The Arithmetical Machine of Christian Ludwig Gersten

Christian Ludwig Gersten (07.02.1701-13.08.1762) was born in Gießen, a town in the German federal state (Bundesland) of Hessen. He studied law and mathematics at the University of his home town. In the beginning of 1730s he went to England to extend his mathematical knowledge and in 1733 became a fellow of the English Royal Society. In the same 1733 he went back to Gießen, to accept the position of a professor of mathematics at the University.

Gersten is primarily known by his book for a series of experiments, using the barometer, titled "Tentamina Systematis Novi ad Mutationes Barometri ex Natura elateris Aerei demonstrandas, cui adjecta sub finem Dissertatio Roris decidui errorem Antiquum et vulgarem per Observationes et Experimenta Nova excutiens". Gersten as a matter of fact was the first scientist to find out, based on observations, that dew did not fall from the heavens, but ascends from earth, especially from plants.

In 1735 Gersten traveled again to London, to present to the Royal Society his project of arithmetical machine. In this description he claims, that this machine has been designed 12 or 13 years before, most probably in 1722.

In his 19-pages detailed presentation Gersten mentioned, that he has been acquainted with the machines of Morland, Leibniz, Poleni and Leupold. The first prototype of the machine was wooden, and after the device has been presented to the friends of Gersten, they encouraged him to continue the development. The second copy was made from brass and in the end of 1725 Gersten presented it to the Langrave of Hessen Darmstadt, who admired the inventor. Nothing more is known for the machine of Gersten. At the present day exists only a replica of the device (see the nearby figure).

Let's examine the arrangement of the machine in sketch from the presentation to the Royal Society (the figure below):

A sketch of Gersten's machine from the presentation to the Royal Society

The dimensions of the machine are—37 cm width, 37 cm height, 7 cm thickness. It has 6 positional input mechanism and 7 positional display mechanism (from the design of the machine is evident, that it can be easily extended with additional positional modules). In the part 1 of the upper figure are shown the first 3 digital positions—for units (marked with AA), for tens (marked with BB), and for hundreds (CC). Every position has 2 sliders, first of them (the upper one) Gersten named operator, the second one—determinator. The determinator indicates what number will be entered in the calculating mechanism, while the entering is done by moving the operator.

The main element in the calculating mechanism in the machine are ratched-wheels. They are used in the digital dials for entering of the numbers, and for tens carry during the calculations.

At the end of his presentation, the inventor acknowledged, that the major constructive problem of the machine is significant friction between the parts of the mechanism, when must be done tens carry for two or more digital positions.

The machine of Gersten is not so elaborate and easy for operation, as the machines of the other early inventors, but nevertheless it is a well designed and fully capable for calculations device.