Page:Scientific Memoirs, Vol. 3 (1843).djvu/718

708 zero is substituted. At the end of a calculation, therefore, every column ought as a general rule to be zero, excepting those for results. Thus it will be seen by the diagram, that when $\scriptstyle{m}$, the value on $\scriptstyle{\mathbf{V}_0}$, is used for the second time by Operation 5, $$\scriptstyle{\mathbf{V}_0}$$ becomes 0, since $$\scriptstyle{m}$$ is not again needed; that similarly, when $\scriptstyle{(mn'-m'n)}$, on $\scriptstyle{\mathbf{V}_{12}}$,|undefined is used for the third time by Operation 11, $$\scriptstyle{\mathbf{V}_{12}}$$ becomes zero, since $$\scriptstyle{(mn'-m'n)}$$ is not again needed. In order to provide for the one or the other of the courses above indicated, there are two varieties of the Supplying Variable-cards. One of these varieties has provisions which cause the number given off from any Variable to return to that Variable after doing its duty in the mill. The other variety has provisions which cause zero to be substituted on the Variable, for the number given off. These two varieties are distinguished, when needful, by the respective appellations of the Retaining supply-cards and the Zero Supply-cards. We see that the primary office (see Note B.) of both these varieties of cards is the same; they only differ in their secondary office.

Every Variable thus has belonging to it one class of Receiving Variable-cards and two classes of Supplying Variable-cards. It is plain however that only the one or the other of these two latter classes can be used by any one Variable for one operation; never both simultaneously; their respective functions being mutually incompatible.

It should be understood that the Variable-cards are not placed in immediate contiguity with the columns. Each card is connected by means of wires with the column it is intended to act upon.

Our diagram ought in reality to be placed side by side with M. Menabrea's corresponding table, so as to be compared with it, line for line belonging to each operation. But it was unfortunately inconvenient to print them in this desirable form. The diagram is, in the main, merely another manner of indicating the various relations denoted in M. Menabrea's table. Each mode has some advantages and some disadvantages. Combined, they form a complete and accurate method of registering every step and sequence in all calculations performed by the engine.

No notice has yet been taken of the upper indices which are added to the left of each $$\scriptstyle{\mathbf{V}}$$ in the diagram; an addition which we have also taken the liberty of making to the $\scriptstyle{\mathbf{V}}$'s|undefined in M. Menabrea's tables of pages 681, 684, since it does not alter anything therein represented by him, but merely adds something to the previous indications of those tables. The lower indices are obviously indices of locality only, and are wholly independent of the operations performed or of the results obtained, their value continuing unchanged during the performance of calculations. The upper indices, however, are of a different nature. Their office is to indicate any alteration in the value which a Variable represents; and they are of course liable to changes during the processes of a calculation. Whenever a Variable has only zeros upon it, it is called $\scriptstyle{^0\mathbf{V}}$;|undefined the moment a value appears on it (whether that value be placed there arbitrarily, or appears in the natural course of a calculation), it becomes $\scriptstyle{^1\mathbf{V}}$.|undefined If this value gives place to another value, the Variable becomes $\scriptstyle{^2\mathbf{V}}$,|undefined and so forth. Whenever a value again gives place to zero, the Variable again becomes $\scriptstyle{^0\mathbf{V}}$,|undefined even if it have been $$\scriptstyle{_n\mathbf{V}}$$ [sic] the moment before. If a value then again be substituted, the Variable becomes $$\scriptstyle{^{n+1}\mathbf{V}}$$ (as it would have done if it had not passed through the intermediate $\scriptstyle{^0\mathbf{V}}$);|undefined &amp;c. &amp;c. Just before any calculation is commenced, and after the data have been given, and everything adjusted and