Viktor Bunyakovsky

When you realize nothing is lacking, the whole world belongs to you.
Lao Tzu

Viktor Yakovych Bunyakovsky (1804-1888)
Viktor Yakovych Bunyakovsky (1804-1888)

Viktor Yakovych Bunyakovsky (Віктор Якович Буняковский) (1804-1888) is a famous Russian mathematician, member, and later vice-president of the Petersburg Academy of Sciences. He made significant contributions in the areas of number theory and probability theory and is credited with an early discovery of the Cauchy-Schwarz inequality. Besides being an eminent mathematician Bunyakovsky was a good mechanic also, and he invented several devices like a planimeter, pantograph, etc.

Bunyakovsky became interested in calculating devices in 1828, then a young teacher in mathematics at the military cadet corps, when he wrote a review for the type of abacus, made by the mathematician general Svobodsky (Федор Михайлович Свободский). Bunyakovsky paid particular attention to the problem of tens carry and had the intention of creating a device, to resolve this problem. Thus in the middle 1860s, Bunyakovsky invented a calculating device (so-called самосчеты, i.e. automated abacus), which was demonstrated to the Academy on 14 February 1867. It seems only one (the original prototype) was made, preserved now in the collection of the Polytechnic Museum in Moscow (see the image below).

The automated abacus of Bunyakovsky (Самосчеты Буняковского)
The automated abacus of Bunyakovsky (Самосчеты Буняковского)

The calculating device of Bunyakovsky has dimensions 24.5 х 21 х 0.7 сm, and consists of (see the drawing below):
1 — A metal circle, freely rotating around its axis (with three fixed teeth, marked with 8).
2 — Results digits in small circles (0-9, repeated three times, total 30).
3 — Rods with spherical handles (mounted together with the digits (2)), and used for rotating of the disk (1).
4 — Fixed arcuate plank with two numerical rows. The outer row is used during the addition, inner row—during the subtraction.
5 — Plank with three result windows—(A1, A2, A3), control window (A), and buttons of digital disks (Б, Б1).
6 — Ratchet wheels.
7 — Fixing mechanism (a spring).

A drawing of automated abacus of Bunyakovsky (Самосчеты Буняковского)
A drawing of the automated abacus of Bunyakovsky (Самосчеты Буняковского)

During the addition, the metal circle is rotated counter-clockwise, while during the subtraction rotation is clockwise. The result can be seen in the windows (A1, A2, A3). Calculations on the device are reduced to the sequential addition of units separately, then tens, hundreds, and so on of all terms, the results obtained are recorded on the small abacus in the lower left corner of the device or a tablet. During subtraction, the counter is set to the value to be reduced, and the subtraction of units, tens, etc. is performed sequentially.

A drawing of tens carry mechanism of automated abacus of Bunyakovsky
A drawing of tens carry mechanism of automated abacus of Bunyakovsky

The tens carry mechanism of the device consisted of (see the nearby drawing):
6 — Digital disks for tens (right) and hundreds (left).
8 — Three teeth, fixed on the metal circle, rotating around its axis, for carrying to tens disk.
9 — Column openings (contacting with teeth for tens carry).
10 — A tooth, fixed on the disk for tens, for carrying to hundreds disk.

The capacity of the device is quite limited—the input numbers are limited to 14, while the result is limited to 999. The device is also lacking a mechanism to avoid the mechanical inertia of the moving parts.

Bunyakovsky used his abacus for some scientific calculations, but it seems nobody else had used the device. It exists although an improved version of the device from 1876 (two devices survived), which has been used for some time.