Note 18 — NOTE A.—Page 9.

The machine might have been constructed so as to tabulate for a higher value of than seven. Since, however, every unit added to the value of increases the extent of the mechanism requisite, there would on this account be a limit beyond which it could not be practically carried. Seven is sufficiently high for the calculation of all ordinary tables.

The fact that, in the Analytical Engine, the same extent of mechanism suffices for the solution of , whether , , or = any number whatever, at once suggests how entirely distinct must be the nnature of the principles through whose application matter has been enabled to become the working agent of abstract mental operations in each of these engines respectively; and it affords an equally obvious presumption, that in the case of the Analytical Engine, not only are those principles in themselves of a higher and more comprehensive description, but also such as must vastly extend the practical value of the engine whose basis they constitute.