ON BABBAGE’S ANALYTICAL ENGINE, 705 
either permanently remain on its column during the succeeding cal- 
culations, so that when all the functions had been computed, their va- 
2s would simultaneously exist on V,, V;, V,, &c.; or each result might 
er being printed off, or used in any specified manner) be effaced, to 
nake way for its successor. The square under V, ought, for the latter 
_ arrangement, to have the functions a2”, 2*”,an a, &c. successively 
_ inscribed in it. 
____ Let us now suppose that we have ¢wo expressions whose values have 
en computed by the engine independently of each other (each having 
its Own group of columns for data and results). Let them be a2”, 
6.p.y. They would then stand as follows on the columns :— 
V2 : V3 V; Ve 
oococo 
Va 
+ 5 + 
19) 19) 0 
19) 0 0 
0. 0 0 
0 0 0 
ae tle a 
We may now desire to combine together these two results, in any 
manner we please ; in which case it would only be necessary to have 
an additional card or cards, which should order the requisite opera- 
tions to be performed with the numbers on the two result-columns, V, 
and V,, and the result of these further operations to appear on a new 
column, V,. Say that we wish to divide aa” by b.p.y. The nu- 
Merical value of this division would then appear on the column V,, 
[=] oooo+ 
[‘ | cooo4+s 
~ 
a) 
1 
4 
ae 
beneath which we have inscribed —. The whole series of opera- 
tions from the beginning would be as follows (m being = 7) :— 
Bs. {7( x) 2(%) 5 fsor {9(x), + }. 
This example is introduced merely to show that we may, if we 
please, retain separately and permanently any intermediate results (like 
ax", b.p.y.), which occur in the course of processes having an ulterior 
and more complicated result as their chief and final object (like es )s 
bpy 
_ Any group of columns may be considered as representing a general 
function, until a special one has been implicitly impressed upon them 
hrough the introduction into the engine of the Operation and Variable- 
made out for a particular function. Thus, in the preceding 
ple, V,, V. V3, Vss V., V, represent the general function 
4 : sac 2 
c (a, n; b, ps 2; y) until the function 5 
and implicitly expressed by the placing of the right cards in the en- 
gine. The actual working of the mechanism, as regulated by these 
cards, then explicitly developes the value of the function. The inscrip- 
ion of a function under the brackets, and in the square under the 
-Tesult-column, in no way influences the processes or the results, and 
_ is merely a memorandum for the observer, to remind him of what is 
joing on. It is the Operation and the Variable-cards only, which in 
reality determine the function. Indeed it should be distinctly kept in 
343 
has been determined on, 
‘ 
4 
? 
* 
