July 17, 1908] 



SCIENCE 



75 



courses in spherical harmonics, vector an- 

 alysis, theory of functions and the mathe- 

 matical theory of heat, electricity, etc., to 

 the end that the student with exceptional 

 mathematical ability might lay a broader 

 foundation for the theoretical side of engi- 

 neering. In this connection, it may well 

 be questioned whether the technical schools 

 of this country are in general offering suf- 

 ficient opportunity for that training which 

 has made it possible for such men as Stein- 

 metz, Osborne Reynolds and Stodola to 

 accomplish the work which has made them 

 famous. 



Table III. shows also the sequence and 

 the distribution by years of the required 

 work in mathematics. We are quite as 

 much interested, however, in the character 

 as in the amount and distribution of the 

 mathematical instruction given to engineer- 

 ing students. The close observer will have 

 noticed the change which has been made 

 and is now being made in this respect. In 

 recent years there has swept over the coun- 

 try a wave of enthusiastic discussion con- 

 cerning a closer and better correlation of 

 mathematics with the physical sciences. 

 This has been due for the most part to the 

 influence felt in this country of the Perry 

 movement in England. Much is to be 

 learned from this movement, and still more 

 is to be avoided. The discussions which 

 have arisen from it have on the whole had 

 a beneficial effect upon the teaching of 

 mathematics both in America and in Eng- 

 land. 



It has first of all led to the introduction 

 into our text-books, and still more gener- 

 ally into our teaching, of a very much 

 better selection of problems— problems 

 which widen the student's fund of infor- 

 mation of physical phenomena and apply 

 the mathematical principles which he is 

 acquiring more extensively than was for- 

 merly the case to the physical laws with 



which he is familiar. Such problems as 

 the following, taken from a recent number 

 of an educational journal purporting to 

 serve the interests of mathematical teach- 

 ers in the secondary schools, is no longer 

 thought to be in good form by our best 

 instructors : 



"I bought 674,867 sheep at less than $10 

 per head: I paid for them in ten-dollar 

 bills and received back in change $7.39. 

 How many bills did I give ? ' ' 



Need I call attention to the absurdity of 

 putting such problems into the hands of 

 pupils? How many farmers in any wool- 

 producing state of the country ever even 

 saw that many sheep in his entire life, and, 

 should he have occasion to buy them, would 

 for a moment think of paying for them by 

 counting out 663,395 ten-dollar bills. So 

 long as such problems are given out for 

 the consideration of pupils, just so long we 

 may expect even the best of them to ask the 

 question so often heard in our algebra 

 classes: "What is all of this 'stuff' good 

 for, anyway?" 



Contrast with this problem the following, 

 taken at random from an algebra recently 

 published : 



"Two boys, A and B, having a 30-lb. 

 weight and a teeter board, proceed to de- 

 termine their respective weights as follows : 

 They find that they balance when B is 6 

 feet and A 5 feet from the fulcrum. If 

 B places the 30-lb. weight on the board 

 beside him, they balance when B is 4 and 

 A is 5 feet from the fulcrum. How heavy 

 is each boy ? " 



In solving this problem the boy has 

 learned just as much mathematics as in 

 solving the first. In addition, his mathe- 

 matics has been brought into contact with 

 a fundamental physical law, and incident- 

 ally he is made to feel that, after all, his 

 mathematics is of consequence to him in 

 solving the sort of questions in which he 



