and
, that they may be transferred to the mill, which will multiply them into each other, and will then command the machine to represent the result, say on the column
. But as these numbers are each to be used again in another operation, they must again be inscribed somewhere; therefore, while the mill is working out their product, the machine will inscribe them anew on any two columns that may be indicated to it through the cards; and, as in the actual case, there is no reason why they should not resume their former places, we will suppose them again inscribed on
and
, whence in short they would not finally disappear, to be reproduced no more, until they should have gone through all the combinations in which they might have to be used.
We see, then, that the whole assemblage of operations requisite for resolving the two[8] above equations of the first degree, may be definitively represented in the following table:—