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On the basis of the theorem, Slonimsky has made the table consisting of 280
       columns – by 9 numbers in eash one. This table is put on the cylinders that
       are the basic element of the device. The cylinders can move in two directions:
       along an axis and around  it. Two mini-cylinders are also on the axis, where
       the cylinder. On the surface of one the mini- cylinders the numbers from
       0 to 9 are plotted, and on the surface of the other one – charactera a, b, c, d
       and numbers (from 1 to 7).
       On the cover of the device there are 11 lines of windows of reading, in the first
       (lower) line the set number (multiplicand) is visible. In the second and third
       lines of windows characters and digits appear at installation of in setting mul-
       ticand. Their combination is the key for an operator. Due to it he knows, what screw and haw far is necessary to
       turn. After that in the 4-11-th lines of windows there appear numbers: in the 4-th line – product of multiplicand
       by 2, in the 5-th - by 3, in the 6-th by 4 and so on. Thus,  there is the product of the multiplicand by all bits of the
       factor at our disposal. Now all that is left to combine these results and to receive the unknown quantity product
       by the ordinaly way (on a sheet of paper).
       Certainly, all that is not so convenient, and the Slonimsky device was hardly used by somebody requearly. How-
       ever, it served as the prototype of one more simple multiplying device (Yoffe bars), that got mush wider use.

             It turns out that Slonimski did not seem to have published the theorem at all. He presented it to the
             St. Petersburg Academy, where it was recorded in the minutes. Moreover, he never proved it himself.
          However, it is interesting that a German mathematician August Leopold Crelle, who was familiar with the
          theorem from Slonimski’s personal communication during his visit to Berlin in 1844, and later published
          Slonimski’s paper on his machine [8], took time and proved Slonimski’s theorem and published the result
                                                    in his own journal.

       Chebyshev’s machine

                               In 1876, the famous Russian mathematician Pafnuty L. Chebyshev made his report
                               “Adding Machine of Continuous Motion” at the French Association of Assistance to
                               Prosperity.It was a ten decimal places adding machine with a continuous tens carry, the
                               first known machine with this type of carry. In a regular calculating with discrete carry,
                               the wheel of higher rank moves on by one point, while the lower rank wheel moves
                               from 9 to 0. During the continuous tens carry, the wheel of higher rank moves from
                               one point to the next gradually and continuously, while the the lower rank wheel turns
                               by one revolution. Chebyshev reached this effect by implementing a planetary trans-
                               mission. Two years later Chebyshev created a second improved model of his adding
                               device, which was presented in 1878 to the Paris Museum of Arts and Crafts. Later, he
                               made a dividing-multiplying extension unit for the machine, which was also sent to the
       Pafnuty L . Chebyshev   Paris museum in 1881. So the machine became a real arithmometre (can be used for
            (1821–1894)        the all arithmetical operations), which has two separate blocks – one for addition and
                               subtraction, and one for multiplication and division.
       The main purpose of the machine was to demonstrate the new principle of continuous tens carry. The divid-
       ing-multipying unit also had some innovations, e.g. the automatic shifting of the carriage from decimal place to
       decimal place. The unit itself served as the carriage part, that is the moving part of the mechanism. It was mounted
       on the adding machine, thus imposing one single device. To perform multiplication, the operator only needed to
       turn the handle. The number of turns was equal to the sum of numbers of the multiplication factor, added to the
       number of its decimal places minus one. After multiplying by a number (digit) of one decimal place, the mecha-
       nism automatically stopped multiplication and shifted the carriage to the next dec-
       imal place. This was repeated with the next decimal place digit, etc. The number
       of the handle turns was automatically controlled by means of a special counter,
       connected to the mechanism for setting the factor.
       Since the donation of the machine to the museum was not followed by any publi-
       cations, this invention didn’t become famous. As late as 1890 the French scientist
       Eduard Lucka displayed a variety of Chebyshev’s mechanisms, including the arith-
       mometre, on a special stand at the Paris Museum and gave several lectures about
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