second a mode of comparing ideas; but with these exceptions I have not yet met with so much as a suggestion of a reasoning machine. It may be added that Mr. Smee’s designs, though highly ingenious, appear to be impracticable, and in any case they do not attempt the performance of logical inference.[80] [80] See his work called *The Process of Thought adapted to Words and Language, together with a Description of the Relational and Differential Machines*. Also *Philosophical Transactions*, [1870] vol. 160, p. 518. The Logical Abacus soon suggested the notion of a Logical Machine, which, after two unsuccessful attempts, I succeeded in constructing in a comparatively simple and effective form. The details of the Logical Machine have been fully described by the aid of plates in the Philosophical Transactions,[81] and it would be needless to repeat the account of the somewhat intricate movements of the machine in this place. [81] *Philosophical Transactions* [1870], vol. 160, p. 497. *Proceedings of the Royal Society*, vol. xviii. p. 166, Jan. 20, 1870. *Nature*, vol, i. p. 343. The general appearance of the machine is shown in a plate facing the title-page of this volume. It somewhat resembles a very small upright piano or organ, and has a keyboard containing twenty-one keys. These keys are of two kinds, sixteen of them representing the terms or letters A, *a*, B, *b*, C, *c*, D, *d*, which have so often been employed in our logical notation. When letters occur on the left-hand side of a proposition, formerly called the subject, each is represented by a key on the left-hand half of the keyboard; but when they occur on the right-hand side, or as it used to be called the predicate of the proposition, the letter-keys on the right-hand side of the keyboard are the proper representatives. The five other keys may be called operation keys, to distinguish them from the letter or term keys. They stand for the stops, copula, and disjunctive conjunctions of a proposition. The middle key of all is the copula, to be pressed when the verb *is* or the sign = is met. The key to the extreme right-hand is called the Full Stop, because it should be pressed when a proposition is completed, in fact in the proper place of the full stop. The key to the extreme left-hand is used to terminate an argument or to restore the machine to its initial condition; it is called the Finis key. The last keys but one on the right and left complete the whole series, and represent the conjunction *or* in its unexclusive meaning, or the sign ꖌ which I have employed, according as it occurs in the right or left hand side of the proposition. The whole keyboard is arranged as shown on the next page--