722 TRANSLATOR’S NOTES TO M. MENABREA’S MEMOIR 
highly important for some of the future wants of science in its manifold, 
complicated and rapidly-developing fields of inquiry, to arrive at. 
Without, however, stepping into the region of conjecture, we will 
mention a particular problem which occurs to us at this moment as 
being an apt illustration of the use to which such an engine may be 
turned for determining that which human brains find it difficult or im- 
possible to work out unerringly. In the solution of the famous pro- 
blem of the Three Bodies, there are, out of about 295 coefficients of 
lunar perturbations given by M. Clausen (Astro®. Nachrichten, No. 
406) as the result of the calculations by Burg, of two by Damoiseau, and 
of one by Burckhardt, fourteen coefficients that differ in the nature 
of their algebraic sign ; and out of the remainder there are only 101 (or 
about one-third) that agree precisely both in signs and in amount. 
These discordances, which are generally small in individual magnitude, 
may arise either from an erroneous determination of the abstract co- 
efficients in the development of the problem, or from discrepancies in 
the data deduced from observation, or from both causes combined. 
The former is the most ordinary source of error in astronomical com- 
putations, and this the engine would entirely obviate. 
We might even invent laws for series or formulz in an arbitrary 
manner, and set the engine to work upon them, and thus deduce nu- 
merical results which we might not otherwise have thought of obtain- 
ing. But this would hardly perhaps in any instance be productive of 
any great practical utility, or calculated to rank higher than as a kind 
of philosophical amusement. A. A. L. 
Nore G.—Page 689. 
It is desirable to guard against the possibility of exaggerated ideas 
that might arise as to the powers of the Analytical Engine. In consi- 
dering any new subject, there is frequently a tendency, first, to over- 
rate what we find to be already interesting or remarkable; and, se- 
condly, by a sort of natural reaction, to undervalue the true state of the 
case, when we do discover that our notions have surpassed those that 
were really tenable. 
The Analytical Engine has no pretensions whatever to originate any 
thing. It can do whatever we know how to order it to perform. It can 
follow analysis ; but it has no power of anticipating any analytical re- 
lations or truths. Its province is to assist us in making available what 
we are already acquainted with. This it is calculated to effect prima- 
rily and chiefly of course, through its executive faculties; but it is 
likely to exert an indirect and reciprocal influence on science itself in 
another manner. For, in so distributing and combining the truths 
and the formule of analysis, that they may become most easily and 
rapidly amenable to the mechanical combinations of the engine, the 
relations and the nature of many subjects in that science are necessarily 
thrown into new lights, and more profoundly investigated. This is a 
decidedly indirect, and a somewhat speculative, consequence of such an 
invention. It is however pretty evident, on general principles, that 
in devising for mathematical truths a new form in which to record and 
throw themselves out for actual use, views are likely to be induced, 
which should again react on the more theoretical phase of the subject. 
There are in all extensions of human power, or additions to human 
