and repeated sequence are not the same thing. He went on to prove by his Analytical Engine (existing only in drawings) that "It is more probable that any law, at the knowledge of which we have arrived by observation, shall be subject to one of those violations, which, according to Hume's definition, constitutes a miracle, than that it should not be so subjected." He rests this proposition on the statement that his Analytical Engine could be set to compute the successive terms of a given algebraic law, but so that one chosen term would be different, and then to resume the production of the true terms ever after. Provision could be made by the maker of the machine for a single suspension of the law at a given point.
Babbage devoted 37 years of his life to perfecting the invention of the Analytical Engine and no inconsiderable part of his fortune was spent thereon. This invention must be carefully distinguished from the Difference Engine; they are often popularly confounded but are confused in some scientific writings. When the fragment of the Difference Engine was put together in 1833, Babbage found that, as he had anticipated, it possessed powers beyond those for which it was intended, something in the same way as algebra displays powers beyond those of generalized arithmetic for which it was designed. Babbage saw that, by interposing a few connecting wheels, the column of Result could be made to influence the last Difference, and he proposed to arrange the axes circularly so that these columns should be near each other. He called this arrangement "the engine eating its own tail." This soon led to the idea of controlling the engine by entirely independent means, and to the idea of an engine which could calculate the numerical values of any function which the mathematician can express in a series of integral powers.
To realize the first idea—that is, to make the adjustment of the engine automatic—he had recourse to the device of punched cards similar to those invented by Jacquard for the weaving loom. The machine was to consist of three parts; first, the store; second, the mill; third, the cards. The store was to consist of 100 columns each of fifty wheels for indicating
