# Page:Scientific Memoirs, Vol. 3 (1843).djvu/712

702
TRANSLATOR'S NOTES TO M. MENABREA'S MEMOIR

which the whole mass of its mechanism will assume is not yet finally determined.

We may conveniently represent the columns of discs on paper in a diagram like the following:—

 ${\displaystyle \scriptstyle {\mathbf {V} _{1}}}$ ${\displaystyle \scriptstyle {\mathbf {V} _{2}}}$ ${\displaystyle \scriptstyle {\mathbf {V} _{3}}}$ ${\displaystyle \scriptstyle {\mathbf {V} _{4}}}$ &c. ◯ ◯ ◯ ◯ &c. 0 0 0 0 0 0 0 0 &c. 0 0 0 0 0 0 0 0 □ □ □ □ &c.

The ${\displaystyle \scriptstyle {\mathbf {V} }}$'s are for the purpose of convenient reference to any column, either in writing or speaking, and are consequently numbered. The reason why the letter ${\displaystyle \scriptstyle {\mathbf {V} }}$ is chosen for this purpose in preference to any other letter, is because these columns are designated (as the reader will find in proceeding with the Memoir) the Variables, and sometimes the Variable columns, or the columns of Variables. The origin of this appellation is, that the values on the columns are destined to change, that is to vary, in every conceivable manner. But it is necessary to guard against the natural misapprehension that the columns are only intended to receive the values of the variables in an analytical formula, and not of the constants. The columns are called Variables on a ground wholly unconnected with the analytical distinction between constants and variables. In order to prevent the possibility of confusion, we have, both in the translation and in the notes, written Variable with a capital letter when we use the word to signify a column of the engine, and variable with a small letter when we mean the variable of a formula. Similarly, Variable-cards signify any cards that belong to a column of the engine.

To return to the explanation of the diagram: each circle at the top is intended to contain the algebraic sign + or −, either of which can be substituted[1] for the other, according as the number represented on the column below is positive or negative. In a similar manner any other purely symbolical results of algebraical processes might be made to appear in these circles. In Note A. the practicability of developing symbolical with no less ease than numerical results has been touched on.

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[2] 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.

1. A fuller account of the manner in which the signs are regulated, is given in Mons. Menabrea's Memoir, pages 682, 683. He himself expresses doubts (in a note of his own at the bottom of the latter page) as to his having been likely to hit on the precise methods really adopted; his explanation being merely a conjectural one. That it does accord precisely with the fact is a remarkable circumstance, and affords a convincing proof how completely Mons. Menabrea has been imbued with the true spirit of the invention. Indeed the whole of the above Memoir is a striking production, when we consider that Mons. Menabrea had had but very slight means for obtaining any adequate ideas respecting the Analytical Engine. It requires however a considerable acquaintance with the abstruse and complicated nature of such a subject, in order fully to appreciate the penetration of the writer who could take so just and comprehensive a view of it upon such limited opportunity.
2. This adjustment is done by hand merely.