The zeros beneath the symbolic circles represent each of them a disc, supposed to have the digit 0 presented in front. Only four tiers of zeros have been figured in the diagram, but these may be considered as representing thirty or forty, or any number of tiers of discs that may be required. Since each disc can present any digit, and each circle any sign, the discs of every column may be so adjusted[21] as to express any positive or negative number whatever within the limits of the machine; which limits depend on the perpendicular extent of the mechanism, that is, on the number of discs to a column. [Pg 37] Each of the squares below the zeros is intended for the inscription of any general symbol or combination of symbols we please; it being understood that the number represented on the column immediately above, is the numerical value of that symbol, or combination of symbols. Let us, for instance, represent the three quantities , , , and let us further suppose that , , . We should have— +[22] + + + 0 0 0 0 0 0 9 0 5 7 8 0 We may now combine these symbols in a variety of ways, so as to form any required function or functions of them, and we may then inscribe each such function below brackets, every bracket uniting together those quantities (and those only) which enter into the function inscribed below it. We must also, when we have decided on the particular function whose numerical value we desire to calculate, assign another column to the right-hand for receiving the results, and must inscribe the function in the square below this column. In the above instance we might have any one of the following functions:— Let us select the first. It would stand as follows, previous to calculation;— + + + + 0 0 0 0 0 0 0 0 0 0 9 0 5 7 8 0 The data being given, we must now put into the engine the cards proper for directing the operations in the case of the particular function chosen. These operations would in this instance be,— Firstly, six multiplications in order to get ) for the above particular data). Secondly, one multiplication in order then to get ). In all, seven multiplications to complete the whole process. We may thus represent them:—