On this part of the invention, which is yet a subject of experiment for the selection of the most eligible among divers modes of accomplishing it, I shall not dwell longer; as it is not for that superaddition, but for the machine in the finished form of a calculating instrument, that I am to make an acknowledgement in the name of this Society, to Mr. Babbage for his very useful invention.
I speak of it as complete with reference to a model which satisfactorily exhibited the machine's performance, and am apprised that a more finished engine, which is in progress of preparation, may not yet for some time be in a forward state to be put in activity and receive its practical application.
In no department of science or of the arts, does this discovery promise to be so eminently useful as in that of astronomy and its kindred sciences, with the various arts dependent on them. In none are computations more operose than those which astronomy in particular requires: in none are preparatory facilities more needful: in none is error more detrimental. The practical astronomer is interrupted in his pursuit, is diverted from his task of observation, by the irksome labour of computation; or his diligence in observing becomes ineffectual for want of yet greater industry of calculation. Let the aid, which tables previously computed afford, be furnished to the utmost extent which mechanism has made attainable through Mr. Babbage's invention, the most irksome portion of the astronomer's task is alleviated, and a fresh impulse is given to astronomical research.
Nor is it among the least curious results of the ingenious device, of which I am speaking, that it affords a new opening for discovery; since it is applicable, as has been shown by its inventor, to surmount novel difficulties of analysis. Not confined to constant differences, it is available in every case of differences that follow a definite law, reducible therefore to an equation. An engine, adjusted to the purpose, being set to work, will produce any distant term, or uccession of terms, required: thus presenting the numerical solution of a problem, even though the analytical solution of it be yet undetermined.
It may not therefore be deemed too sanguine an anticipation, when I express the hope, that an instrument, which in its simpler form attains to the
