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XXII. On the Mechanical Performance of Logical Inference. By W. Stanley Jevons, 
M.A. ( Bond .), Professor of Logic, &c. in Owens College, Manchester. Communicated 
hy Professor H. E. Roscoe, F.P.S. 
Received October 16, 1869, — Read January 20, 1870. 
1. It is an interesting subject for reflection that from the earliest times mechanical assist- 
ance has been required in mental operations. The word calculation at once reminds us 
of the employment of pebbles for marking units, and it is asserted that the word dpiOpbc 
is also derived from the like notion of a pebble or material sign *. Even in the time of 
Aristotle the wide extension of the decimal system of numeration had been remarked 
and referred to the use of the fingers in reckoning ; and there can be no doubt that the 
form of the most available arithmetical instrument, the human hand, has reacted upon 
the mind and moulded our numerical system into a form which we should not otherwise 
have selected as the best. 
2. From early times, too, distinct mechanical instruments were devised to facilitate 
computation. The Greeks and Romans habitually employed the abacus or arithmetical 
board, consisting, in its most convenient form, of an oblong frame with a series of cross 
wires, each bearing ten sliding beads. The abacus thus supplied, as it were, an unlimited 
series of fingers, which furnished marks for successive higher units and allowed of the 
representation of any number. The Russians employ the abacus at the present day 
under the name of the shtshob, and the Chinese have from time immemorial made use 
of an almost exactly similar instrument called the schwawpan. 
3. The introduction into Europe of the Arabic system of numeration caused the 
abacus to be generally superseded by a far more convenient system of written signs ; but 
mathematicians are well aware that their science, however much it may advance, always 
requires a corresponding development of material symbols for relieving the memory and 
guiding the thoughts. Almost every step accomplished in the progress of the arts and 
sciences has produced some mechanical device for facilitating calculation or representing 
its result. I may mention astronomical clocks, mechanical globes, planetariums, slide 
rules, &c. The ingenious rods known as Napier’s Bones, from the name of their inventor, 
or the Promptuarium Multiplicationis of the same celebrated mathematician'!’, are curious 
examples of the tendency to the use of material instruments, 
* Professor De Morgan “ On the word ’AptOjuos,” Proceedings of the Philological Society (p. 9). 
t Rabdologice seu numerationis per virgulas libri duo : cum appendice de expeditissimo multiplicationis 
Promptuario. Quibus accessit et Arithmeticas Localis Liber Unus. Authore et Inventore Joanne Nepf.ro, 
Barone Merchistonii &c. Lugduni, 1626. 
3 Y 
MDCCCLXX. 
