[2] The idea that the one engine is the offspring and has grown out of the other, is an exceedingly natural and plausible supposition, until reflection reminds us that no necessary sequence and connexion need exist between two such inventions, and that they may be wholly independent, M. Menabrea has shared this idea in common with persons who have not his profound and accurate insight into the nature of either engine. In Note A. (see the Notes at the end of the Memoir) it will be found sufficiently explained, however, that this supposition is unfounded. M. Menabrea’s opportunities were by no means such as could be adequate to afford him information on a point like this, which would be naturally and almost unconsciously assumed, and would scarcely suggest any inquiry with reference to it.—NOTE BY TRANSLATOR. [3] See Note A. [4] This must not be understood in too unqualified a manner. The engine is capable, under certain circumstances, of feeling about to discover which of two or more possible contingencies has occurred, and of then shaping its future course accordingly.—NOTE BY TRANSLATOR. [5] See Note B. [6] Zero is not always substituted when a number is transferred to the mill. This is explained further on in the memoir, and still more fully in Note D.—NOTE BY TRANSLATOR. [7] See Note C. [8] See Note D. [9] Not having had leisure to discuss with Mr. Babbage the manner of introducing into his machine the combination of algebraical signs, I do not pretend here to expose the method he uses fur this purpose; but I considered that I ought myself to supply the deficiency, conceiving that this paper would have been imperfect if I had omitted to point out one means that might be employed for resolving this essential part of the problem in question. [10] See Note E. [11] For an explanation of the upper left-hand indices attached to the s in this and in the preceding table, we must refer the reader to Note D., amongst those appended to the memoir.—NOTE BY TRANSLATOR. [12] See Note F. [13] See Note G. [14] This sentence has been slightly altered in the translation in order to express more exactly the present state of the engine.—NOTE BY TRANSLATOR. [15] 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.—NOTE BY TRANSLATOR. NOTES BY THE TRANSLATOR. NOTE A.—Page 9. The particular function whose integral the Difference Engine was constructed to tabulate, is The purpose which that engine has been specially intended and adapted to fulfil, is the computation of nautical and astronomical tables. The integral of