Lock | http://meta-studies.net/pmwiki/uploads/Locke.gif |
(ii) | 1759–69 | Edward Roberts Everard pattern gauger’s rule | http://meta-studies.net/pmwiki/uploads/Everard.jpg |
Proportional Rack Calculators
Proportional Rack Calculators
Evolutionary cul-de-sac: the search for true multiplication and division
Evolutionary cul-de-sac: the search for true multiplication and division
Harnessing electricity
Harnessing electricity
The Vanishing point: electronics and the arrival of the HP35
The Vanishing point: electronics and the arrival of the HP35
Commercial calculating machines
Arithmometers
Commercial calculating machines
Arithmometers
Comptometers
Comptometers
Pinwheels
Pinwheels
Curta: The peak of minituarisation (1947–1970)
Curta: The peak of minituarisation (1947–1970)
Arithmometers
Arithmometers
Comptometers
Comptometers
Commercial calculating machines
Arithmometers
Commercial calculating machines
Arithmometers
Comptometers
Comptometers
Pinwheels
Pinwheels
Proportional Rack Calculators
Proportional Rack Calculators
Curta: The peak of minituarisation (1947–1970)
Curta: The peak of minituarisation (1947–1970)
“Arms races” and mechanical evolution
“Arms races” and mechanical evolution
Evolutionary cul-de-sac: the search for true multiplication and division
Evolutionary cul-de-sac: the search for true multiplication and division
Harnessing electricity
Harnessing electricity
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 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
1903: Adix Adding Machine. Original model
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.
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.
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
Felt and Tarrant - a “model T” for industrial calculation.
Comptometers
Ohdner’s Pinwheels
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
~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
Proportional Rack Calculators
1923: Mercedes-Euklid Model 29 Demonstration calculator
1923: Mercedes-Euklid Model 29 calculator
~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
1904–1905: Bamberger’s Omega Calculating Machine
1912: Millionaire Calculating Machine serial 2015 (10×10×20)
~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
July1972: Hewlett Packard HP 35 Calculator serial 1230A 79429, 1972 (second version)
December 1973: Hewlett Packard HP 45 Calculator serial 1350A 36719, 1973
Simple linear mechanisms
Simple linear devices
Addiator, Golden Gem, Locke Adder Slide Rule
Simple rotational mechanisms
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
Webb Patent Adder (1869) Stevens Adder (1890s) Lightning (1940s) SEE
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
~1910 Adall Concentric-disk Adding Machine
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.
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.
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.
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.
- 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).
- 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,526 the height of columns of water).
Simple linear 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. 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.
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
Other simple approaches
Commercial calculating machines
http://meta-studies.net/pmwiki/uploads/Convertiseur.png
http://meta-studies.net/pmwiki/uploads/Convertiseur.png
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, 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.
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 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.
The dominant role of ready reckoners at this period is indicated by M. Norton Wise’s comment in relation to Victorian England that:
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.
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.
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.528 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.
Ropp’s Commercial Calculator, 1892
Ropp’s Commercial Calculator, 1892
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.
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.
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.
http://meta-studies.net/pmwiki/uploads/Ropp.jpg
http://meta-studies.net/pmwiki/uploads/Ropp.jpg Ropp’s Commercial Calculator, 1892 (collection Calculant)
http://meta-studies.net/pmwiki/uploads/Ropp.jpg
http://meta-studies.net/pmwiki/uploads/Ropp.jpg
Ready reckoners
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.
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.
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.
It was Thomas de Colmar who decisively built
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.
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.
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.
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.
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).
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, 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).
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.
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.
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).
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).
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.
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.
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.
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.
http://meta-studies.net/pmwiki/uploads/Convertiseur.png
Conversion device (from Aunes to Metres) ~1790
(collection Calculant)
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.
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.
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.
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.
« Part 2 The Modern Era | History Contents | »
1 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. (↑)
2 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. (↑)
3 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. (↑)
4 Patent no. 1420, 18 November 1820 (↑)
5 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. (↑)
6 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. (↑)
7 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 (↑)
8 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 (↑)
9 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. (↑)
10 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. (↑)
11 Diana H. Hook and Jeremy M. Norman, Origins of Cyberspace, Novato, California, 2002, p. 255. (↑)
12 Diana H. Hook and Jeremy M. Norman, Origins of Cyberspace, Novato, California, 2002, p. 255. (↑)
13 “Walther Company History”, http://www.carl-walther.de/cw.php?lang=en&content=history, viewed 23 July 2013. (↑)
14 Ray Mackay, “The Walther Company: Historic Recollections”, December 1997. http://www.xnumber.com/xnumber/walther.htm, viewed 22 July 2013. (↑)
15 John Wolff, “John Wolff’s Web Museum: Walther Calculators Overview” http://home.vicnet.net.au/~wolff/calculators/Walther/Walther.htm, viewed 23 July 2013. (↑)
16 “Walther Company History”, http://www.carl-walther.de/cw.php?lang=en&content=history, viewed 23 July 2013. (↑)
17 Ray Mackay, “The Walther Company: Historic Recollections”, December 1997. http://www.xnumber.com/xnumber/walther.htm, viewed 22 July 2013. (↑)
18 John Wolff, “John Wolff’s Web Museum: Walther Calculators Overview” http://home.vicnet.net.au/~wolff/calculators/Walther/Walther.htm, viewed 23 July 2013. (↑)
19 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. (↑)
20 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. (↑)
21 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. (↑)
22 ibid. (↑)
23 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.' (↑)
24 Johnston, “Making the arithmometer count”. (↑)
25 Brunel to Adams, 18 March 1866, Bristol University Library, Brunel Collection, Letter Book VII, f. 106, cited in Johnston, ibid. (↑)
26 Calculated using the http://www.measuringworth.com calculator on 21 July 2013 (↑)
27 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. (↑)
28 ibid. (↑)
29 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.' (↑)
30 Johnston, “Making the arithmometer count”. (↑)
31 Brunel to Adams, 18 March 1866, Bristol University Library, Brunel Collection, Letter Book VII, f. 106, cited in Johnston, ibid. (↑)
32 Calculated using the http://www.measuringworth.com calculator on 21 July 2013 (↑)
33 ibid (↑)
34 ibid (↑)
35 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
36 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
37 For more on this see Camilleri and Falk, Worlds in Transition, pp. 134–44. (↑)
38 For more on this see Camilleri and Falk, Worlds in Transition, pp. 134–44. (↑)
39 see Bruce O.B. Williams and Roger G. Johnson, “Ready Reckoners”, IEEE Annals of the History of Computing, October-December, 2005, pp. 64–80. (↑)
40 see Bruce O.B. Williams and Roger G. Johnson, “Ready Reckoners”, IEEE Annals of the History of Computing, October-December, 2005, pp. 64–80. (↑)
41 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. (↑)
42 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. (↑)
43 Patent no. 1420, 18 November 1820 (↑)
44 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. (↑)
45 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. (↑)
46 Patent no. 1420, 18 November 1820 (↑)
47 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. (↑)
48 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. (↑)
49 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
50 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
51 /’Origins of Cyberspace, p. 244. (↑)
52 ‘/Origins of Cyberspace, p. 244. (↑)
53 /’An Interview with Curt Herzstark/’, OH 140, conducted by Erwin Tomash on 10–11 September 1987, Nendeln, Liechtenstein, (English Translation). (↑)
54 An Interview with Curt Herzstark, OH 140, conducted by Erwin Tomash on 10–11 September 1987, Nendeln, Liechtenstein, (English Translation). (↑)
55 /’An Interview with Curt Herzstark/’ (↑)
56 /’The CURTA Calculator Page/’, http://www.vcalc.net/cu.htm, viewed 25 July 2013. (↑)
57 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. (↑)
58 1890: Leon Bollée Calculating Machine, "A New Calculating Machine of very General Applicability", The Manufacturer and Builder, July 1890, p. 156. Original print article. (↑)
59 1890: Leon Bollée Calculating Machine, "A New Calculating Machine of very General Applicability", The Manufacturer and Builder, July 1890, p. 156. Original print article. (↑)
60 1890: Leon Bollée Calculating Machine, "A New Calculating Machine of very General Applicability", The Manufacturer and Builder, July 1890, p. 156. Original print article. (↑)
61 1890: Leon Bollée Calculating Machine, "A New Calculating Machine of very General Applicability", The Manufacturer and Builder, July 1890, p. 156. Original print article. (↑)
62 /’Origins of Cyberspace/’ p. 242. (↑)
63 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. (↑)
64 Calculated using the http://www.measuringworth.com calculator on 24 July 2013 (↑)
65 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant). (↑)
66 Origins of Cyberspace p. 242. (↑)
67 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. (↑)
68 Calculated using the http://www.measuringworth.com calculator on 24 July 2013 (↑)
69 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant). (↑)
70 /’An Interview with Curt Herzstark/’, OH 140, conducted by Erwin Tomash on 10–11 September 1987, Nendeln, Liechtenstein, (English Translation). (↑)
71 An Interview with Curt Herzstark, OH 140, conducted by Erwin Tomash on 10–11 September 1987, Nendeln, Liechtenstein, (English Translation). (↑)
72 /’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. (↑)
73 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. (↑)
74 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 (↑)
75 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 (↑)
76 For more on this see Camilleri and Falk, Worlds in Transition, pp. 134–44. (↑)
77 For more on this see Camilleri and Falk, Worlds in Transition, pp. 134–44. (↑)
78 Werner Heisenberg, The Physicist’s Conception of Nature, Hutchinson Scientific and Technical, London, 1958, p. 11. (↑)
79 Werner Heisenberg, The Physicist’s Conception of Nature, Hutchinson Scientific and Technical, London, 1958, p. 11. (↑)
80 see Bruce O.B. Williams and Roger G. Johnson, “Ready Reckoners”, IEEE Annals of the History of Computing, October-December, 2005, pp. 64–80. (↑)
81 see Bruce O.B. Williams and Roger G. Johnson, “Ready Reckoners”, IEEE Annals of the History of Computing, October-December, 2005, pp. 64–80. (↑)
82 M.N. Wise, The Values of Precision, Princeton University Press, USA, 1995, p. 318. (↑)
83 M.N. Wise, The Values of Precision, Princeton University Press, USA, 1995, p. 318. (↑)
84 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 (↑)
85 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 (↑)
86 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. (↑)
87 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. (↑)
88 Patent no. 1420, 18 November 1820 (↑)
89 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. (↑)
90 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. (↑)
91 Patent no. 1420, 18 November 1820 (↑)
92 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. (↑)
93 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. (↑)
94 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. (↑)
95 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. (↑)
96 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. (↑)
97 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. (↑)
98 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
99 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. (↑)
100 ibid. (↑)
101 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.' (↑)
102 Johnston, “Making the arithmometer count”. (↑)
103 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
104 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. (↑)
105 ibid. (↑)
106 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.' (↑)
107 Johnston, “Making the arithmometer count”. (↑)
108 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 (↑)
109 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 (↑)
110 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. (↑)
111 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. (↑)
112 Diana H. Hook and Jeremy M. Norman, Origins of Cyberspace, Novato, California, 2002, p. 255. (↑)
113 Diana H. Hook and Jeremy M. Norman, Origins of Cyberspace, Novato, California, 2002, p. 255. (↑)
114 ibid (↑)
115 Hook and Norman, Origins of Cyberspace, p. 255. (↑)
116 ibid (↑)
117 Hook and Norman, Origins of Cyberspace, p. 255. (↑)
118 Martin, The Calculating Machines (↑)
119 http://www.rechnerlexikon.de/en/artikel/Spezial:Allpages (↑)
120 http://home.vicnet.net.au/~wolff/calculators/ (↑)
121 Martin, The Calculating Machines (↑)
122 http://www.rechnerlexikon.de/en/artikel/Spezial:Allpages (↑)
123 http://home.vicnet.net.au/~wolff/calculators/ (↑)
124 //Origins of Cyberspace, p. 244. (↑)
125 /’Origins of Cyberspace, p. 244. (↑)
126 An Interview with Curt Herzstark, OH 140, conducted by Erwin Tomash on 10–11 September 1987, Nendeln, Liechtenstein, (English Translation). (↑)
127 /’An Interview with Curt Herzstark/’, OH 140, conducted by Erwin Tomash on 10–11 September 1987, Nendeln, Liechtenstein, (English Translation). (↑)
128 An Interview with Curt Herzstark (↑)
129 The CURTA Calculator Page, http://www.vcalc.net/cu.htm, viewed 25 July 2013. (↑)
130 /’An Interview with Curt Herzstark/’ (↑)
131 /’The CURTA Calculator Page/’, http://www.vcalc.net/cu.htm, viewed 25 July 2013. (↑)
132 1890: Leon Bollée Calculating Machine, "A New Calculating Machine of very General Applicability", The Manufacturer and Builder, July 1890, p. 156. Original print article. (↑)
133 1890: Leon Bollée Calculating Machine, "A New Calculating Machine of very General Applicability", The Manufacturer and Builder, July 1890, p. 156. Original print article. (↑)
134 1890: Leon Bollée Calculating Machine, "A New Calculating Machine of very General Applicability", The Manufacturer and Builder, July 1890, p. 156. Original print article. (↑)
135 1890: Leon Bollée Calculating Machine, "A New Calculating Machine of very General Applicability", The Manufacturer and Builder, July 1890, p. 156. Original print article. (↑)
136 Origins of Cyberspace p. 242. (↑)
137 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. (↑)
138 Calculated using the http://www.measuringworth.com calculator on 24 July 2013 (↑)
139 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant). (↑)
140 /’Origins of Cyberspace/’ p. 242. (↑)
141 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. (↑)
142 Calculated using the http://www.measuringworth.com calculator on 24 July 2013 (↑)
143 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant). (↑)
144 An Interview with Curt Herzstark, OH 140, conducted by Erwin Tomash on 10–11 September 1987, Nendeln, Liechtenstein, (English Translation). (↑)
145 /’An Interview with Curt Herzstark/’, OH 140, conducted by Erwin Tomash on 10–11 September 1987, Nendeln, Liechtenstein, (English Translation). (↑)
146 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. (↑)
147 /’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. (↑)
148 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 (↑)
149 S. Moreland, A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence 1672, title page. (↑)
150 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 (↑)
151 S. Moreland, A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence 1672, title page. (↑)
152 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. (↑)
153 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. (↑)
154 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
155 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
156 An Interview with Curt Herzstark (↑)
157 The CURTA Calculator Page, http://www.vcalc.net/cu.htm, viewed 25 July 2013. (↑)
158 An Interview with Curt Herzstark (↑)
159 The CURTA Calculator Page, http://www.vcalc.net/cu.htm, viewed 25 July 2013. (↑)
160 see Bruce O.B. Williams and Roger G. Johnson, “Ready Reckoners”, IEEE Annals of the History of Computing, October-December, 2005, pp. 64–80. (↑)
161 see Bruce O.B. Williams and Roger G. Johnson, “Ready Reckoners”, IEEE Annals of the History of Computing, October-December, 2005, pp. 64–80. (↑)
162 see Bruce O.B. Williams and Roger G. Johnson, “Ready Reckoners”, IEEE Annals of the History of Computing, October-December, 2005, pp. 64–80. (↑)
163 see Bruce O.B. Williams and Roger G. Johnson, “Ready Reckoners”, IEEE Annals of the History of Computing, October-December, 2005, pp. 64–80. (↑)
164 see Bruce O.B. Williams and Roger G. Johnson, “Ready Reckoners”, IEEE Annals of the History of Computing, October-December, 2005, pp. 64–80. (↑)
165 see Bruce O.B. Williams and Roger G. Johnson, “Ready Reckoners”, IEEE Annals of the History of Computing, October-December, 2005, pp. 64–80. (↑)
166 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. (↑)
167 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. (↑)
168 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. (↑)
169 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. (↑)
170 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 (↑)
171 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 (↑)
172 Diana H. Hook and Jeremy M. Norman, Origins of Cyberspace, Novato, California, 2002, p. 255. (↑)
173 Diana H. Hook and Jeremy M. Norman, Origins of Cyberspace, Novato, California, 2002, p. 255. (↑)
174 ibid (↑)
175 Hook and Norman, Origins of Cyberspace, p. 255. (↑)
176 ibid (↑)
177 Hook and Norman, Origins of Cyberspace, p. 255. (↑)
178 //Origins of Cyberspace, p. 244. (↑)
179 //Origins of Cyberspace, p. 244. (↑)
180 An Interview with Curt Herzstark, OH 140, conducted by Erwin Tomash on 10–11 September 1987, Nendeln, Liechtenstein, (English Translation). (↑)
181 An Interview with Curt Herzstark, OH 140, conducted by Erwin Tomash on 10–11 September 1987, Nendeln, Liechtenstein, (English Translation). (↑)
182 see Bruce O.B. Williams and Roger G. Johnson, “Ready Reckoners”, IEEE Annals of the History of Computing, October-December, 2005, pp. 64–80. (↑)
183 see Bruce O.B. Williams and Roger G. Johnson, “Ready Reckoners”, IEEE Annals of the History of Computing, October-December, 2005, pp. 64–80. (↑)
184 M.N. Wise, The Values of Precision, Princeton University Press, USA, 1995, p. 318. (↑)
185 M.N. Wise, The Values of Precision, Princeton University Press, USA, 1995, p. 318. (↑)
186 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 (↑)
187 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 (↑)
188 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. (↑)
189 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. (↑)
190 Patent no. 1420, 18 November 1820 (↑)
191 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. (↑)
192 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. (↑)
193 Patent no. 1420, 18 November 1820 (↑)
194 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. (↑)
195 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. (↑)
196 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. (↑)
197 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. (↑)
198 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. (↑)
199 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. (↑)
200 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. (↑)
201 ibid. (↑)
202 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.’ (↑)
203 Johnston, “Making the arithmometer count”. (↑)
204 Brunel to Adams, 18 March 1866, Bristol University Library, Brunel Collection, Letter Book VII, f. 106, cited in Johnston, ibid. (↑)
205 Calculated using the http://www.measuringworth.com calculator on 21 July 2013 (↑)
206 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. (↑)
207 ibid. (↑)
208 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.' (↑)
209 Johnston, “Making the arithmometer count”. (↑)
210 Brunel to Adams, 18 March 1866, Bristol University Library, Brunel Collection, Letter Book VII, f. 106, cited in Johnston, ibid. (↑)
211 Calculated using the http://www.measuringworth.com calculator on 21 July 2013 (↑)
212 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 (↑)
213 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 (↑)
214 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. (↑)
215 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. (↑)
216 Diana H. Hook and Jeremy M. Norman, Origins of Cyberspace, Novato, California, 2002, p. 255. (↑)
217 Diana H. Hook and Jeremy M. Norman, Origins of Cyberspace, Novato, California, 2002, p. 255. (↑)
218 1890: Leon Bollée Calculating Machine, “A New Calculating Machine of very General Applicability”, The Manufacturer and Builder, July 1890, p. 156. Original print article. (↑)
219 1890: Leon Bollée Calculating Machine, "A New Calculating Machine of very General Applicability", The Manufacturer and Builder, July 1890, p. 156. Original print article. (↑)
220 1890: Leon Bollée Calculating Machine, “A New Calculating Machine of very General Applicability”, The Manufacturer and Builder, July 1890, p. 156. Original print article. (↑)
221 1890: Leon Bollée Calculating Machine, "A New Calculating Machine of very General Applicability", The Manufacturer and Builder, July 1890, p. 156. Original print article. (↑)
222 Origins of Cyberspace p. 242. (↑)
223 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. (↑)
224 Calculated using the http://www.measuringworth.com calculator on 24 July 2013 (↑)
225 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant). (↑)
226 Origins of Cyberspace p. 242. (↑)
227 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. (↑)
228 Calculated using the http://www.measuringworth.com calculator on 24 July 2013 (↑)
229 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant). (↑)
230 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. (↑)
231 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. (↑)
232 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 (↑)
233 S. Moreland, A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence 1672, title page. (↑)
234 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 (↑)
235 S. Moreland, A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence 1672, title page. (↑)
236 1890: Leon Bollée Calculating Machine, “A New Calculating Machine of very General Applicability”, The Manufacturer and Builder, July 1890, p. 156. Original print article. (↑)
237 1890: Leon Bollée Calculating Machine, “A New Calculating Machine of very General Applicability”, The Manufacturer and Builder, July 1890, p. 156. Original print article. (↑)
238 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. (↑)
239 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. (↑)
240 1890: Leon Bollée Calculating Machine, “A New Calculating Machine of very General Applicability”, The Manufacturer and Builder, July 1890, p. 156. Original print article. (↑)
241 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. (↑)
242 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. (↑)
243 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. (↑)
244 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 (↑)
245 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 (↑)
246 An Interview with Curt Herzstark (↑)
247 The CURTA Calculator Page, http://www.vcalc.net/cu.htm, viewed 25 July 2013. (↑)
248 An Interview with Curt Herzstark (↑)
249 The CURTA Calculator Page, http://www.vcalc.net/cu.htm, viewed 25 July 2013. (↑)
250 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. (↑)
251 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. (↑)
252 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 (↑)
253 S. Moreland, A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence 1672, title page. (↑)
254 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 (↑)
255 S. Moreland, A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence 1672, title page. (↑)
256 An Interview with Curt Herzstark (↑)
257 The CURTA Calculator Page, http://www.vcalc.net/cu.htm, viewed 25 July 2013. (↑)
258 An Interview with Curt Herzstark (↑)
259 The CURTA Calculator Page, http://www.vcalc.net/cu.htm, viewed 25 July 2013. (↑)
260 An Interview with Curt Herzstark (↑)
261 An Interview with Curt Herzstark (↑)
262 The CURTA Calculator Page, http://www.vcalc.net/cu.htm, viewed 25 July 2013. (↑)
263 An Interview with Curt Herzstark, OH 140, conducted by Erwin Tomash on 10–11 September 1987, Nendeln, Liechtenstein, (English Translation). (↑)
264 An Interview with Curt Herzstark, OH 140, conducted by Erwin Tomash on 10–11 September 1987, Nendeln, Liechtenstein, (English Translation). (↑)
265 An Interview with Curt Herzstark, OH 140, conducted by Erwin Tomash on 10–11 September 1987, Nendeln, Liechtenstein, (English Translation). (↑)
266 An Interview with Curt Herzstark, OH 140, conducted by Erwin Tomash on 10–11 September 1987, Nendeln, Liechtenstein, (English Translation). (↑)
267 An Interview with Curt Herzstark (↑)
268 An Interview with Curt Herzstark, OH 140, conducted by Erwin Tomash on 10–11 September 1987, Nendeln, Liechtenstein, (English Translation). (↑)
269 An Interview with Curt Herzstark, OH 140, conducted by Erwin Tomash on 10–11 September 1987, Nendeln, Liechtenstein, (English Translation). (↑)
270 An Interview with Curt Herzstark, OH 140, conducted by Erwin Tomash on 10–11 September 1987, Nendeln, Liechtenstein, (English Translation). (↑)
271 An Interview with Curt Herzstark, OH 140, conducted by Erwin Tomash on 10–11 September 1987, Nendeln, Liechtenstein, (English Translation). (↑)
272 An Interview with Curt Herzstark, OH 140, conducted by Erwin Tomash on 10–11 September 1987, Nendeln, Liechtenstein, (English Translation). (↑)
273 An Interview with Curt Herzstark, OH 140, conducted by Erwin Tomash on 10–11 September 1987, Nendeln, Liechtenstein, (English Translation). (↑)
274 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. (↑)
275 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. (↑)
276 US Patent 809075, Filed by Alexander Rechnitzer of Viennea, US Patent Office, 29 June 1901, granted 2 January 1906, page 9, clauses 80–110. (↑)
277 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. (↑)
278 US Patent 809075, Filed by Alexander Rechnitzer of Viennea, US Patent Office, 29 June 1901, granted 2 January 1906, page 9, clauses 80–110. (↑)
279 US Patent 809075, Filed by Alexander Rechnitzer of Viennea, US Patent Office, 29 June 1901, granted 2 January 1906, page 9, clauses 80–110. (↑)
280 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. (↑)
281 US Patent 809075, Filed by Alexander Rechnitzer of Viennea, US Patent Office, 29 June 1901, granted 2 January 1906, page 9, clauses 80–110. (↑)
282 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. (↑)
283 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. (↑)
284 Origins of Cyberspace, p. 242. (↑)
285 Origins of Cyberspace, p. 242. (↑)
286 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. (↑)
287 Origins of Cyberspace, p. 242. (↑)
288 //Origins of Cyberspace, p. 244. (↑)
289 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 (↑)
290 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 (↑)
291 Origins of Cyberspace, p. 242. (↑)
292 Origins of Cyberspace p. 242. (↑)
293 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. (↑)
294 Calculated using the http://www.measuringworth.com calculator on 24 July 2013 (↑)
295 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant). (↑)
296 Origins of Cyberspace p. 242. (↑)
297 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. (↑)
298 Calculated using the http://www.measuringworth.com calculator on 24 July 2013 (↑)
299 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant). (↑)
300 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. (↑)
301 Calculated using the http://www.measuringworth.com calculator on 24 July 2013 (↑)
302 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant). (↑)
303 Origins of Cyberspace p. 242. (↑)
304 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. (↑)
305 Calculated using the http://www.measuringworth.com calculator on 24 July 2013 (↑)
306 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant). (↑)
307 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. (↑)
308 Calculated using the http://www.measuringworth.com calculator on 24 July 2013 (↑)
309 Price list in Edmonds Collins, The Millionaire Calculating Machine, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. (↑)
310 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. (↑)
311 Calculated using the http://www.measuringworth.com calculator on 24 July 2013 (↑)
312 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant). (↑)
313 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant) (↑)
314 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. (↑)
315 Calculated using the http://www.measuringworth.com calculator on 24 July 2013 (↑)
316 Price list in Edmonds Collins, The Millionaire Calculating Machine, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. (↑)
317 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. (↑)
318 Calculated using the http://www.measuringworth.com calculator on 24 July 2013 (↑)
319 Price list in Edmonds Collins, The Millionaire Calculating Machine, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. (↑)
320 Calculated using the http://www.measuringworth.com calculator on 24 July 2013 (↑)
321 Price list in Edmonds Collins, The Millionaire Calculating Machine, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. (↑)
322 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant) (↑)
323 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. (↑)
324 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant) (↑)
325 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. (↑)
326 Calculated using the http://www.measuringworth.com calculator on 24 July 2013 (↑)
327 Price list in Edmonds Collins, The Millionaire Calculating Machine, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. (↑)
328 Price list in Edmonds Collins, The Millionaire Calculating Machine, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. (↑)
329 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant) (↑)
330 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. (↑)
331 Calculated using the http://www.measuringworth.com calculator on 24 July 2013 (↑)
332 Price list in Edmonds Collins, The Millionaire Calculating Machine, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. (↑)
333 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant) (↑)
334 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. (↑)
335 Edmonds Collins, The Millionaire Calculating Machine, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. (↑)
336 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant) (↑)
337 see also price of US$500 at 1914 prices (about $11,700 in 2013 USCalculated 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. (↑)
338 Price list in Edmonds Collins, The Millionaire Calculating Machine, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. (↑)
339 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant) (↑)
340 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. (↑)
341 Edmonds Collins, The Millionaire Calculating Machine, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. (↑)
342 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant) (↑)
343 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. (↑)
344 Edmonds Collins, The Millionaire Calculating Machine, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. (↑)
345 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant) (↑)
346 see also price of US$500 at 1914 prices (about $11,700 in 2013 USCalculated 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. (↑)
347 Edmonds Collins, The Millionaire Calculating Machine, pamphlet, Edmond Collins, 35 Dearborn St, Central Chicago, ~1912. (↑)
348 Letter from H.W. Egli Ltd, Zurich, dated 20 November 1967 (collection Calculant) (↑)
349 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. (↑)
350 Martin, The Calculating Machines (↑)
351 http://www.rechnerlexikon.de/en/artikel/Spezial:Allpages (↑)
352 http://home.vicnet.net.au/~wolff/calculators/ (↑)
353 Martin, The Calculating Machines (↑)
354 http://www.rechnerlexikon.de/en/artikel/Spezial:Allpages (↑)
355 http://home.vicnet.net.au/~wolff/calculators/ (↑)
356 Martin, The Calculating Machines (↑)
357 http://www.rechnerlexikon.de/en/artikel/Spezial:Allpages (↑)
358 http://home.vicnet.net.au/~wolff/calculators/ (↑)
359 Martin, The Calculating Machines (↑)
360 http://www.rechnerlexikon.de/en/artikel/Spezial:Allpages (↑)
361 http://home.vicnet.net.au/~wolff/calculators/ (↑)
362 Martin, The Calculating Machines (↑)
363 http://www.rechnerlexikon.de/en/artikel/Spezial:Allpages (↑)
364 http://home.vicnet.net.au/~wolff/calculators/ (↑)
365 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. (↑)
366 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. (↑)
367 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 (↑)
368 S. Moreland, A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence 1672, title page. (↑)
369 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 (↑)
370 S. Moreland, A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence 1672, title page. (↑)
371 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 (↑)
372 S. Moreland, A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence 1672, title page. (↑)
373 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 (↑)
374 S. Moreland, A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence 1672, title page. (↑)
375 (↑)
376 S. Moreland, A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence 1672, title page. (↑)
377 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 (↑)
378 S. Moreland, A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence 1672, title page. (↑)
379 (↑)
380 S. Moreland, A New and Most Useful Instrument for Addition and Subtraction of Pounds, Shillings and Pence 1672, title page. (↑)
381 ibid (↑)
382 ibid (↑)
383 Hook and Norman, Origins of Cyberspace, p. 255. (↑)
384 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. (↑)
385 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. (↑)
386 ibid (↑)
387 The Gentleman’s Magazine, 1857. (↑)
388 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. (↑)
389 The Gentleman’s Magazine, 1857. (↑)
390 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. (↑)
391 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. (↑)
392 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. (↑)
393 “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. (↑)
394 John Wolff, “John Wolff’s Web Museum: Walther Calculators Overview” http://home.vicnet.net.au/~wolff/calculators/Walther/Walther.htm, viewed 23 July 2013. (↑)
395 “Walther Company History”, http://www.carl-walther.de/cw.php?lang=en&content=history, viewed 23 July 2013. (↑)
396 Ray Mackay, “The Walther Company: Historic Recollections”, December 1997. http://www.xnumber.com/xnumber/walther.htm, viewed 22 July 2013. (↑)
397 John Wolff, “John Wolff’s Web Museum: Walther Calculators Overview” http://home.vicnet.net.au/~wolff/calculators/Walther/Walther.htm, viewed 23 July 2013. (↑)
398 “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. (↑)
399 John Wolff, “John Wolff’s Web Museum: Walther Calculators Overview” http://home.vicnet.net.au/~wolff/calculators/Walther/Walther.htm, viewed 23 July 2013. (↑)
400 “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. (↑)
401 John Wolff, “John Wolff’s Web Museum: Walther Calculators Overview” http://home.vicnet.net.au/~wolff/calculators/Walther/Walther.htm, viewed 23 July 2013. (↑)
402 Ray Mackay, “The Walther Company: Historic Recollections”, December 1997. http://www.xnumber.com/xnumber/walther.htm, viewed 22 July 2013. (↑)
403 “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. (↑)
404 John Wolff, “John Wolff’s Web Museum: Walther Calculators Overview” http://home.vicnet.net.au/~wolff/calculators/Walther/Walther.htm, viewed 23 July 2013. (↑)
405 ibid (↑)
406 ibid (↑)
407 Ray Mackay, “The Walther Company: Historic Recollections”, December 1997. http://www.xnumber.com/xnumber/walther.htm, viewed 22 July 2013. (↑)
408 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 (↑)
409 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 (↑)
410 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 (↑)
411 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 (↑)
412 ibid (↑)
413 Diana H. Hook and Jeremy M. Norman, Origins of Cyberspace, Novato, California, 2002, p. 255. (↑)
414 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. (↑)
415 ibid. (↑)
416 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.’ (↑)
417 Johnston, “Making the arithmometer count”. (↑)
418 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. (↑)
419 ibid. (↑)
420 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.’ (↑)
421 Johnston, “Making the arithmometer count”. (↑)
422 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. (↑)
423 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. (↑)
424 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. (↑)
425 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. (↑)
426 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. (↑)
427 ibid. p 198. (↑)
428 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 (↑)
429 ibid. p 198. (↑)
430 ibid. p 198. (↑)
431 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 (↑)
432 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 (↑)
433 Brunel to Adams, 18 March 1866, Bristol University Library, Brunel Collection, Letter Book VII, f. 106, cited in Johnston, ibid. (↑)
434 Brunel to Adams, 18 March 1866, Bristol University Library, Brunel Collection, Letter Book VII, f. 106, cited in Johnston, ibid. (↑)
435 Calculated using the http://www.measuringworth.com calculator on 21 July 2013 (↑)
436 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 (↑)
437 ibid (↑)
438 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 (↑)
439 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. (↑)
440 ibid. (↑)
441 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.’ (↑)
442 Johnston, “Making the arithmometer count”. (↑)
443 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. (↑)
444 ibid. (↑)
445 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.’ (↑)
446 Johnston, “Making the arithmometer count”. (↑)
447 Brunel to Adams, 18 March 1866, Bristol University Library, Brunel Collection, Letter Book VII, f. 106, cited in Johnston, ibid. (↑)
448 ibid. (↑)
449 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.’ (↑)
450 Johnston, “Making the arithmometer count”. (↑)
451 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. (↑)
452 ibid. (↑)
453 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.’ (↑)
454 Johnston, “Making the arithmometer count”. (↑)
455 ibid. (↑)
456 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”. (↑)
457 ibid. (↑)
458 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.’ (↑)
459 Johnston, “Making the arithmometer count”. (↑)
460 Patent no. 1420, 18 November 1820 (↑)
461 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. (↑)
462 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. (↑)
463 Patent no. 1420, 18 November 1820 (↑)
464 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. (↑)
465 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. (↑)
466 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
467 ibid. (↑)
468 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
469 ibid. (↑)
470 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”. (↑)
471 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
472 ibid. (↑)
473 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
474 ibid. (↑)
475 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
476 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
477 ibid. (↑)
478 Patent no. 1420, 18 November 1820 (↑)
479 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. (↑)
480 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
481 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. (↑)
482 Patent no. 1420, 18 November 1820 (↑)
483 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. (↑)
484 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. (↑)
485 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
486 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. (↑)
487 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 (↑)
488 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. (↑)
489 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 (↑)
490 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. (↑)
491 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. (↑)
492 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. (↑)
493 Patent no. 1420, 18 November 1820 (↑)
494 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. (↑)
495 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
496 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 (↑)
497 Patent no. 1420, 18 November 1820 (↑)
498 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. (↑)
499 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
500 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. (↑)
501 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 (↑)
502 Patent no. 1420, 18 November 1820 (↑)
503 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. (↑)
504 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
505 Patent no. 1420, 18 November 1820 (↑)
506 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. (↑)
507 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
508 Patent no. 1420, 18 November 1820 (↑)
509 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. (↑)
510 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
511 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 (↑)
512 Patent no. 1420, 18 November 1820 (↑)
513 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. (↑)
514 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
515 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 (↑)
516 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 (↑)
517 Patent no. 1420, 18 November 1820 (↑)
518 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. (↑)
519 Stephen Johnston, “Making the arithmometer count”, Bulletin of the Scientific Instrument Society, Volume 52, 1997, pp. 12–21. (↑)
520 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 (↑)
521 1890: Leon Bollée Calculating Machine, “A New Calculating Machine of very General Applicability”, The Manufacturer and Builder, July 1890, p. 156. Original print article. (↑)
522 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. (↑)
523 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. (↑)
524 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. (↑)
525 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 (↑)
526 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 (↑)
527 M.N. Wise, The Values of Precision, Princeton University Press, USA, 1995, p. 318. (↑)
528 see Bruce O.B. Williams and Roger G. Johnson, “Ready Reckoners”, IEEE Annals of the History of Computing, October-December, 2005, pp. 64–80. (↑)
Dynamic change.
A time of change.
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.2 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:
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.
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.3 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:
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.
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.4 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.
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.5 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:
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.6 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
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.7 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.
Usefulness arises in a context, and the social, political, economic and technological context was in a process of unprecedented transformation. From
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.8 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 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.
Dynamic change.
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.
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!
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
“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.
Thomas de Colmar - the advent of the commercially useful calculating machine
Thomas de Colmar - a commercial calculator
Many variations. Eg Frieden’s cam timed “Frieden wheel”.
Thomas de Colmar
Thomas de Colmar - the advent of the commercially useful calculating machine
Mechanical minituarisation at its best - the Curta Calculator (1947–1970)
Curta: The peak of minituarisation (1947–1970)
Building on Napier’s rods: the search to automate multiplication and division
Electricity could be utilised once there was a national grid….
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.
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.
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….
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,
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….
Vanishing point: electronics and the arrival of the HP35
The Vanishing point: electronics and the arrival of the HP35
The blind alley - the search for true multiplication and division
Evolutionary cul-de-sac: the search for true multiplication and division
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.
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.
The blind alley - the search for true multiplication and division
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.
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,
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.
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).-
Ohdner’s Pinwheels
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)
Mechanical minituarisation at its best - the Curta Calculator (1947–1970)
Vanishing point: the arrival of the HP35
Vanishing point: electronics and the arrival of the HP35
To be continued….
To be continued….
Notes as I think about what I will write next!
Notes as I think about what I will write next!
The expansion of the market in the late Modern period.
The expansion of the market in the late Modern period.
Simple devices
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.
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 be continued….
To be continued….
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.
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.
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.
Late Modern 1800 - mid 2000
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.
(:title The Late Modern Period (from 1800) :)
« Part 2 The Modern Era | History Contents |
»
(:title The Late Modern Period (from 1800) :)
(:title The Late Modern Period (from 1800)
(:title The Late Modern Period (from 1800) :)
(:title The Late Modern Period (1800 -) and commercial mechanical calculation:)
Part 3. The Advent of Commercial Mechanical Calculation.
(:title The Late Modern Period (from 1800)
Part 3. The Advent of Commercial Mechanical Calculation.
(:toc:)
Commercial mechanical calculation
(:title The Late Modern Period (1800 -) and commercial mechanical calculation:)
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