690 L. F. MENABREA ON BABBAGE’S ANALYTICAL ENGINE. 
numerical tables, the machine can be brought into play so as to 
give several results at the same time, which will greatly abridge 
the whole amount of the processes. Thirdly, economy of intelli- 
gence: a simple arithmetical computation requires to be per- 
formed by a person possessing some capacity ; and when we pass 
to more complicated calculations, and wish to use algebraical for- 
muiz in particular cases, knowledge must be possessed which 
pre-supposes preliminary mathematical studies of some extent. 
Now the engine, from its capability of performing by itself all 
these purely material operations, spares intellectual labour, which 
may be more profitably employed. Thus the engine may be con- 
sidered as a real manufactory of figures, which will lend its aid 
to those many useful sciences and arts that depend on numbers. 
Again, who can foresee the consequences of such an invention ? 
In truth, how many precious observations remain practically 
barren for the progress of the sciences, because there are not 
powers sufficient for computing the results! And what discou- 
ragement does the perspective of a long and arid computation 
cast into the mind of aman of genius, who demands time exclu- 
sively for meditation, and who beholds it snatched from him by 
the material routine of operations! Yet it is by the laborious 
route of analysis that he must reach truth; but he cannot pur- 
sue this unless guided by numbers; for without numbers it is 
not given us to raise the veil which envelopes the mysteries of 
nature. Thus the idea of constructing an apparatus capable 
of aiding human weakness in such researches, is a conception 
which, being realized, would mark a glorious epoch in the history 
of the sciences. The plans have been arranged for all the various 
parts, and for all the wheel-work, which compose this immense 
apparatus, and their action studied; but these have not yet been 
fully combined together in the drawings* and mechanical no- 
tation +. The confidence which the genius of Mr. Babbage 
must inspire, affords legitimate ground for hope that this enter- 
prise will be crowned with success; and while we render homage 
to the intelligence which directs it, let us breathe aspirations 
for the accomplishment of such an undertaking. 
* This sentence has been slightly altered in the translation in order to ex- 
press more exactly the present state of the engine.—Norr by TransLaTor. 
+ The notation here alluded to is a most interesting and important subject, 
and would have well deserved a separate and detailed Note upon it, amongst 
those appended to the Memoir. It has, however, been impossible, within the 
space allotted, even to touch upon so wide a field—Nore sy Transtaror, 
