per-centage of the population who have never heard of the Queen; an examination of resident dons would probably reveal the awful fact that many of them do not know who is head of the river. Moreover, they are sometimes happy and in full possession of their faculties.

I have only one more fact to mention before leaving my athletic friends. The rarity with which the highest intellectual and physical distinction is combined might be anticipated. But is not the devotion to athletic sports injurious even to the attainment of lower excellence? Does it not contribute to plucks, and prevent a man from soaring from the third to the second class? I will only say now that some of the admirers of rowing admit that it does so, but deny that this is an evil. It was argued in a late University pamphlet that the captain of a boat-club received a better intellectual training from his position as captain than he did from studying for the ordinary degree. And, indeed, any one who has tried the experiment will admit that it is a severe trial of the judgment to keep eight oarsmen in due subjection.

IV.

MATHEMATICS.

A TRANSITION from physical to intellectual exercise may appear somewhat violent. If I do not mistake, however, there is a closer analogy than might at first sight be evident between the directions taken by our muscular and cerebral energy. To go no further, we expend a great deal of both upon objects intrinsically useless, and, moreover, their uselessness is often put forward as a recommendation. We don't learn rowing or cricket with a view to turning them to practical account. We are not about to set up as watermen or professional bowlers. A man may occasionally find his youthful accomplishments profitable; as, for example, in starting as a billiard-marker; but

it is not likely that that was his primary aim in learning billiards. We are quite content if we have had our fun, won our little meed of glory, and incidentally developed our muscles. Now, apologizing beforehand to philosophers, nothing can be less generally useful than cricket, except mathematics. As an amusement it is first-rate. A man may spend a happy life in cultivating an almost indecent familiarity with curves of the higher orders, in investigating extravagant formulæ, and in exhausting all the letters of all known alphabets to express his discoveries. So he may in playing whist, in solving chess problems, or unravelling Indian puzzles. As a mere intellectual toy, mathematics is far ahead of any known invention. Metaphysical studies are equally absorbing, but they don't even profess to come to any result, and they are apt to spoil the temper.

Of course, certain branches of mathematical knowledge have a direct bearing upon practical life. Somebody must be able to calculate eclipses and investigate the theory of tides, or how could we boast about modern science? And, for anything I know, there is something besides amusement to be

gained even in the abstruse recesses where the high priests of mathematics utter mysterious sentences, in a tongue not understood by the vulgar. But the true enthusiast rejects and scorns the application of any test of practical utility. Knowledge, he thinks, is knowledge; the more remote it is from all contact with concrete things the better; the special merit of mathematics is that you can sit in your own room and spin it like a spider out of your own inside without ever even looking out of the window. Mathematical theorems have a certain beauty of their own, which like that of some artistic products, is tarnished by the introduction of utilitarian ends. However this may be, mathematical, and indeed all other studies, are not even professedly pursued for their own sakes. To have been in love with some women is, we are told, to have received a liberal education; though love may not lead to marriage. A three years' flirtation with mathematics is supposed to produce the same effect. We may never meet them again, or meet them only to pass scrupulously by on the other side. But our minds have been strengthened and prepared for dealing with other subjects.

When the intelligent foreigner of fiction expresses his surprise at our English devotion to classics and mathematics, this is the answer which is invariably thrown at his head. Your students, he says, are kept hard at work till twenty-one upon matters which nine-tenths of them have utterly forgotten at thirty. They have been filling their minds pertinaciously with a lumber which is only to be consigned to vaults and cellars. Ought they not rather to be supplied with some useful stock-in-trade for future life? What can be the use of keeping them grinding at this mental treadmill, which is actually recommended by the inutility of its products? Ah, we reply, see how it strengthens the prisoners' thews and sinews. When we once let them out, there is no nut which they won't be able to crack, and no work which they won't find easy by comparison. We teach classics and mathematics because they are the best of all mental gymnastics. They strengthen the intellectual faculties, as lifting weights and jumping bars strengthen the muscles. If asked why they are the best, we appeal to "all experience" an appeal to experience being a well-known method