In the above case of , the Operation-cards merely order seven multiplications, that is, they order the mill to be in the multiplying state seven successive times (without any reference to the particular columns whose numbers are to be acted upon). The proper Distributive Variable-cards step in at each successive multiplication, and cause the distributions requisite for the particular case. The engine might be made to calculate all these in succession. Having completed , the function might be written under the brackets instead of , and a new calculation commenced (the appropriate Operation and Variable-cards for the new function of course coming into play). The results would then appear on . So on for any number of different functions of the quantities , , . Each result might either permanently [Pg 39] remain on its column during the succeeding calculations, so that when all the functions had been computed, their values would simultaneously exist on , , , &c.; or each result, might (after being jointed off, or used in any specified manner) be effaced to make way for its successor. The square under ought, for the latter arrangement, to have the functions , , , &c. successively inscribed in it. Let us now suppose that we have two expressions whose values have been computed by the engine independently of each other (each having its own group of columns for data and results). Let them be , . They would then stand as follows on the columns:— + + + + + + + + + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 We may now desire to combine together these two results, in any manner we please; in which case it would only be necessary to have an additional card or cards, which should order the requisite operations to be performed with the numbers on the two result-columns, and , and the result of these further operations to appear on a new column, . Say that we wish to divide by . The numerical value of this division would then appear on the column , beneath which we have inscribed . The whole series of operations from the beginning would be as follow ( being = 7):— This example is introduced merely to show that we may, if we please, retain separately and permanently any intermediate results (like ), which occur in the course of processes having an ulterior and more complicated result as their chief and final object .