676 UL. F. MENABREA ON BABBAGE’S ANALYTICAL ENGINE. 
we have just named. To conceive how the machine can now 
go through its functions according to the laws laid down, we 
will begin by giving an idea of the manner in which it materially 
represents numbers. 
Let us conceive a pile or vertical column consisting of an in- 
definite number of circular discs, all pierced through their cen- 
tres by a common axis, around which each of them can take an 
independent rotatory movement. If round the edge of each of 
these discs are written the ten figures which constitute our nu- 
merical alphabet, we may then, by arranging a series of these 
figures in the sarae vertical line, express in this manner any num- 
ber whatever. It is sufficient for this purpose that the first disc 
represent units, the second tens, the third hundreds, and so on. 
When two numbers have been thus written on two distinct 
columns, we may propose to combine them arithmetically with 
each other, and to obtain the result on a third column. In 
general, if we have a series of columns* consisting of discs, which 
columns we will designate as V,, V,, V., V3, V4, &c., we may re- 
quire, for instance, to divide the number written on the column 
V, by that on the column V,, and to obtain the result on the 
column V,. To effect this operation, we must impart to the ma- 
chine two distinct arrangements ; through the first it is prepared 
for executing a division, and through the second the columns 
it is to operate on are indicated to it, and also the column on 
which the result is to be represented. If this division is to be 
followed, for example, by the addition of two numbers taken on 
other columns, the two original arrangements of the machine 
must be simultaneously altered. If, on the contrary, a series of 
operations of the same nature is to be gone through, then the 
first of the original arrangements will remain, and the second 
alone must be altered. Therefore, the arrangements that may 
be communicated to the various parts of the machine, ey be 
distinguished into two principal classes : 
First, that relative to the Operations. 
Secondly, that relative to the Variables. 
By this latter we mean that which indicates the columns to 
be operated on. As for the operations themselves, they are exe- 
cuted by a special apparatus, which is designated by the name 
of mill, and which itself contains a certain number of columns, 
similar to those of the Variables. When two numbers are to be 
* See Note B. 
