ON BABBAGE’S ANALYTICAL ENGINE. 703 
_ Each of the squares below the zeros is intended for the inscription of 
any general symbol or combination of symbols we please; it being under- 
_ stood that the number represented on the column immediately above, 
_ is the numerical value of that symbol, or combination of symbols. Let 
_ us, for instance, represent the three quantities a, 2, x, and let us further 
"suppose that a=5,n=7,x=98. We should have— 
ae V; Ve V3 V, &e. 
S + * af ae + 
a A 0 0 0 0 
4 0. 0 0 0 &ce. 
0 0 9 0 
5 8 0 &e. 
Bll i 
We may now combine these symbols in a variety of ways, so as to 
form any required function or functions of them, and we may then 
_inseribe each such function below brackets, every bracket uniting to- 
ether those quantities (and those only) which enter into the function 
inscribed below it. We must also, when we have decided on the par- 
ticular function whose numerical value we desire to calculate, assign 
another column to the right-hand for receiving the results, and must 
inscribe the function in the square below this column. In the above 
a 
Le CAS Li aks ont a+nr-+a, &e. &e. 
Let us select the first. It would stand as follows, previous to calcula- 
Vi V2 V3 V, &c. 
+ : EM 3 + 
0 0 0 0 &e. 
0 0 0 0 
0 0 9 0 
5 7 8 0 &e. 
| a | [=| ax” | &e. 
Re a 
axXn 
_ The data being given, we must now put into the engine the cards 
_ proper for directing the operations in the case of the particular func- 
tion chosen. These operations would in this instance be,— 
_ Firstly, six multiplications in order to get x (= 987 for the above 
particular data). 
__ Secondly, one multiplication in order then to get a. a” (= 5.98’). 
__ In all, seven multiplications to complete the whole process. We may 
lus represent them :— 
4 Xo) ha Ma Ma 5 OS MOR TE x De 
._ The multiplications would, however, at successive stages in the so- 
ution of the problem, operate on pairs of numbers, derived from dif- 
Serent columns. In other words, the same operation would be performed 
* It is convenient to omit the circles whenever the signs + or «= can be 
ally represented. 
VOL, Ill, PART XII. 3A 
