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Jacobson’s Calculating Machine

The earliest of the mechanical calculating machines that survived till contemporary times in the USSR is displayed in the RAS Museum of Anthropology and Ethnography named after M. V. Lomonosov in Leningrad (now St. Petersburg). It is of original and unique design which of no doubt is of tremendous interest to the museum goers.

The calculating machine has the form of a brass box 34.2 cm long, 21.8 cm wide and 3.4 cm high and is standing on four chiseled legs 1.6 cm in diameter and 1 cm high. There are a number of inscriptions and numerals on the lavishly ornamented upper lid of the device. Let’s study the most interesting of the signatures more attentively.  

There is one and the same inscription in German and in Polish: Mechanische Rechnungs Maschine; Machina Mechaniszna do Rachunku, that is, a mechanical calculating machine.  There is an inscription in German with several words and roots of Latin origin included; this inscription complements the first one. It runs as follows: Zu der Aufgabe des Addirens, Subtantirens, Multiplicirens, und Devidirens von den Nummer Eins bis zu Tausend Millionen und ubrig bleibt von der Division und das kann man hier in der Bruchen zertheilen, which means: the task of adding, subtracting, multiplying and dividing from one to a thousand million and the resulting figure can be fractioned.

The most interesting inscription also consists of German and Latin words. It reads as follows: Erfunden und verfertigen von dem Hebreer Jewna Jacobson, Uhrmacher und Mechanicis in der Stadt Nieswiez in Lithauen, Gouvernement Minsk, which means – the machine was invented and constructed by Ewno Jacobson, the clockmaker and mechanic in the town of Nesvizh in Lithuania, Minsk voivodeship. The exact time of the construction is not indicated, but it can be identified. The appearance and type of some elements of the device – the form of some details, the methods of their mechanical processing, smoothing, the fonts in the inscriptions, the ornaments of decorative engraving; the form and the pattern of plated decorative rosettes etc. – all this permits to conclude the machine construction is dated to the 18th century.     

The last of the above mentioned inscriptions also testifies to this effect. The town of Nesvizh is described there as the town of the Minsk voivodeship in Polish-Lithuanian Principality, in reality the town existed as such only until its incorporation into Russia in 1793 during the second division of Poland. This proves the calculating machine could not be made later than the indicated year.  

Studying the history of Nesvizh more precisely, one can determine the time of the machine construction by Jacobson even more definitely. 

In 1726 a well-known Polish magnate Mikhail Radzivill turned Nesvizh into his personal residence. Being a great amateur of science and connoisseur of arts he founded an arsenal, a library, a picture gallery, a printing shop, where his newspaper was published; he also began to invite painters, engravers, gunsmiths and other craftsmen of all specialties. And Jacobson evidently was among the latter.

In the course of 40-s-80-s of the 18th century all these painters, engravers and craftsmen made a lot of highly valuable works of art and handicraft, demonstrating craftsmanship which left a significant imprint in the history of decorative art and handicraft. It is in these years that the calculating machine of Jacobson was evidently constructed. The decorative elements of the device allow supposing that it was made not later than 1770. Unfortunately no biographical data concerning Jacobson have survived till our days.   In the end of the 19th century not far from Poznan in the Gnezno settlement there was a chalice of gold in the kostel (a Polish Roman Catholic Church) with an engraved inscription, which read that it was made by Ew. Jacobson in 1786 [18.p. 138]. It is quite probable that alongside clock making and constructing other mechanisms Jacobson from Nesvizh was also engaged in jewelry. Such cases were far from rare. If it were the same person, then the time when the chalice of Gnezno settlement was made could serve one more proof that the man worked precisely in these years and corroborate the construction date of the calculating machine.




The Upper Lid








The Mechanism of Jacobson’s Machine


The mechanisms of the calculating machine are installed on the upper lid from the inside, and on the surface of the lid all the drivers and the scales to make calculations are concentrated.

Along the upper side of the surface of the lid nine drivers go out through special holes; the drivers serve as axes for the discs located under the lid, on which the digits from 0 to 9 are depicted. The end of each driver has a square section, that is why it can be easily turned by means of a special key.  All the other drivers designed for different purposes are made in the similar way. It is difficult to state now if all the drivers of the calculating machine were turned by one key only (the section of each driver is the same – 0.2 х 0.2 sm) or there existed a separate key for every driver, as no key has been preserved till the present days. All the keys, which were directly used to make calculations, had arrows which made it possible to stop the drivers, when the latter were rotated, opposite definite digits placed on the arc-wise scales (to be described below).  

Under each of the nine drivers there is a round hole resembling a window, in which any digit of the disc can be read during its rotation around the axis. These discs are neither interconnected, nor connected to any other part of the calculating mechanism. They are designed to fix the initial data and the intermediate results of the calculations.  

A little bit lower than the earlier mentioned drivers there are another nine drivers, above each of them a semi-circle is depicted – an arc-wise scale with digits from 0 to 9 engraved on it. Under each of the scales the numerals are shown: Eins, Zehn, Hundert, Eins Tausend, Zehn Tausend, Hundert Tausend, Eins Million, Zehn Million, Hundert Million, that is single numbers (digits), dozens, hundreds, thousands and so on to hundreds of millions. The scales are located from the right to the left from smaller to larger numerals.

There are also special windows below this row of drivers. But in contrast to the first row of windows they are not round, but square, although located in the cavity-like holes approximately of the same diameter as the windows in the first row. Through these windows the figures are visible, engraved on the discs. This row is designed for adding any numbers; the only condition is that their sum should not exceed 109.

The mathematical operation is made in the following way: by means of a key or keys with an arrow one dials the first summand, for this purpose the driver is turned so as to point at the corresponding digit on the scale of single numbers, on the scale of dozens – at the corresponding dozen, on the scale of hundreds – at a hundred and so on. 

After the key has been driven to point at each of the necessary figures one lets it go and the key, driven by a special spring, automatically returns to the initial position, pointing with an arrow at 0 (zero).

As a result of this operation there appears the first summand in the square windows, and the calculating machine is ready to dial the second summand. This summand is dialed in the same way as the first one. After that the sum of the first two numerals appears in the windows, and the machine is ready for dialing the next summand.

There is one more row of drivers below which move the calculating mechanism to the initial position, when in all the windows only zeros are displayed.

Still below there is another scale and a row of drivers, only the digits from 0 to 9 are engraved counterclockwise. This is a row for subtraction of any number from the number less than 10. This is what the inscription «Subtrahierens» means.

To subtract from any number, which has been already dialed in the addition row, the number to be subtracted must be dialed in the subtraction row. After each round of dialing the drivers automatically return into initial position driven by springs. After that the result can be read in the windows. The machine is then ready for the next calculation (addition or subtraction), as these mathematical operations can be made in any sequence. 

To register the intermediate results and the initial data, there exists a special removable ruler, which has six in-built discs depicting digits from 0 to 9 and the corresponding drivers.

There is no special multiplication mechanism in the calculating machine. But this mathematical operation can be performed by means of repeated addition. To this end the multiplication table is engraved above the arc-wise scales of the subtraction row. The multiplication table can be used as a division table as well. In the multiplication row the digits are engraved in the following way: a certain number opposite each driver. Opposite the first driver there stands number 1, opposite the second – number 2 and so on to number 9. And above the numbers of the arc-wise scales there is also a row of digits specific for every scale. The driver with number 5 has an arc-wise scale with the digits 0, 1, 2, 9; above them the following numerals are displayed: number 10 above 2; number 15 above 3; number 45 above 9. Such multiplication table is engraved above all the arc-wise scales of this row, containing drivers from 1 to 9.

Kinematic scheme of Jacobson’s Calculating Machine

Division is fulfilled as consecutive subtraction with registering the number of these subtractions. The dividend is dialed in the addition row, and the divisor is dialed also consecutively by means of a number of subtractions until only zeros or the number less than the divisor appear in the windows, that is, until the remainder appears. The number of subtractions made, that is the quotient, is displayed in the windows of the subtraction row. Let’s see how the machine works when making different mathematical operations by using its kinematic scheme.

When the driver of the single numbers addition row turns, the semi-disk 1 also turns counterclockwise. Along the edge of the semi-disk the teeth are located similar to those which are made on the ratchet gear. When the semi-disk turns they hook onto the teeth of the ratchet gear 3 and make it rotate clockwise passing the number of teeth, corresponding to the number of turns of the driver. After one lets the driver go, the semi-disk 1 with the help of a spring 2 returns to the initial position. The ratchet gear 3 has a disk firmly attached to it with engraved digits from 0 to 9, which can be read through the windows. After the necessary number is dialed the corresponding figure appears in the window. When the second number is dialed the ratchet gear 3 turns once again and the sum of the two dialed numbers is displayed. If this sum exceeds 10, the mechanism of dozens is activated. The ratchet gear 3 has a long knuckle 4 firmly attached to it which hooks onto the wheel 5 when the wheel 3 passes 10 teeth. In this case knuckle 4 rotates the wheel 5 counterclockwise and passes 1 tooth, and the wheel 5 rotates the wheel 6 passing one tooth clockwise. As the wheel 6 has a disk of dozens attached to it, so number 1 is displayed in the window for dozens. The coupling for dozens is made in the same way as for single numbers and is connected to hundreds also by means of a long knuckle, and so forth. This way addition is carried out.   For subtraction the semi-disk 8 is rotated clockwise. It also hooks onto the wheel 3 and rotates it passing the corresponding number of single figures counterclockwise, that is in the opposite direction, than in the addition operation. The disk with digits also rotates in the direction opposite to that which is used to dial the summands in addition. The mechanism of displaying dozens remains the same. So subtraction consists in rotating wheel 3 in the opposite direction, than in addition.

Division, as was mentioned earlier, consists in consecutive subtractions. The number of subtracting operations is counted in the following way: in subtracting any numeral semi-disk 8 is rotated clockwise. Simultaneously the plate with a spring located in the lower part of the semi-disk is pressed into the semi-disk by one of the pins 10 mounted on the disk 11. On the other side of this semi-disk the digits from 0 to 9 are engraved which are visible in the low row of windows. Having disconnected from the pin 10 the plate 9 driven by the spring disengages from semi-disk 8. When the semi-disk driven by the spring returns to the initial position, the plate strikes pin 10 with its edge thus rotating disk 11 by one point clockwise. Such turn of the disk 11 by one point occurs in every subtraction, that is why the number of subtractions made, or the quotient, can be read in the lower row of windows.

There are also some details in the calculating machine, which make its work more reliable. For example, there are small cavities under the arc-wise scales in the addition and subtraction rows, that make it possible to precisely fix the key and the driver with an arrow in the necessary position , that is opposite a certain digit.  The wheels 3, 7 and 12 are provided with special springs, preventing accidental turns.

All the details of the calculating mechanism, connected with a certain digit, are numbered (they have a stamp on them) from one to nine, which look as follows; ., .., v, v., v.., v..., v. when cleaning and repairing the machine, if need be, the stamps exclude accidental rearrangement of the parts if the machine has to be at least partly disassembled.





The Scheme of Operation of the Calculating Machine


The displaying of dozens with the help of a long knuckle has been in use for a long time beginning with Pascal and Schickard, but some knots and details are an original invention. First of all this concerns the mechanism of dialing the quotient, though this mechanism has a few considerable drawbacks, the lack of dialing dozens among them. That is why in subtracting operations when one gets large numerals in the quotient, they are difficult to fix. The use of a semi-disk with the teeth also helps to solve the problem of dialing and displaying the numerals.  One should also note the compact size of the calculating machine – the knots of the neighbouring digits are located at different levels, and that considerably reduces the size of the calculating device. All this testifies to the effect, that Jacobson’s calculating machine was in its time a step forward in the development of the calculating mechanisms. And Jacobson can be considered an outstanding designer of computing machines.

Jacobson’s calculating machine has been used for a long time. The imprints on the upper lid made by the turning drivers with arrows prove this. These imprints are especially deep until they reach the sixth digit and further they are hardly visible. This is only natural, as one usually operates with the numerals of the first four digits when counting.