JuxT 17, 1908] 



SCIENCE 



77 



the principal reason for teaching calculus, 

 not all are agreed, however, as to the best 

 method of accomplishing this purpose. 

 Some would maintain that it should be 

 taught by the mathematical department 

 and in connection with calculus ; others and 

 perhaps the larger number feel that it 

 should be given by the engineering depart- 

 ments and made to follow and supplement 

 the calculus, giving the student his first 

 real introduction into the applications of 

 his mathematics to the fundamental prin- 

 ciples underlying all engineering courses. 

 However this may be, there is little 

 doubt that more applications to mechanics 

 should be introduced into the course in 

 calculus than is now usually the ease, even 

 to the exclusion, if need be, of some of the 

 applications to geometry frequently given.^ 

 Problems in work, energy and stress form 

 just as legitimately an integral part of a 

 course in calculus as problems in order of 

 contact, asymptotes or envelopes. The 

 applications to geometry and to mechanics 

 should be given about the same relative 

 importance in a well-balanced course in 

 calculus. 



Descriptive geometry is another subject 

 in the engineering course which might well 

 be revised and made more mathematical in 

 its treatment. It is to be regretted that 

 the subject has in this country degenerated 

 into little more than mechanical drawing. 

 It would be greatly improved for engi- 

 neers, as well as the general student, if we 

 should inject into it something of the scien- 

 tific spirit given it in European schools. 



No presentation of the subject under dis- 

 cussion would be complete without some 

 consideration of the preparation which the 

 teacher of mathematics has, or should have, 

 who is to teach the subject to engineering 

 students. There is a strong feeling in some 

 quarters that such an instructor should be 

 a trained engineer in order that he may the 

 better appreciate the kind of applications 



which are best suited to the training of an 

 engineer and to make sure that the proper 

 emphasis be placed upon those topics con- 

 sidered essential in such training. Some 

 would go still farther and insist that even 

 in the elementary courses in mathematics 

 usually given in the first two years, the 

 purpose and aim of the prospective engi- 

 neer is so radically different from that of 

 the general student that the content of the 

 course itself should be very different from 

 what is best suited to the student who 

 elects mathematics as a part in a general 

 education. 



It goes without saying that we should 

 eliminate from the courses for engineering 

 students that which is non-essential, and 

 we should make them as practical as we 

 may by the generous use of those physical 

 applications which will give the students 

 both skiU and facility in applying mathe- 

 matics to such concrete cases as may arise 

 later in his experience. On the other hand, 

 it would be disastrous to go to the extent 

 of teaching any of the principles of mathe- 

 matics empirically or of permitting stu- 

 dents to assume as already established for- 

 mulas which he has merely to learn how to 

 apply. We should avoid the danger of 

 going too far in allowing the student to 

 disregard the necessity of a formal demon- 

 stration and to regard lightly the logic and 

 the philosophy of mathemat^s. What is 

 needed first of all is the ability on the part 

 of the student to think mathematically and 

 to have not only a ready but an intelligent 

 command of the fundamental principles of 

 the subject. We should introduce the ap- 

 plications of mathematics not for the sole 

 purpose of giving the student a foretaste of 

 the things which are in store for him, but 

 because such applications give him addi- 

 tional opportunity for gaining a clearer 

 comprehension of mathematical processes: 

 and principles which might otherwise be 

 hazy; and I wish to add that this is more 



