Note 1 — ARTICLE XXIX.

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 10), where it is explained that an engine which can effect these four operations can in fact effect every species of calculation. The apparent discrepancy 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 distinction 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 referred 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 perfectly clear, it will become soon perusing the rest of the Memoir, and the Notes that are appended to it.—NOTE BY TRANSLATOR.