704 TRANSLATOR’S NOTES TO M. MENABREA’S MEMOIR 
on different subjects of operation. And here again is an illustration of 
the remarks made in the preceding Note on the independent manner in 
which the engine directs its operations. In determining the value of 
ax”, the operations are homogeneous, but are distributed amongst dif- 
ferent sulyects of operation, at successive stages of the computation. It 
is by means of certain punched cards, belonging to the Variables them- 
selves, that the action of the operations is so distributed as to suit each 
particular function. The Operation-cards merely determine the suc- 
cession of operations in a general manner. They in fact throw all that 
portion of the mechanism included in the mill, into a series of different 
states, which we may call the adding state, or the multiplying state, &c. 
respectively. In each of these states the mechanism is ready to act in 
the way peculiar to that state, on any pair of numbers which may be 
permitted to come within its sphere of action. Only one of these ope- 
rating states of the mill can exist at a time; and the nature of the me- 
chanism is also such that only one pair of numbers can be received and 
acted on ata time. Now, in order to secure that the mill shall receive a | 
constant supply of the proper pairs of numbers in succession, and that 
it shall also rightly locate the result of an operation performed upon any 
pair, each Variable has cards of its own belonging toit. It has, first, a 
class of cards whose business it is to allow the number on the Variable 
to pass into the mill, there to be operated upon. These cards may be 
called the Supplying-cards. They furnish the mill with its proper food. 
Each Variable has, secondly, another class of cards, whose office it is to 
allow the Variable to receive a number from the mill. These cards may 
be called the Receiving-cards. They regulate the location of results, 
whether temporary or ultimate results. The Variable-cards in general 
(including both the preceding classes) might, it appears to us, bé 
even more appropriately designated the Distributive-cards, since it is 
through their means that the action of the operations, and the results 
of this action, are rightly distributed. 
There are two varieties of the Supplying Variable-cards, respectively 
adapted for fulfilling two distinct subsidiary purposes: but as these 
modifications do not bear upon the present subject, we shall notice them 
in another place. 
In the above case of aw, the Operation-cards merely order seven 
multiplications, that is, they order the mill to be in the maltiplying state 
seven successive times (without any reference to the particular co- 
lumns whose numbers are to be acted upon). The proper Distributive 
Variable-cards step in at each successive multiplication, and cause the 
distributions requisite for the particular case. 
For 2%” the operations would be 34 (x 
tee Do Mok tne ads sot), C9, a ME Ae 
a 
te see vis sa (+, x) 
wo. A+nN+2 oy, “se we (+, +), or 2 (+) 
The engine might be made to calculate all these in succession. Having 
completed a2”, the function a” might be written under the brackets 
instead of aa", and a new calculation commenced (the appropriate 
Operation and Variable-cards for the new function of course coming 
into play). The results would then appear on V,. So on for any 
number of different functions of the quantities a, , x. Each result might 
