Mechanical calculators

The first calculating machines were built in the 17th century by gifted mathematicians moved by the intense desire to simplify the repetitive nature of arithmetical operations. At the end of the Middle Ages, the growing trade  asked for more evolved instruments to calculate faster and more accurate than the cumbersome slide rule or abacus.Finally the Renascence offered a financial and social strong base for the development of new inventions, including the mechanical calculating machine.

Contrary to some sources, it is generally accepted that not the invention of John Napier's bones but the adding machine of Wilhelm Shickard, maths professor at the University of Tübingen in 1623, has been the first mechanical calculator. His machine was based on the movement of six dented weels, geared through a mutilated wheel which with every full turn allowed the wheel located at the right to rotate 1/10th of a full turn. It could add and substract up to six-digit numbers.

But only one or two prototypes were constructed so even highly notified tradespeople still had to work with abacus or slide rule.  Until a certain 17 year old Blaise Pascal, son of a tax collector in Rouen, started with the development of a new calculating system for his father. The "Pascaline" built in 1643, was probably the first mechanical adding device actually used for a practical purpose.

He pursued the object of the whole self-acting course of the calculations normally made with slide rule or abacus. For that reason, he based his appliance on the already existing 'automatic transport' but equipped with the dial of a telephone.

The machine was built on a brass rectangular box, where a set of notched dials (5 or 6 or even 8) moved internal wheels in a way that a full rotation of a wheel caused the wheel at the left to advance one 10th. A pin was used to rotate the dials.

As opposed to Schickard's machine, the wheels moved only clockwise and were designed to add numbers. Pascal's machine is essentially an adding device; substraction is performed by the addition of complements. The construction of this instrument was expensive and caused numberless difficulties. As a result it didn't get wide acceptance but even until the beginning of the 20th century, several inventors built calculating machines on this design.

Blaise Pascal(1623-1662)was a unique and multilateral man. As a philosopher he searched after the survival of the human soul,  as writer-poet he wrote down his contemplations "on the greatness and misery of man". But he is best known as a physicist and a gifted mathematician. He is considered as the  coinventor of the probability theory with Fermat.   His love for physics and maths moved him to develop : 'the law of Pascal : the mystic hexagram theorem in geometry ' and 'the triangle of Pascal and the application of binomial expansions to probability' and the science of hydraulics. In the end he turned his back on the world for reasons of his strong religious convictions.

In 1678 the Frenchman le Grillet De Roven designed a calculating machine in which the system with the rods of Napier are equipped with the 'transport' of Pascal.But the most important step forwards was the "staffelwals or stepped rechoner" made by G.W. Von Leibniz in 1673.

"For it is unworthy of excellent men to lose hours like slaves in the labour of calculation which would safely be relegated to anyone else if machines were used" (G.W. Von Leibniz)

Gottfried Wilhelm Von Leibniz(1646-1716), German philosopher and mathematician, made a calculating machine able to perform all four basic arithmetical operations. With his technique, similar to the technique used by Pascal, multiplications and divisions were seen as a repetition of respectively additions and substractions. This was possible because of the use of cogwheels. Even though this principle, together with Pascal's design, was a basis for many mechanical calculators, this out- standing polymaths died in poverty and unrewarded.

An Italian marquis, Giovanni Poleni, designed in 1709 an other calculating machine, not based on the 'staffelwals' but on the so called 'nokkelwiel' principle. This professor tried to make a machine without the techniques of Leibniz and Pascal. He wanted to do all the manipulations automatically without the traditional poles, buttons and levers. But the working was too difficult for the common people.

Special consideration deserves Phillip Mathieus Hahn who developed in 1773 the first functional calculator, based on Leibniz's stepped drum, containing a set of 12 drums in a circular arrangement actuated by a crank located in the axis of the arrangement. Hahn made these machines until his death in 1790. But his two sons and his brother-in-law, Johann Christopher Schuster, continued with the manufacturing so that in 1820 in France a grandiose fabrication was going on, which in Germany had failed.

In 1820 Charles Xavier Thomas de Colmar made a machine, the 'arithmometer', based on Leibniz's design which was capable of performing the four operations in a simple and reliable way. His machine was very successful, ca. 1500 Thomas' machines were constructed between 1820 and 1878.

In the mean time, due to the developments of techniques in the 19th century, it became possible to make precious mechanical pieces; with the consequence that inventors didn't have to construct their own materials. The result was that the newest machines followed each other even more quickly.

In 1894 appeared the arithmometer of Maurel, known as 'arithmaurel'and in 1883 a calculating machine with a circular form was designed by Edmonson. During the following years many forms and models appeared on the market.
But al these machines could only make manipulations with the 'transport' principle of Poleni.

New techniques unfurled but the most important renovation was introduced by the English mathematician Charles Babbage(1792-1871).
In 1728 a French engineer, Falcon invented the punched card system, this modus was used in automatic weaving mills and other factories. But it had never been used with calculating machines. Only Babbage got the idea to apply this system on calculators. In fact Babbage would never have had the idea without Falcon's work.

Charles Babbage designed namely a machine, which could make sixty-six manipulations in one minute. He started in 1833 to build a machine were the punched cards would give the dedications, just like with the weaving machines. He wanted a machine that could do the most difficult algebraic manipulations with the help of a 'memory' of two hundred groups of each 25 cogwheels. (Which had to keep the dedication of the punch cards).

calcbabar.gif (4867 bytes) Unfortunately during his life there weren't enough financial possibilities to practise his work. But the basis for the designs for electronical calculating machines was raised.

Later some of his colleague scientists made this machine.

Later developments:

In 1850 D.D.Parmelee designed the first calculating machine with keyboard; later also Dorr E.Felt and Tarrant presented in 1887 an adder with full keyboard on which could be inscribed all the figures of a number in the same way as a chord is struck on a piano. Also in 1887 Léon Bollée made a machine that could make automatical multiplications.

The latest important development in the history of the mechanical calculators came from the German constructor Hamann. In 1925 he made a machine which by proportional levers executed different manipulations.

At least there were also the 'Marchant' calculating machines, originating from America, which were rather typical because of their proportional cograilways.

Conclusion

In the history of the mechanical calculating machines, the ideas of Pascal were very important. 

His dream was to make an apparatus with a mechanical intellect that could do all the manipulations. His principle together with many improvements made by other inventors turned his dream almost into reality.

Pascal ever said:
'The science from the soul, I will put that into a mechanical handling.'

This thought marks the end of the history of mechanical calculators, let's watch the electronic brain now !

 

Sofie Moorthamers

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