—E 
L. F. MENABREA ON BABBAGE’S ANALYTICAL ENGINE. 675 
the product of two binomials (a + 6) (m + nz), the result will 
be represented by am+(an+bm) x +bnz*, in which ex- 
pression we must first calculate am, an, bm, bn; then take the 
sum of an + bm; and lastly, respectively distribute the coeffi- 
cients thus obtained, amongst the powers of the variable. In 
order to reproduce these operations by means of a machine, the 
latter must therefore possess two distinct sets of powers: first, 
that of executing numerical calculations ; secondly, that of rightly 
distributing the values so obtained. 
But if human intervention were necessary for directing each of 
these partial operations, nothing would be gained under the heads 
of correctness and ceconomy of time; the machine must there- 
fore have the additional requisite of executing by itself all the 
successive operations required for the solution of a problem 
proposed to it, when once the primitive numerical data for this 
same problem have been introduced. Therefore, since from 
the moment that the nature of the calculation to be executed or 
of the problem to be resolved have been indicated to it, the 
machine is, by its own intrinsic power, of itself to go through 
all the intermediate operations which lead to the proposed result, 
it must exclude all methods of trial and guess-work, and can 
only admit the direct processes of calculation*. 
It is necessarily thus ; for the machine is not a thinking being, 
but simply an automaton which acts according to the laws im- 
posed upon it. This being fundamental, one of the earliest 
researches its author had to undertake, was that of finding means 
for effecting the division of one number by another without using 
the method of guessing indicated by the usual rules of arith- 
metic. The difficulties of effecting this combination were far 
from being among the least; but upon it depended the success 
of every other. Under the impossibility of my here explaining 
the process through which this end is attained, we must limit 
ourselves to admitting that the four first operations of arithmetic, 
that is addition, subtraction, multiplication and division, can be 
performed in a direct manner through the intervention of the 
machine. This granted, the machine is thence capable of per- 
forming every species of numerical calculation, for all such cal- 
culations ultimately resolve themselves into the four operations 
* This must not be understood in too unqualified a manner. The engine is 
capable, under certain circumstances, of feeling about to discover which of two 
or more possible contingencies has occurred, and of then shaping its future 
course accordingly.—Norr ny TRANSLATOR, 
