L. F. MENABREA ON BABBAGE’S ANALYTICAL ENGINE, 679 
as an example the resolution of two equations of the first degree 
with two unknown quantities. Let the following be the two 
equations, in which # and y are the unknown quantities :— 
me+ny=d 
mae+tny =d'. 
dn’ —d'n 
aaalt and for y an analogous expression. 
Let us continue to represent by Vo, V,, V., &c. the different 
columns which contain the numbers, and let us suppose that the 
first eight columns have been chosen for expressing on them the 
numbers represented by m, n, d, m’, n', d', n and n', which 
We deduce x = | 
n'm 
Sunplies' that V,=m,'Vj=n, Vj;=d, V;=m', V,=n', V,=d', 
en, V/—7n'. 
The series of operations commanded by the cards, and the 
results obtained, may be represented in the following table :— 
Operation- Cards of the variables, 
cards. 
Number. |————_] 
of the Symbols Columns Galuning Progress of the 
operations.} indicating on which whighiseanive operations, 
bg Peo? operations Seaiotati 
of the are to be * 
operations.| _ performed. Opener 
1 x Wir Veil Mig cqunnn<anine =dn’ 
2 x Vier "Vg, conccsecbane =d'n 
3 x Vg X Vo =| Vj0 veceeees eee | = 2m 
4 me ree kta Hiemedeer ences =nm 
5 - Steg Min ssteteccsrese =dn'—d'n 
6 - Vio — Viz = | Vig sseceeveess «| =n'm — nm! 
7 / 
J WD we 2 27 du’ — d’n 
7 — Vv = Vigasegdeczedens rae Saas ere 
13 2m — nm 
Since the cards do nothing but indicate in what manner and on 
what columns the machine shall act, it is clear that we must still, 
in every particular case, introduce the numerical data for the 
calculation. Thus, in the example we have selected, we must 
previously inscribe the numerical values of m, n, d, m,n’, d', in 
the order and on the columns indicated, after which the machine 
when put in action will give the value of the unknown quantity 
wx for this particular case. To obtain the value of y, another 
series of operations analogous to the preceding must be per- 
formed. But we see that they will be only four in number, since 
the denominator of the expression for y, excepting the sign, is 
the same as that for v, and equal to 7!m—nm!. In the pre- 
ceding table it will be remarked that the column for operations 
indicates four successive multiplications, two subtractions, and 
