### Hayyim Selig Slonimski

The Polish Jew Hayyim Selig Slonimski was born on March 31st, 1810, in Byelostok, Russian Empire (modern Białystok, Poland).

When Slonimski was only twenty-four years old, he finished writing a textbook on mathematics, but due to lack of funds, only the first part was published in 1834. In 1835 Slonimski released *Sefer Kukba di-Shebit* (1835), a collection of essays on the Halley comet and other astronomy related topics such as laws of Kepler and Newton. This work significantly increased his popularity, because Halley's comet was widely discussed topic as the return of this periodic comet was expected in 1835.

In 1838 Chaim Zelig Slonimski settled in Warsaw and immediately became a regular guest in the home of Abraham Jakub Stern (1768-1842), the popular mathematician and inventor of various machines, including calculating. In the same year Slonimski’s work on astronomy, *The History of the Heavens*, appeared in Warsaw with introductions in Polish by two prominent Polish astronomers. This occurred for the young author and scholar who had recently been divorced, thanks to Stern, who wanted him as a son-in-law for his youngest daughter, Sara (Salomea) Gitel (1824-1897). The match was finalized at the beginning of 1842, one month before Stern’s death. Slonimski inherited his father-in-law’s inventions, and with the help of his wife he began to present them as his own. Besides this valuable legacy, Slonimski must have been a very smart man, judging by the rest of his life.

In 1853 Slonimski invented a chemical process for plating iron vessels with lead, and in 1856 an electrochemical device for sending quadruple telegrams, which enabled simultaneous double
transmission and reception—four active communication channels were open through one
wire at the same time. The system of multiple telegraphy, which was used by Lord Kelvin in 1858, was based on Slonimski's discovery. Later, the same invention was repeated by Thomas Edison, who
could hardly have known anything about Slonimski's work. First in history, he began writing and publishing science books in Hebrew to enlighten the Jewish population in Eastern Europe. He started publishing a popular science magazine, *Hazefirah*, 1862, in Hebrew, which continued after his death, till 1931.

Two calculating machines were invented and produced by Slonimski before 1843, one for addition and subtraction, and another for multiplication. The multiplication machine was based on a newly discovered theorem from number theory, called the *Slonimski Theorem*. The operation of the multiplication machine, which is more important, has been described by Slonimski himself in Russian. In principle, it was an implementation of multiplication tables, which resulted from application of the Theorem. Since the amount of related numbers was not that large, they were put on the cylinders, which—when moved appropriately—were showing the multiplication results in small windows.

Slonimski’s machines got high recognition during his life time. In August, 1844, he brought his machines to Berlin, where he demonstrated them first to some prominent scientist as Humboldt, Bessel and others, then to the *Royal Prussian Academy of Sciences*, and his work was highly appreciated. Next year, on April 4th, 1845, he presented the multiplication machine to the *Academy of Sciences* in St. Petersburg, and obtained its recommendation for the *Demidov Prize* of the Second grade (The Second grade prize amounted to 2500 Rubles. For comparison, one should say that a university scholarship of 20 Roubles per 1 month could easily cover a student's living and educational expenditures.), which was awarded to him on June 24, 1845. He was also granted patent for this machine on November 24th, 1845, for the period of ten years.

In 1847 Slonimski applied for a patent in USA, stating that there was a company in New York (of two Jews from Warsaw named Samuel Neustadt and David Barnett), who were interested in financing his invention and they apparently paid $300—at that time a very large sum of money—in order to get a patent. For unknown reason, this application was unsuccessful. He also applied for patent in Great Britain, apparently again unsuccessfully.

The theorem of Slonimski is derived from the Farey numbers (a sequence of the irreducible irrational numbers a/b where b<=n, which belongs to the segment /0, 1/ and is arranged in increasing order). Using this theorem, Slonimski composed a table with 280 columns, each of which contained 9 numbers. The table was engraved on the cylinders; as the main component of the device, these cylinders can both revolve around the axis (the shaft) and move (reciprocate) along it. Aside from the main cylinders, there are also 2 small cylinders with digits from 0 to 9 on one of them and the letters a, b, c, d, together with digits 1 to 7 on the other. The cylinders are driven with the use of handles, fastened to the shaft end. While the small cylinders are immobile, the main cylinders are moved along their axis with toothed gearing, driven with screws, mounted on the cover. There are also handles on the cover, which set the numbers (multiplicands).

Slonimski's multiplying machine (in the right side is shown a single cylinder from the multiplying device)

The whole instrument is made of a flat wooden box, similar to a chessboard, 40 cm long, 33 cm wide and 5 cm high. On the cover of the machine, there are 11 rows of windows. The first (lower) window shows the multiplicand. When the number is set in the first row, both letters and numbers appear in the windows of the second and third rows. Their combination is the code, which informs the operator which screw should be turned (and which cylinder is to be shifted). After this, windows 4-11 show the resulting numbers. The 4th row shows the product of multiplication by 2, the 5th by 3, the 6th by 4, etc. Finally the products of all ranks are displayed. After adding them on paper, the desired product is obtained. Apparently, the convenience of this method was rather questionable, and it is no wonder, that there is no evidence of its systematic practical use.

More importantly, this machine was the only available device for discrete calculating. The basic principle of its work was the theory of numbers, rather than complicated mechanism alone. I was the *mathematical art* of the device, which was so highly appreciated by the Academy, and personally by the famous mathematician Ostrogradsky. As the Academy report noted, "the discovery of the basic feature of multiple numbers was the principle but not the only condition for composing this calculating machine... The inventor also should arrange the aforementioned 280 types in a proper order and also invent a phantom key (the code). Finally, the surface of each of the six cylinders is covered with complicated system of 2280 numbers and 600 letters with indicators. This artificial ordering demonstrates the shrewdness of its author's mind, which raises Mr. Slonimski's device to the level of an analytical mathematical instrument. It is not just a calculator, of which the main idea is represented by the numbers of its pinions."

The Academy commissioned Slonimski to publish the proof of his theorem, together with a detailed description of the machine in Russian language. The task was performed within a short time, and the book appeared in 1845.

Later on, other inventors made similar devices—August Leopold Crelle, Henry Knight, Herschell Filipowski. In 1881, a Russian Jew—the mathematician Zebi Hirsch Joffe, created a popular counting tool (a set, consisting of 70 rectangular bars with totally 280 columns on all sides), named *Joffe's Counting Bars*, based on the Slonimski's theorem.

Slonimski invented also a second calculating device—for addition and subtraction (see the sketch below).

Sketch of the calculating mechanism of Slonimski's adding machine

This device consists of several 24-teeth wheels, which can be rotated by means of a pin. Its tens carry mechanism however is not completely automated and as a whole, it seems is a rather primitive device, compared with the devices of Staffel, Roth and other inventors of this time.

A working example of Slonimski's adding machine survived to the present and is kept in the collection of Museum of the Jagiellonian University, Poland (see the lower photos of the device).

Slonimski's adding machine (© Museum of the Jagiellonian University, Poland)

Hayyim Selig Slonimski died in Warsaw on May 15th, 1904.