Arrangements analogous to those just described have been introduced into the Analytical Engine. It contains two principal species of cards: first, Operation cards, by means of which the parts of the machine are so disposed as to execute any determinate series of operations, such as additions, subtractions, multiplications, and divisions; secondly, cards of the Variables, which indicate to the machine the columns on which the results are to be represented. The cards, when put in motion, successively arrange the various portions of the machine according to the nature of the processes that are to be effected, and the machine at the same time executes these processes by means of the various pieces of mechanism of which it is constituted. In order more perfectly to conceive the thing, let us select as an [Pg 14] example the resolution of two equations of the first degree with two unknown quantities. Let the following be the two equations, in which and are the unknown quantities:— We deduce , and for an analogous expression. Let us continue to represent by , , , &c. the different columns which contain the numbers, and let us suppose that the first eight columns have been chosen for expressing on them the numbers represented by , , , , , , and , which implies that , , , , , , , . The series of operations commanded by the cards, and the results obtained, may be represented in the following table:— Number of the operations. Operation-cards Cards of the variables. Progress of the operations. Symbols indicating the nature of operations. Columns on which operations are to be performed. Columns which receive results of operations. 1 2 3 4 5 6 7