22 THE POPULAR SCIENCE MONTHLY. 



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 indi- 

 cations on every hand that we very soon shall have them in the great- 

 est abundance, and that modern language-teaching and English lan- 

 guage-teaching are very soon to be relieved of the reproach of empiri- 

 cism 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 lan- 

 guage, the mathematics spring into life. By themselves, they are to 

 most minds a series of barren puzzles, hardly rising in dignity or edu- 

 cational 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. 1 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 dis- 

 gustfulness, and become a necessary, if a narrow and partial instru- 



1 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 marvel ously 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. 



