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sense which is not in some relation one, as a tree, a grove, a forest, a world, a universe; and none which may not be divided and thus yield plurality. Now this action of. the judgment and attention must all go on under the notion of number, and, till this is furnished, all objects must remain undistinguished either as single or manifold. Objects of sense may reach the mind without drawing from it a numerical estimate. One may gather berries without regarding the number taken or left, though both be clearly seen. Distinction in the senses is not distinction in the intellect, and does not necessitate it; any more than distinction in existence is distinction in thought. A dozen calls may bring a dog, though he has taken no note of them as a dozen. Articulate sounds may convey the designed thought to the mind, a thought dependent on the exact number of elements, without attention directed to them as twenty, less or more.

This separable character of number from the objects perceived, is seen in the fact, that two impressions on the senses, as on the eyes of men, or many, as on the eye of an insect, become one object in the intellect; and still more strongly in the fact, that numbers are treated independently in arithmetic and algebra, are accumulated in amounts entirely beyond experience, and are divided and compounded by processes not founded on observation, or proved by it; but which belong to the necessary character of numerical conceptions. Our powerful algebraic solvents are general formulae, are wrought out wholly independently of things, and are brought to explain outside facts otherwise numerically unintelligible. Thus most evident is it, that in the more abtruse application of numbers, as to curves and to complex motion, phenomena receive their solution from the numerical conception and do not, through the senses, yield it. Moreover, these estimates are reached