Yet, before we enter upon this examination, let us endeavour to throw some further light upon the general aspect of the proposition, which has just been laid down. Of all visible things, colour is to our English eye the most striking. Of all ideas, as conceived by the English mind, number appears to be the most rigidly definite, so that we adopt it as a standard for reducing all other things to definiteness; as when we say that this field or this house is five, ten, or twenty times as large as that. Our merchants, and even our schoolchildren, are good calculators. So that there is a sense of something strikingly paradoxical, to us in particular, when we speak of Homer as having had only indeterminate ideas of these subjects. ~_Conceptions of Number not always definite._~ There are however two practical instances, which may be cited to illustrate the position, that number is not a thing to be as matter of course definitely conceived in the mind. One of these is the case of very young children. To them the very lowest numbers are soon intelligible, but all beyond the lowest are not so, and only present a vague sense of multitude, that cannot be severed into its component parts. The distinctive mark of a clear arithmetical conception is, that the mind at one and the same time embraces the two ideas, first of the aggregate, secondly of each one of the units which make it up. This double operation of the brain becomes more arduous, as we ascend higher in the scale. I have heard a child, put to count beads or something of the sort, reckon them thus: ‘One, two, three, four, a hundred.’ The first words express his ideas, the last one his despair. Up to four, his mind could contain the joint ideas of unity and of severalty, but not beyond; so he then passed to an expression wholly general, and meant to express a sense like that of the word multitude. But though the transition from number definitely conceived to number without bounds is like launching into a sea, yet the conception of multitude itself is in one sense susceptible of degree. We may have the idea of a limited, or of an unbounded, multitude. The essential distinction of the first is, that it might possibly be counted; the notion of the second is, that it is wholly beyond the power of numeration to overtake. Probably even the child, to whom the word ‘hundred’ expressed an indefinite idea, would have been faintly sensible of a difference in degree between ‘hundred’ and ‘million,’ and would have known that the latter expressed something larger than the former. The circumscribing outline of the idea apprehended is loose, but still there is such an outline. The clearness of the double conception is indeed effaced; the whole only, and not the whole together with each part, is contemplated by the mind; but still there is a certain clouded sense of a real difference in magnitude, as between one such whole and another.