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SCIENCE 



[N. S. Vol. XXVIII. No. 710 



engineer demanding more knowledge of 

 principles. No fair discussion of this sub- 

 ject can be had without considering for a 

 moment the conditions and definition of 

 engineering itself. The most common defi- 

 nition was promulgated more than half a 

 century ago by Thomas Tredgold, to the 

 effect that civil engineering, which was the 

 only branch of engineering then known, so 

 the definition may be considered as being 

 general, that "civil engineering is the art 

 of directing the great sources of power in 

 nature to the use and convenience of man. ' ' 

 I should say that "civil engineering to- 

 day is the art and science of directing the 

 great sources of power in nature to the use 

 and convenience of man," and from that 

 standpoint I am willing to discuss the ques- 

 tion as to how much and how far mathe- 

 matical instruction should enter. 



If engineering is merely an art, then 

 mathematics as a science has no place in 

 the training of the engineer, but if engi- 

 neering is a science, then mathematics has 

 a place. Engineering stands to-day in the 

 act of rising to the status of a science, but 

 is still hampered by the tradesman. On 

 the one hand, we have the demand that the 

 student's training be such as primarily to 

 make him useful to some one to-morrow; 

 and, on the other side, that it make him 

 useful to the world perhaps ten years 

 hence. The two requirements are incon- 

 sistent and do not belong together. One is 

 that of the trade school, and many should 

 not go farther than that because they have 

 not the mental capacity, and the other is 

 the demand of the profession into which a 

 smaller number are qualified to enter. The 

 trade school has caused most of the trouble 

 with the teaching of mathematics because 

 those who are products of the trade school 

 have no use for mathematics as a science. 

 The complaint about the teaching of mathe- 

 matics does not come from engineers; they 

 are ready to use mathematics as a science. 



In civil engineering it is fortunate that the 

 profession has developed along lines laid 

 down by Rankine rather than by Traut- 

 wine. Both have had their use, but one 

 of them produced the scientist and the 

 other produced the tradesman. 



It is maintained in the institution which 

 I have the honor to represent that they 

 who would teach engineering must prac- 

 tise it, and by analogy we might say that 

 those who teach mathematics to engineers 

 should themselves be engineers. It seems 

 to me that a time may come when such a 

 condition will be desirable, but let me say 

 now that there are few engineers to-day 

 who have had sufficient training in mathe- 

 matics to teach it themselves, much less to 

 tell mathematicians how it should be 

 taught. "We can perhaps judge of the 

 deficiency of the student who comes to us, 

 but my feeling is that the remedy is not a 

 question of what, but of Jiow. Men in my 

 institution are sending us students well 

 prepared in mathematics. Others do not 

 seem to be so fortunate. Both are teach- 

 ing the same subjects. We have to realize 

 that the student himself is a factor in this 

 question. Some students become mathe- 

 maticians under any one; others would not 

 under any one. To be taught mathematics 

 properly, the point at which engineering 

 minds must begin, is a long way back. I 

 am inclined to think they must begin some 

 generations before birth. The mathematics 

 of grammar schools needs overhauling more 

 than the mathematics of any other part of 

 our educational system, and probably the 

 mathematics of high schools stands next. 

 The essential thing that we ask of mathe- 

 matics is that it should develop the quanti- 

 tative reasoning power, and the student 

 must be able to think mathematically. If 

 he has not acquired that, then he should 

 drop out of engineering and take up a 

 trade. It was mentioned by a previous 

 speaker that a relatively small percentage 



