August 7, 1908] 



SCIENCE 



167 



of the graduates from a certain engineer- 

 ing school were engaged in occupations in 

 which mathematics was of importance. 

 From a somewhat intimate acquaintance 

 with the graduates of that institution, I 

 may add that a much less proportion had 

 sufficient mathematical training to take 

 positions in which mathematics was an im- 

 portant requirement. Until recently, that 

 college has stood for hardly more than a 

 highly developed trade school, and it is not 

 fair to cite its statistics as showing condi- 

 tions of engineering schools. The director 

 of that institution stated many years ago 

 that he did not consider descriptive geom- 

 etry necessary for mechanical engineers, 

 and his students, having had their course 

 in machine design in the junior year were 

 frequently found taking their only course 

 of descriptive geometry when seniors. 



The question has been raised as to the 

 increase of mathematics for entrance to 

 engineering schools. My view of that is 

 that it would not be wise to raise the 

 requirements at this time. Cornell has, it 

 is true, increased the requirements, but at 

 the sacrifice of both physics and chemistry, 

 and to my mind it is best that physics and 

 chemistry be taught at the age of high 

 school students, rather than analytics and 

 trigonometry. If you can not do both it 

 is better that the young mind have im- 

 pressed upon it some physical science 

 rather than encounter the more abstract 

 demands of mathematics. In the training 

 of students in mathematics I would wipe 

 out f ormulffi. We want principles. There 

 is generally taught too much of the for- 

 mula, as that is what the trade school has 

 demanded. Some have objected to the 

 statement that mathematics should be a 

 tool. To my mind it is certainly an in- 

 strument. It is one of the things that the 

 engineer must use, and in order that he 

 may use it, he must be sufficiently familiar 

 with it, so that it will respond to his use 



when he desires it. The question of elec- 

 tion in mathematics has been suggested. 

 I am certainly favorable to elections in that 

 subject, but I question the advisability of 

 such opportunity in any subject for the 

 ordinary student, before the fourth year. 

 My own observation leads me to conclude 

 that very few students are able to elect 

 intelligently before that time. The re- 

 marks relative to the employment of inex- 

 perienced instructors instead of competent 

 professors show a fault to lie with the 

 heads of the various departments them- 

 selves. If they are willing to accept, for 

 the purpose of instructing students, the 

 men who have been unable to find positions 

 elsewhere, and employ only such as will 

 work for seven to nine hundred dollars per 

 year, the unsatisfactory results are their 

 own fault. The responsible parties, the 

 trustees and regents of educational institu- 

 tions, will furnish what is shown to be 

 necessary. If it is necessary that you have 

 better men, then say so and get them, but 

 if you are satisfied with what you now 

 have, then you can expect to see decorative 

 cornices and stained glass windows, rather 

 than intellect and culture, the characteris- 

 tics of our universities. 



Gardner S. Williams 

 Univeesity op Michigan 



It may save time to state briefly at the 

 beginning my thought on what is needed 

 in the teaching of mathematics to engi- 

 neering students. It seems to me that, 

 outside of the general cultural and devel- 

 opmental purpose of the study of mathe- 

 matics, the instruction of engineering stu- 

 dents may be discussed under three dif- 

 ferent phases, which for want of better 

 terms may be named: (1) theory, (2)' 

 practise, (3) philosophy; that successful 

 teaching of mathematics to engineering 

 students depends upon giving the right 



