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form of canon, or they have omitted altogether to inquire into the axioms which must be adopted as the groundwork of the reasoning process. I have long felt persuaded of the truth enounced by that most clear thinker, Condillac-that "équations, propositions, jugemens, sont au fond la même chose, et que, par conséquent, on raisonne de la, même manière dans toutes les sciences ;" and it has been my endeavour at once to transform the proposition into the equation, and to employ it with an axiom of adequate simplicity and generality, not spoiling good new material with old tools.

69. I write this tract under the discouraging feeling that the public is little inclined to favour or to inquire into the value of anything of an abstract nature. There are numberless scientific journals and many learned societies, and they readily welcome the minutest details concerning a rare mineral, or an undescribed species, the newest scientific toy, or the latest observations concerning a change in the weather. All these things are in public favour because they come under the head. of physical science. Mathematicians, again, are in favour because they help the physical philosophers: accordingly the most incomprehensible specula1 La Logique; Œuvres de Condillac, vol. xxii. p. 173.

tions concerning a quintic, or a resolvent, or a new theory of groups, are readily (and deservedly) printed, although not a score of men in England can understand them. But Logic is under the ban of metaphysics. It is falsely supposed to lead to no useful works-to be mere speculation; and, accordingly, there is no journal, and no society whatever, devoted to its study. Hardly can a paper on a logical subject be edged into the Proceedings of any learned society except under false pretences. This state of things is doubtless due to an excessive reaction against the former pre-eminence of logical studies. Bacon, in protesting against the absurdities of the scholastic logicians, and the deference paid to an ancient author, placed himself at the head of this reaction. Were he living now, he would probably see that the slow pendulum of public opinion has swung to the opposite extreme, and would employ his great intellect in showing how absurd it is to cultivate the branches of the tree of knowledge, and neglect the root-which root is undoubtedly to be found in a true comprehension of logical method.



ALTHOUGH a brief account of the abacus is given in the text (p. 55), it seems desirable to add a more minute description, which, in connexion with the drawings placed in front of the title-page, will enable copies of the abacus to be made with ease. The contrivance is of so simple a character, that an instrument-maker, or even an ordinary cabinet-maker, would probably be able to construct it from the figures and description.

The abacus consists, in the first place, of an ordinary black board of deal wood, such as is used in schools or lecture-rooms. This board should be about 3 feet square, and must have four ledges (1, 1) of wood, about I inch deep and inch thick, fixed across it at equal and parallel distances, a space of about 15 inches being left at the upper part of the board. The ledges may be made to extend quite across the width of the board, and they should be painted, like the board, of a dull black colour. When in use, the board is supported on a suitable stand in a slightly inclined position, as shown by the side view (6)


in the figure, so that the slips of wood placed upon the ledges, as at (6, 7) will stand securely.

It is convenient to have altogether four sets of lettered slips, namely:

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At (9, 11, 13, 15, and 17) are shown side views of the same slips. They are made of the best baywood, inch thick, I inch broad, and of the lengths stated above, so as to give a surface of one square inch for each letter. Each wooden slip is marked with a different combination of letters, printed upon white paper and pasted on the face of the slip.1 The nature of the combinations will be readily gathered from pp. 52, 54, and 56, and a set of sixteen of the slips is shown in the figure at (7), resting upon one of the ledges in the usual manner.

In the face of each wooden slip are fixed pins of thin brass or steel wire, projecting from the wood about inch in an inclined direction. Every slip has a pin near to its upper end, as at (18), but the positions of the other pins are varied according to the combination of letters represented on the slip. Each large capital or positive letter is furnished with a pin in the upper part of the space allotted to it, as at (19, 20, 21, &c.), while each small or negative letter has a pin in the lower part of its space, as at (22, 23, 24, &c.). At the lower end of each

1 I shall be happy to send a set of the printed letters to any person who may desire to have an abacus constructed.

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