personal termination to the verb use the separate forms corresponding to the ten class-prefixes of the nouns, it must be in accordance with the general spirit and system of these tribes. The various plural forms, if they persist, will reflect contemporary modes of life. Numbers were at first immersed in the persons, and then, as things came to be considered also, in the things numbered. The mind seems to have proceeded slowly from the vague one to definite numbers. And the first decided step was taken towards an apprehension of numbers when two was distinguished from one, and the distinction was made part of the personal terminations. The plural was a further step in the same direction: the real value of which, however, did not become apparent until the numerals had been separately established in forms of their own. When that was accomplished, the special form of the dual became useless: it had outlived its purpose, and henceforth it ceased to have, any but that poetical beauty of old association which often adorns the once natural, but now obsolete growths of the past. When the numerals were thus emancipated from their material and sensuous environment, quantity was translated from outward being in its embodiments into a form of thought. At first, indeed, it was placed in an ethereal or imaginative space, the counterpart as it were of the sensuous space in which it had been previously immersed. It became a denizen of the mental region, as it had been before a habitant of the sense-world. The mind was informed with quantity in the shape of number: but it does not follow from this, that the new product was comprehended, or the process of its production kept in view. Like all new inventions (and numeration may fairly be classed under that head), it was laid hold of, and all its consequences, results, and uses estimated and realised by the practical and defining intellect. In one direction, it became, like many new inventions in the early days of society, a magic charm, and was invested with mystery, sacredness, and marvellous powers. But the intelligent mind,--the understanding,--resolved to make better use of the new instrument: and that in two ways, in practical work and in theory. On the one hand it was applied practically in the dealings of life,--in commerce, contracts, legislation, and religion. On the other hand, the new conception of number, which common sense and the instinctive action of men had evolved, was carried out in all its theory: it was analysed in all directions, and its elements combined in all possible ways. The result was the science of arithmetic, and mathematics in general. Such consequences did the reflective understanding derive from the analysis of its datum,--the fact of quantity freed from its sensuous envelope.