698 TRANSLATOR’S NOTES TO M. MENABREA’S MEMOIR 
To this it may be replied that an analysing process must equally have 
been performed in order to furnish the Analytical Engine with the neces- 
sary operative data; and that herein may also lie a possible source of error. 
Granted that the actual mechanism is unerring in its processes, the 
cards may give it wrong orders. This is unquestionably the case ; but 
there is much less chance of error, and likewise far less expenditure 
of time and labour, where operations only, and the distribution of these 
operations, have to be made out, than where explicit numerical results 
are to be attained. In the case of the Analytical Engine we have 
undoubtedly to lay out a certain capital of analytical labour in one parti- 
cular line ; but this is in order that the engine may bring us in amuch 
larger return in another line. It should be remembered also that 
the cards when once made out for any formula, have all the generality 
of algebra, and include an infinite number of particular cases. 
We have dwelt considerably on the distinctive peculiarities of each 
of these engines, because we think it essential to place their respective 
attributes in strong relief before the apprehension of the public; and 
to define with clearness and aceuracy the wholly different nature of the 
principles on which each is based, so as to make it self-evident to the 
reader (the mathematical reader at least) in what manner and degree 
the powers of the Analytical Engine transcend those of an engine, 
which, like the Difference Engine, can only work out such results as 
may be derived from one restricted and particular series of processes, 
such as those included in A” w, =0. We think this of importance, 
because we know that there exists considerable vagueness and inaccu- 
racy in the mind of persons in general on the subject. There is a 
misty notion amongst most of those who have attended at all to it, 
that éwo “ calculating machines” have been successively invented by 
the same person within the last few years; while others again have 
never heard but of the one original “ calculating machine,” and are not 
aware of there being any extension upon this. For either of these 
two classes of persons the above considerations are appropriate. While 
the latter require a knowledge of the fact that there are éwo such in- 
ventions, the former are not less in want of accurate and well-defined 
information on the subject. No very clear or correct ideas prevail as 
to the characteristics of each engine, or their respective advantages or 
disadvantages ; and, in meeting with those incidental allusions, of a 
more or less direct kind, which occur in so many publications of the 
day, to these machines, it must frequently be matter of doubt which 
“ calculating machine ” is referred to, or whether both are included in 
the general allusion. 
We are desirous likewise of removing two misapprehensions which 
we know obtain, to some extent, respecting these engines. In the first 
place it is very generally supposed that the Difference Engine, after it 
had been completed up to a certain point, suggested the idea of the 
Analytical Engine; and that the second is in fact the improved offspring 
of the first, and grew out of the existence of its predecessor, through 
some natural or else accidental combination of ideas suggested by this 
one. Such a supposition is in this instance contrary to the facts; 
although it seems to be almost an obvious inference, wherever two 
inventions, similar in their nature and objects, succeed each other 
closely in order of ime, and strikingly in order of value; more espe- 
