670 UL. F. MENABREA ON BABBAGE’S ANALYTICAL ENGINE. 
of such calculations or for abridging them; and thence have 
arisen several inventions having this object in view, but which 
have in general but partially attained it. For instance, the much- 
admired machine of Pascal is now simply an object of curiosity, 
which, whilst it displays the powerful intellect of its inventor, 
is yet of little utility in itself. Its powers extended no further 
than the execution of the four* first operations of arithmetic, 
and indeed were in reality confined to that of the two first, since 
multiplication and division were the result of a series of additions 
and subtractions. The chief drawback hitherto on most of such 
machines is, that they require the continual intervention of a 
human agent to regulate their movements, and thence arises a 
source of errors; so that, if their use has not become general for 
large numerical calculations, it is because they have not in fact 
resolved the double problem which the question presents, that 
of correctness in the results, united with economy of time. 
Struck with similar reflections, Mr. Babbage has devoted 
some years to the realization of a gigantic idea. He proposed 
to himself nothing less than the construction of a machine capa- 
ble of executing not merely arithmetical calculations, but even 
all those of analysis, if their laws are known. The imagination 
is at first astounded at the idea of such an undertaking ; but the 
more calm reflection we bestow on it, the less impossible does 
success appear, and it is felt that it may depend on the discovery 
of some principle so general, that if applied to machinery, the 
latter may be capable of mechanically translating the operations 
which may be indicated to it by algebraical notation. The illus- 
trious inventor having been kind enough to communicate to me 
* This remark seems to require further comment, since it is in some degree 
calculated to strike the mind as being at variance with the subsequent passage 
(page 675), where it is explained that an engine which can effect these four 
operations can in fact effect every species of calculation. The apparent discre- 
pancy is stronger too in the translation than in the original, owing to its being 
impossible to render precisely into the English tongue all the niceties of distinc- 
tion which the French idiom happens to admit of in the phrases used for the 
two passages we refer to. The explanation lies in this: that in the one case 
the execution of these four operations is the fundamental starting-point, and the 
object proposed for attainment by the machine is the subsequent combination 
of these in every possible variety; whereas in the other case the execution of 
some one of these four operations, selected at pleasure, is the ultimatum, the 
sole and utmost result that can be proposed for attainment by the machine re- 
ferred to, and which result it cannot any further combine or work upon. The 
one begins where the other ends. Should this distinction not now appear per- 
fectly clear, it will become so on perusing the rest of the Memoir, and the Notes 
that are appended to it.—Nore py Transtaror. 
