whole treatment of external nature is to be found in this one proposition: wheresoever we look for figure, he looks for life. His waves (as well as his fire) when they are stirred, shout, in the very word (iáxew) that he gives to the Assembly of Achæans: when they break in foam, they put on the plume of the warrior's helmet (Koper): when their lord drives over them, they open wide for joye: and when he strides upon the field of battle, they, too, boil upon the shore, in an irrepressible sympathy with his effort and emotion f

c Il. xxiii. 216. i. 482.

• Γηθοσύνῃ δὲ θάλασσα διίστατο, Il. xiii. 29.

d Il. iv. 424.

f Il. xiv. 392.

SECT. III.

Homer's perceptions and use of Number.

WHILE the faculties of Homer were in many respects both intense and refined in their action, beyond all ordinary, perhaps we might say beyond all modern, examples, there were other points in which they bear the marks of having been less developed than is now common even among the mass of many civilized nations. In the power of abstraction and distinct introspective contemplation, it is not improbable that he was inferior to the generality of educated men in the present day. In some other lower faculties, he is probably excelled by the majority of the population of this country, nay even by many of the children in its schools. I venture to specify, as examples of the last-named proposition, the faculties of number, and of colour. It may be true of one or both of these, that a certain indistinctness in the perception of them is incidental everywhere to the early stages of society. But yet it is surprising to find it where, as with Homer, it accompanies a remarkable quickness and maturity not only of great mental powers, but of certain other perceptions more akin to number and colour, such as those of motion, of sound, and of form. But let us proceed to examine, in the first place, the former of these two subjects.

It may be observed at the outset, that probably none of us are aware to how great an extent our aptitudes with respect to these matters are traditionary, and dependent therefore not upon ourselves, but upon the

acquisitions made by the human race before our birth, and upon the degree in which those acquisitions have circulated, and have been as it were filtered through and through the community, so as to take their place among the elementary ideas, impressions, and habits of the population. For such parts of human knowledge, as have attained to this position, are usually gained by each successive generation through the medium of that insensible training, which begins from the very earliest infancy, and which precedes by a great interval all the systematic, and even all the conscious, processes of education. Nor am I for one prepared by any means to deny that there may be an actual 'traducianism' in the case: on the contrary, in full consistency with the teaching of experience, we may believe that the acquired aptitudes of one generation may become, in a greater or a less degree, the inherited and inborn aptitudes of another.

We must, therefore, reckon upon finding a set of marked differences in the relative degrees of advancement among different human faculties in different stages of society, which shall be simply referable to the source now pointed out, and distinct altogether from such variations as are referable to other causes. It is not difficult to admit this to be true in general: but the question, whether in the case before us it applies to number and colour, can of course only be decided by an examination of the Homeric text.

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,

Conceptions of Number not always definite.

427

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.

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 essen

tial 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.

And this leads me to the second of the two illustrations, to which reference has been made. That loss of definiteness in the conception of number, which the child in our day suffers before he has counted over his fingers, the grown man suffers also, though at a point commonly much higher in the scale. What point that may be, depends very much upon the particular habits and aptitudes of the individual. A student in a library of a thousand volumes, an officer before his regiment of a thousand men upon parade, may have a pretty clear idea of the units as well as of the totals; but when we come to a thousand times a thousand, or a thousand times a million, all view of the units, for most men, probably for every man, is lost: the million for the grown man is in a great degree like the hundred for the child. The numerical term has now become essentially a symbol; not only as every word is by its essence a symbol in reference to the idea it immediately denotes; but, in a further sense, it is a symbol of a