56 THE POPULAR SCIENCE MONTHLY. 



made it a settled policy. The seniors add one hour to the German 

 and now study literature, if one may so express it, in and for its 

 own beauty. Civics are well represented under the triple head 

 of American history, government, and economics. 



The mathematical sequence is always an open problem. A 

 contemporary philosopher who has written much that is wise and 

 helpful as regards education contends that modern schools make 

 entirely too much of mathematics. He holds that there are prom- 

 ising minds quite disqualified for such studies, and that it is un- 

 wise to force them along these lines as well as unfair to judge of 

 their ability by reference to so alien a standard. His heresy 

 seems likely to spread. I should agree with him were mathemat- 

 ics an isolated subject ; but when one comes to think about it, we 

 are dealing here not with a separate branch of study, but with an 

 element common to all branches of exact study the quantitative 

 element. It is the expression of an acknowledged master that we 

 have only so much science as we have mathematics. To omit or 

 curtail such a study would be to omit or curtail exactitude of 

 thought, and at the present juncture in human affairs we can ill 

 afford such a result. The manual training school, therefore, as 

 an exponent of modern education does well, I think, to lay full 

 stress on mathematics, and I am only sorry that its work in this 

 direction can not be more thorough and more extensive than it is. 

 The present sequence begins with algebra and runs through ge- 

 ometry, plane trigonometry, and higher algebra to analytics. Up 

 to the senior year the work is restricted to pure mathematics, but 

 at this point two practical applications are introduced surveying 

 and bookkeeping. The sequence is much the same at all of the 

 larger manual training schools. An inversion of the earlier part 

 is now contemplated at the Northeast School. We propose to 

 start with geometry. The motive for this somewhat unusual se- 

 quence is a serious one. Of the several branches of lower mathe- 

 matics geometry makes the most direct appeal to the imagination 

 of a child, and it does this by reason of its graphic method of pres- 

 entation. Its concreteness makes it easier than either algebra or 

 arithmetic. Algebra is nearly always difficult, and can best be in- 

 troduced, it seems to me, after a boy has gained a somewhat more 

 lively conception of quantity and relation than that given by the 

 study of arithmetic. Such a sequence holds, I am told, in a num- 

 ber of English schools. 



As it is essentially a modern -language and mathematical 

 school, so also is the manual training school essentially a scien- 

 tific school. The daily curriculum always includes a science les- 

 son. The work begins with natural history (geology, botany, and 

 zoology), progresses through physics, and ends with chemistry 

 and electrical engineering. The two latter branches have long 



