Page:Scientific Memoirs, Vol. 3 (1843).djvu/691

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 * Columns on which are in&shy;scribed the primitive data.
 * 
 * Cards of the operations.
 * Variable cards.
 * Statement of results.
 * 
 * 
 * Columns acted on by each operation.
 * Columns that receive the result of each operation.
 * Indication of change of value on any column.
 * $$\scriptstyle{^1\mathbf{V}_{0~}=m}$$
 * 1
 * 1
 * $$\scriptstyle{\times}$$
 * $$\scriptstyle{^1\mathbf{V}_{0~}\times~^1\mathbf{V}_{4~}=}$$
 * $$\scriptstyle{^1\mathbf{V}_{6~}\ldots\ldots}$$
 * $$\scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{0~}=~^1\mathbf{V}_{0~}}\\&\scriptstyle{^1\mathbf{V}_{4~}=~^1\mathbf{V}_{4~}}\end{align}\right\}}$$
 * $$\scriptstyle{^1\mathbf{V}_{6~}=mn'}$$
 * $$\scriptstyle{^1\mathbf{V}_{1~}=n}$$
 * 2
 * $$\scriptstyle{\times}$$
 * $$\scriptstyle{^1\mathbf{V}_{3~}\times~^1\mathbf{V}_{1~}=}$$
 * $$\scriptstyle{^1\mathbf{V}_{7~}\ldots\ldots}$$
 * $$\scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{3~}=~^1\mathbf{V}_{3~}}\\&\scriptstyle{^1\mathbf{V}_{1~}=~^1\mathbf{V}_{1~}}\end{align}\right\}}$$
 * $$\scriptstyle{^1\mathbf{V}_{7~}=m'n}$$
 * $$\scriptstyle{^1\mathbf{V}_{2~}=d}$$
 * 3
 * $$\scriptstyle{\times}$$
 * $$\scriptstyle{^1\mathbf{V}_{2~}\times~^1\mathbf{V}_{4~}=}$$
 * $$\scriptstyle{^1\mathbf{V}_{8~}\ldots\ldots}$$
 * $$\scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{2~}=~^1\mathbf{V}_{2~}}\\&\scriptstyle{^1\mathbf{V}_{4~}=~^0\mathbf{V}_{4~}}\end{align}\right\}}$$
 * $$\scriptstyle{^1\mathbf{V}_{8~}=dn'}$$
 * $$\scriptstyle{^1\mathbf{V}_{3~}=m'}$$
 * 4
 * $$\scriptstyle{\times}$$
 * $$\scriptstyle{^1\mathbf{V}_{5~}\times~^1\mathbf{V}_{1~}=}$$
 * $$\scriptstyle{^1\mathbf{V}_{9~}\ldots\ldots}$$
 * $$\scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{5~}=~^1V_{5~}}\\&\scriptstyle{^1\mathbf{V}_{1~}=~^1\mathbf{V}_{1~}}\end{align}\right\}}$$
 * $$\scriptstyle{^1\mathbf{V}_{9~}=d'n}$$
 * $$\scriptstyle{^1\mathbf{V}_{4~}=n'}$$
 * 5
 * $$\scriptstyle{\times}$$
 * $$\scriptstyle{^1\mathbf{V}_{0~}\times~^1\mathbf{V}_{5~}=}$$
 * $$\scriptstyle{^1\mathbf{V}_{10}\ldots\ldots}$$
 * $$\scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{0~}=~^0\mathbf{V}_{0~}}\\&\scriptstyle{^1\mathbf{V}_{5~}=~^0\mathbf{V}_{5~}}\end{align}\right\}}$$
 * $$\scriptstyle{^1\mathbf{V}_{10}=d'm}$$
 * $$\scriptstyle{^1\mathbf{V}_{5~}=d'}$$
 * 6
 * $$\scriptstyle{\times}$$
 * $$\scriptstyle{^1\mathbf{V}_{2~}\times~^1\mathbf{V}_{3~}=}$$
 * $$\scriptstyle{^1\mathbf{V}_{11}\ldots\ldots}$$
 * $$\scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{2~}=~^0\mathbf{V}_{2~}}\\&\scriptstyle{^1\mathbf{V}_{3~}=~^0\mathbf{V}_{3~}}\end{align}\right\}}$$
 * $$\scriptstyle{^1\mathbf{V}_{11}=dm'}$$
 * 7
 * 2
 * $$\scriptstyle{-}$$
 * $$\scriptstyle{^1\mathbf{V}_{6~}-~^1\mathbf{V}_{7~}=}$$
 * $$\scriptstyle{^1\mathbf{V}_{12}\ldots\ldots}$$
 * $$\scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{6~}=~^0\mathbf{V}_{6~}}\\&\scriptstyle{^1\mathbf{V}_{7~}=~^0\mathbf{V}_{7~}}\end{align}\right\}}$$
 * $$\scriptstyle{^1\mathbf{V}_{12}=mn'-m'n}$$
 * 8
 * $$\scriptstyle{-}$$
 * $$\scriptstyle{^1\mathbf{V}_{8~}-~^1\mathbf{V}_{9~}=}$$
 * $$\scriptstyle{^1\mathbf{V}_{13}\ldots\ldots}$$
 * $$\scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{8~}=~^0\mathbf{V}_{8~}}\\&\scriptstyle{^1\mathbf{V}_{9~}=~^0\mathbf{V}_{9~}}\end{align}\right\}}$$
 * $$\scriptstyle{^1\mathbf{V}_{13}=dn'-d'n}$$
 * 9
 * $$\scriptstyle{-}$$
 * $$\scriptstyle{^1\mathbf{V}_{10}-^1\mathbf{V}_{11}=}$$
 * $$\scriptstyle{^1\mathbf{V}_{14}\ldots\ldots}$$
 * $$\scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{10}=~^0\mathbf{V}_{10}}\\&\scriptstyle{^1\mathbf{V}_{11}=~^0\mathbf{V}_{11}}\end{align}\right\}}$$
 * $$\scriptstyle{^1\mathbf{V}_{14}=d'm - dm'}$$
 * 10
 * 3
 * $$\scriptstyle{\div}$$
 * $$\scriptstyle{^1\mathbf{V}_{13}\div~^1\mathbf{V}_{12}=}$$
 * $$\scriptstyle{^1\mathbf{V}_{15}\ldots\ldots}$$
 * $$\scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{13}=~^0\mathbf{V}_{13}}\\&\scriptstyle{^1\mathbf{V}_{12}=~^1\mathbf{V}_{12}}\end{align}\right\}}$$
 * $$\scriptstyle{^1\mathbf{V}_{15}=\frac{dn'-d'n}{mn'-m'n}=x}$$
 * 11
 * $$\scriptstyle{\div}$$
 * $$\scriptstyle{^1\mathbf{V}_{14}-~^1\mathbf{V}_{12}=}$$
 * $$\scriptstyle{^1\mathbf{V}_{16}\ldots\ldots}$$
 * $$\scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{14}=~^0\mathbf{V}_{14}}\\&\scriptstyle{^1\mathbf{V}_{12}=~^0\mathbf{V}_{12}}\end{align}\right\}}$$
 * $$\scriptstyle{^1\mathbf{V}_{16}=\frac{d'm-dm'}{mn'-m'n}=y}$$
 * 1
 * 2
 * 3
 * 4
 * 5
 * 6
 * 7
 * 8
 * }
 * 10
 * 3
 * $$\scriptstyle{\div}$$
 * $$\scriptstyle{^1\mathbf{V}_{13}\div~^1\mathbf{V}_{12}=}$$
 * $$\scriptstyle{^1\mathbf{V}_{15}\ldots\ldots}$$
 * $$\scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{13}=~^0\mathbf{V}_{13}}\\&\scriptstyle{^1\mathbf{V}_{12}=~^1\mathbf{V}_{12}}\end{align}\right\}}$$
 * $$\scriptstyle{^1\mathbf{V}_{15}=\frac{dn'-d'n}{mn'-m'n}=x}$$
 * 11
 * $$\scriptstyle{\div}$$
 * $$\scriptstyle{^1\mathbf{V}_{14}-~^1\mathbf{V}_{12}=}$$
 * $$\scriptstyle{^1\mathbf{V}_{16}\ldots\ldots}$$
 * $$\scriptstyle{\left\{\begin{align}&\scriptstyle{^1\mathbf{V}_{14}=~^0\mathbf{V}_{14}}\\&\scriptstyle{^1\mathbf{V}_{12}=~^0\mathbf{V}_{12}}\end{align}\right\}}$$
 * $$\scriptstyle{^1\mathbf{V}_{16}=\frac{d'm-dm'}{mn'-m'n}=y}$$
 * 1
 * 2
 * 3
 * 4
 * 5
 * 6
 * 7
 * 8
 * }
 * 6
 * 7
 * 8
 * }

In order to diminish to the utmost the chances of error in inscribing the numerical data of the problem, they are successively placed on one of the columns of the mill; then, by means of cards arranged for this purpose, these same numbers are caused to arrange themselves on the requisite columns, without the operator having to give his attention to it; so that his undivided mind may be applied to the simple inscription of these same numbers.

According to what has now been explained, we see that the collection of columns of Variables may be regarded as a store of numbers, accumulated there by the mill, and which, obeying the orders transmitted to the machine by means of the cards, pass alternately from the mill to the store, and from the store to the mill, that they may undergo the transformations demanded by the nature of the calculation to be performed.

Hitherto no mention has been made of the signs in the results, and the machine would be far from perfect were it incapable