II. Description of a new instrument for performing mechanically 
the involution and evolution of numbers. By Peter M. Roget, 
M. D. Communicated by William Hyde Wollaston, M. D. 
Sec. R. S. 
Read November 17, 1814. 
T o abridge that species of mental labour which is required 
in conducting arithmetical computations, has been the pro- 
fessed object of a variety of mechanical contrivances. But 
the greater number of arithmetical machines, as they have 
been called, are more ingenious than really useful, and have 
been recorded more as objects of curiosity, than as admitting 
of convenient or ready application in the actual practice of 
arithmetic. The machine invented by Pascal, and others 
constructed on the same principle, were, strictly speaking, 
limited to the simpler operations of addition and subtraction, 
and were incapable of being applied to the finding of products 
or quotients in any other way than by effecting a number of 
successive additions or subtractions. Still less did they aim 
at the immediate performance of the higher operations of in- 
volution, which, even by the most compendious methods of 
arithmetic, is a laborious process; or of the extraction of roots, 
to which the common rules furnish but a circuitous and slow 
approximation. 
The only instruments which promise to afford real assist-/ 
ance to the practical calculator, are those founded on the 
theory of logarithms : a theory, which has been the fertile 
mdcccxv. C 
