Page:Scientific Memoirs, Vol. 3 (1843).djvu/714

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704
TRANSLATOR'S NOTES TO M. MENABREA'S MEMOIR

on different subjects of operation. And here again is an illustration of the remarks made in the preceding Note on the independent manner in which the engine directs its operations. In determining the value of \scriptstyle{ax^n}, the operations are homogeneous, but are distributed amongst different subjects of operation, at successive stages of the computation. It is by means of certain punched cards, belonging to the Variables themselves, that the action of the operations is so distributed as to suit each particular function. The Operation-cards merely determine the succession of operations in a general manner. They in fact throw all that portion of the mechanism included in the mill, into a series of different states, which we may call the adding state, or the multiplying state, &c. respectively. In each of these states the mechanism is ready to act in the way peculiar to that state, on any pair of numbers which may be permitted to come within its sphere of action. Only one of these operating states of the mill can exist at a time; and the nature of the mechanism is also such that only one pair of numbers can be received and acted on at a time. Now, in order to secure that the mill shall receive a constant supply of the proper pairs of numbers in succession, and that it shall also rightly locate the result of an operation performed upon any pair, each Variable has cards of its own belonging to it. It has, first, a class of cards whose business it is to allow the number on the Variable to pass into the mill, there to be operated upon. These cards may be called the Supplying-cards. They furnish the mill with its proper food. Each Variable has, secondly, another class of cards, whose office it is to allow the Variable to receive a number from the mill. These cards may be called the Receiving-cards. They regulate the location of results, whether temporary or ultimate results. The Variable-cards in general (including both the preceding classes) might, it appears to us, be even more appropriately designated the Distributive-cards, since it is through their means that the action of the operations, and the results of this action, are rightly distributed.

There are two varieties of the Supplying Variable-cards, respectively adapted for fulfilling two distinct subsidiary purposes: but as these modifications do not bear upon the present subject, we shall notice them in another place.

In the above case of \scriptstyle{ax^n}, 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.

For \scriptstyle{x^{an}} the operations would be 34 (×)
 … \scriptstyle{a.n.x}     (×, ×), or 2 (×)
 … \scriptstyle{\frac{a}{n}.x}     (÷, ×)
 … \scriptstyle{a+n+x}     (+, +), or 2 (+)

The engine might be made to calculate all these in succession. Having completed \scriptstyle{ax^n}, the function \scriptstyle{x^{an}} might be written under the brackets instead of \scriptstyle{ax^n}, 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 \scriptstyle{\mathbf{V}_5}. So on for any number of different functions of the quantities \scriptstyle{a}, \scriptstyle{n}, \scriptstyle{x}. Each result might