682 .L. Fe. MENABREA ON BABBAGE’S ANALYTICAL ENGINE. 
of expressing and combining amongst each other positive and 
negative quantities. To accomplish this end, there is, above 
every column, both of the mill and of the store, a disc, similar 
to the discs of which the columns themselves consist. According 
as the digit on this disc is even or uneven, the number inscribed 
on the corresponding column below it will be considered as po- 
sitive or negative. This granted, we may, in the following 
manner, conceive how the signs can be algebraically combined 
in the machine. When a number is to be transferred from the 
store to the mill, and vice versd, it will always be transferred 
with its sign, which will be effected by means of the cards, as 
has been explained in what precedes. Let any two numbers 
then, on which we are to operate arithmetically, be placed in 
the mill with their respective signs. Suppose that we are first 
to add them together; the operation-cards will command the 
addition : if the two numbers be of the same sign, one of the two 
will be entirely effaced from where it was inscribed, and will go 
to add itself on the column which contains the other number; 
the machine will, during this operation, be able, by means of a 
certain apparatus, to prevent any movement in the disc of signs 
which belongs to the column on which the addition is made, and 
thus the result will remain with the sign which the two given 
numbers originally had. When two numbers have two different 
signs, the addition commanded by the card will be changed into 
a subtraction through the intervention of mechanisms which 
are brought into play by this very difference of sign. Since 
the subtraction can only be effected on the larger of the two 
numbers, it must be arranged that the disc of signs of the larger 
number shall not move while the smaller of the two numbers 
is being effaced from its column and subtracted from the other, 
whence the result will have the sign of this latter, just as in fact 
it ought to be. The combinations to which algebraical subtrac- 
tion give rise, are analogous to the preceding. Let us pass on 
to multiplication. When two numbers to be multiplied are of 
the same sign, the result is positive; if the signs are different, 
the product must be negative. In order that the machine may 
act conformably to this law, we have but to conceive that on the 
column containing the product of the two given numbers, the 
digit which indicates the sign of that product, has been formed 
by the mutual addition of the two digits that respectively in- 
dicated the signs of the two given numbers; it is then obvious. 
