of the classics, implies an adaptation of the results of modern philology to the purposes of elementary instruction such as has hardly yet been realized; implies a body of teachers of modern linguistic science such as hardly yet exist—teachers whose instruction shall not be inferior in philosophic breadth and thoroughness to the very best of classical teaching. If we have few such books or teachers yet, there are indications on every hand that we very soon shall have them in the greatest abundance, and that modern language-teaching and English language-teaching are very soon to be relieved of the reproach of empiricism which has heretofore prevented them from taking the leading place which, as educating instrumentalities, rightfully belongs to them.
And, finally, time will also be gained by utilizing the at present barren and empty study of mathematics. If there is any thing more preposterous than the abuse of grammar, in our present grindstone-system, it is the abuse of mathematical study. Rightly viewed, the mathematics are the key to scientific, as language is the key to ethical study. At present, both are used as mental tread-mills, unprofitable mental gymnastics, keys to unlock empty chambers never destined to be filled; for their sole value is thought to lie in the mental exercise they give. Robbed thus of all living connection with other knowledge, they become the most disgustful, and therefore the most valueless, of mental exercise. Put into vital connection from the very outset with those great sciences, of whose laws they are only the symbolic language, the mathematics spring into life. By themselves, they are to most minds a series of barren puzzles, hardly rising in dignity or educational value above the game of chess, and so remote from all those paths in which the human mind naturally travels, that it is only one peculiarly-constituted mind in ten thousand that, in their abstract form, can pursue them with either pleasure or profit. Looked at as the language of the laws which govern the world of matter, and used as the instruments to unlock so many of its secrets, they lose their disgustfulness, and become a necessary, if a narrow and partial instru-
- Since writing the above, I have met with an unexpected corroboration of this view in the writings of an eminent mathematician. "I am not likely," says Mr. Todhunter, the distinguished mathematical teacher of English Cambridge, "to underrate the special ability which is thus cherished (by competitive examinations), but I cannot feel that I esteem it so highly as the practice of the university really suggests. It seems to me at least partially to resemble the chess-playing power which we find marvelously developed in some persons. The feats which we see or know to be performed by adepts at this game are very striking, but the utility of them may be doubted, whether we regard the chess-player as an end to himself or to his country."—("The Conflict of Studies," p. 19.) What the teaching of the higher mathematics appears to have become at Cambridge, that the teaching of their elements, divorced from their natural connection with the teaching of physical science, becomes in our schools and colleges. On the fallacy that it was the mathematical studies at Cambridge of certain eminent graduates of Cambridge that was the cause of their eminence, and for some wholesome common-sense, in regard to the general subject, see a recently-published pamphlet, "The Mathematical Tripos," by the Rev. H. A. Morgan, Fellow of Jesus College, Cambridge.