whence in short they would not finally disappear, to be reproduced no more, until they should have gone through all the combinations in which they might have to be used. [Pg 16] We see, then, that the whole assemblage of operations requisite for resolving the two[8] above equations of the first degree, may be definitively represented in the following table:— Columns in which are inscribed the primitive data. Number of the operations. Cards of the operations. Variable cards. Statement of results. Number of the operation cards. Nature of each operation. Columns acted on by each operation. Columns that receive the result of each operation. Indication of change of value on any column. 1 1 2 " 3 " 4 " 5 " 6 " 7 2 8 " 9 " 10 3 11 " 1 2 3 4 5 6 7 8 In order to diminish to the utmost the chances of error in inscribing the numerical data of the problem, they are successively placed on one of the columns of the mill; then, by means of cards arranged for this purpose, these same numbers are caused to arrange themselves on the requisite columns, without the operator having to give his attention to it; so that his undivided mind may be applied to the simple inscription of these same numbers. According to what has now been explained, we see that the collection of columns of Variables may be regarded as a store of numbers, accumulated there by the mill, and which, obeying the orders transmitted to the machine by means of the cards, pass alternately from the mill to the store, and from the store to the mill, that they may undergo the transformations demanded by the nature of the calculation to be performed.