Page:Memoirs of Royal Astronomical Society Volume 01.djvu/533

510 and the counters. They are unconnected with it in purpose, as in form. Mechanical aid of calculation has in truth been before proposed by very eminent persons. invented a very complicated instrument for the simplest arithmetical processes, addition and subtraction, and reaching by very tedious repetition to multiplication and division. proposed another, of which the power extends no further. 's and 's contrivances, which a century ago were applauded by the Academy of Sciences at Paris, are upon the model of 's, and may no doubt be improvements of it, but do not vary or enlarge its objects. 's instruments, described in an early volume of the Philosophical Transactions (the 8th), are confined, the one to addition and subtraction, the other to multiplication. The Rotula Arithmetica of, simpler in construction, reaches not beyond the four arithmetical operations.

The principle, which essentially distinguishes Mr. 's invention from all these, is, that it proposes to calculate a series of numbers following any law by the aid of differences; and that, by setting few figures at the outset, a long series of numbers is readily produced by a mechanical operation. The method of differences, in a very wide sense, is the mathematical principle of the contrivance. A machine to add a number of arbitrary figures together is no economy of time or trouble; since each individual figure must be placed in the machine. But it is otherwise when those figures follow some law. The insertion of a few at first determines the magnitude of the next; and these of the succeeding. It is this constant repetition of similar operations, which renders the computation of tables a fit subject for the application of machinery. Mr. 's invention puts an engine in the place of the computer. The question is set to the instrument; or the instrument is set to the question; and, by simply giving It motion, the solution is wrought and a string of answers is exhibited.

Nor is this all; for the machine may be rendered capable of recording its answer, and even multiplying copies of it. The usefulness of the instrument is thus more than doubled: for it not only saves time and trouble in transcribing results into tabular form and setting types for the printing of the table constructed with them, but it likewise accomplishes the yet more important object of ensuring accuracy, obviating numerous sources of error through the careless hands of transcribers and compositors.