Doing what needs to be done may not make you happy, but it will make you great.

*George Bernard Shaw*

In April 1886, Eduard Selling, a professor of mathematics and astronomy at the University of Würzburg, Germany, received a patent for a calculating machine with a very interesting construction.

The driving force behind this invention was (as usual) the personal need for a better calculating tool. It’s known that since 1877 Selling had been commissioned by various ministries dealing with actuarial matters, especially on the revision of the pension system in Bavaria. For his extensive mathematical calculations, he used a calculating machine of Thomas de Colmar, with which he was not satisfied. That’s why, he decided to create his own entirely different machine, not only suitable for multiplication but also to be offered at a lower price and to avoid all the drawbacks of Thomas’ machine.

The first variant of the device was patented in 1886 (Deutsches Reichs-Patent №39634, 16 April 1886), later on, Selling received three more patents in Germany for improvements of his machine, as well as patents in Austria (pat. №31289 and №20923), Belgium (№74104), Switzerland (№31942), France (№175412), England (№8912 and №23737), Italy (№20326), and USA (see patent US420667A). The machine was described also in his book Eine neue Rechenmaschine, Berlin, Springer, 1887.

The calculating machine of Selling has two main variants (let’s call them the *first machine* and the *second machine*). It was put in production, although in small quantities (some 30-40 machines were produced until the production ended in 1898), by the Workshop for Precision Mechanics of Max Ott, in Munich. The price was 400 marks. The machine of Selling was awarded at the Columbian Exposition (also known as the Chicago World’s Fair) in 1893.

In the construction of the machine took part the teenage son of a friend of Selling—the future genius of mechanic calculating machines, Christel Hamann.

The internal mechanism of the machine is based on the so-called *Nürnberger Schere* (a popular children’s toy at this time), in English, this mechanism is called *Nuremberg scissors* or *lazy-tongs* (see the patent drawing below).

The machine is 35 cm wide, 40 cm long, and 15 cm high.

The multiplicand digits must be entered in a representation that differs from the decimal system, e.g. 18 must be represented as 20-2, although the result is shown in the decimal system.

The calculating wheels of a regular calculating machine (which transfers the motion to the digital wheels) are replaced by lazy-tongs. To the joints of these the ends of racks are pinned, and as they are stretched out the racks are moved forward 0 to 9 steps, according to the joints they are pinned to. The racks gear directly in the digital wheels and the figures are placed on cylinders. The carrying is done continuously by a train of epicycloidal wheels. The working is thus rendered very smooth, without the jerks that the ordinary carrying tooth produces; but the arrangement has the disadvantage that the resulting figures do not appear in a straight line, a figure followed by a 5, for instance, is already carried half a step forward. This is not a serious matter in the hands of a mathematician or an operator using the machine constantly, but it is serious for casual work. Anyhow, it has prevented the machine from being a commercial success. Actually, this was the second machine with continuous tens carry, after the calculating machine of Chebyshev. For ease and rapidity of working it surpasses all other machines. Since the lazy-tongs allow an extension equivalent to five turnings of the handle if the multiplier is 5 or under, one push forward will do the same as five (or fewer) turns of the handle, and more than two pushes are never required.

Obviously, the problem of tens carry was solved in a new, albeit very complex, way. Moreover, besides the vulnerability of the tens carry mechanism, other parts of the machine also have complications. That’s why Selling tried to improve the mechanism in his second machine (see the photo below), although without great success.

In one of his German patents (№88297 from 1894), Selling attempted to design an electric calculating machine (with no engine, but through contacts and electromagnets), but apparently without success.

The calculating machines of Eduard Selling demonstrated exceptional ideas and ingenuity but were fragile, complex, and difficult to manufacture and work, that’s why they didn’t achieve any market success.

#### Biography of Eduard Selling

Eduard Selling was born on 5 November 1834, in Ansbach, Bavaria, Germany, in a family of a professor. He studied mathematics at Georg-August-Universität in Göttingen and Ludwig-Maximilians-Universität in München, where he was a student of the famous German mathematician and astronomer Philipp Ludwig Ritter von Seidel.

In 1859 Selling obtained a Ph.D. degree in mathematics at Universität München (with a thesis on prime numbers, under the supervision of Bernhard Riemann), and in 1860 he was appointed as an associate professor (*professor extraordinarius*) of mathematics at the Bayerische Julius-Maximilians-Universität in Würzburg, recommended by the famous mathematician Leopold Kronecker. Selling held this position and taught mathematics and astronomy until his retirement in 1906.

In 1873 Selling wrote an important paper on binary and ternary quadratic forms which was also translated into French and cited by Henri Poincaré, Émile Picard, and Paul Gustav Heinrich Bachmann. In 1879 Selling was appointed as a curator of the Astronomical Institute. He proved himself as a very good mathematician and published a series of works on number theory and then on insurance mathematics. On behalf of various ministries, he developed models, with which the pension system in Bavaria could be rearranged.

Eduard Selling died on 31 January 1920, in München.