Febbuaet 26, 1904.] 



SCIENCE. 



325 



ai'tieles are published in the Proceedings 

 of the Society for the Promotion of 

 Engineering Education, Volumes II. and 

 V. But among the most suggestive dis- 

 cussions during the last year, as well 

 as all previous years, are the papers 

 of some of our brightest electrical en- 

 gineers presented at the joint meeting 

 last July at Niagara Falls of the so- 

 ciety just mentioned and of the American 

 Institute of Electrical Engineers and pub- 

 lished this year in the proceedings of both 

 societies. To those interested in finding the 

 best educational conditions leading to the 

 average as well as the most important 

 engineering operations of the day these 

 papers come with peculiar weight and au- 

 thority. Judging from the expressions of 

 opinion contained in them the active engi- 

 neer in his occupation, at least, cares noth- 

 ing for the philosophic basis of the concept 

 of number, nor for the geometry of non-eu- 

 clidian space, nor for Grassman's stufe of 

 the fifth or sixth degree, nor for com- 

 putations of plane triangles when the sum 

 of the angles is less than 180 degrees. These 

 subjects may and should interest the pro- 

 fessional mathematician, but the engineer 

 asks first for the ability to use numbers 

 rapidly and to carry numerical computa- 

 tions, no matter how complex, to an ac- 

 curate conclusion. As for ordinary mathe- 

 matics, including of course elementary 

 geometry, algebra and trigonometry, the 

 engineer should know them as he 'knows 

 the currency of his native country. In 

 other words, he ought to be able to make 

 change with ease, quickness and accuracy 

 — not as if one were in a foreign country 

 in a constant state of painful reckoning.' 

 On a basis of barter modern business 

 would be strangled. The very existence of 

 commerce in the modern sense, in which 

 the line of cost and profit is so finely drawn, 

 would be utterly impossible without a stan- 

 dard currency. So without mathematics 



engineering would be a mass of empiricism 

 and tradition. Instead of a pioneer leading 

 the way in the progress of the people it 

 would be an outcast trailing in the rear of 

 every science. 



This proposition that mathematics is the 

 very bone and sinew of an engineering 

 course needs no discussion. It is every- 

 where conceded. The extent and nature 

 of the mathematical element in the curric- 

 ulum, however, are two decided fluents with 

 curves of opposite slope. More mathemat- 

 ics but fewer kinds seems to be the tend- . 

 ency. The opinion appears to be gaining 

 ground that the purely descriptive and 

 highly specialized and professionalized ele- 

 ments in our technical courses should be 

 reduced, while more subjects with a mathe- 

 matical basis, with long unbroken continu- 

 ity and bound together with a strong log- 

 ical element should command the attention 

 of the student to the end of his undergradu- 

 ate period. 



Upon the question what mathematical 

 subjects shall the undergraduate courses 

 include in our technical colleges, opinions 

 are decidedly at variance. Upon the four 

 ordinary elementary subjects the sentiment 

 is practically unanimous, but these should 

 be principally taught in the secondary 

 schools. The practical people, however, are 

 inclined to relegate analytic geometry and 

 the calculus to the scrap pile. 



To such subjects as vectors, theory of 

 functions, theory of groups, they allow no 

 place whatever. 



One can not but feel that this verdict 

 against analytic geometry and the elemen- 

 tary calculus— not to mention higher sub- 

 jects—is a great pity. Especially does it 

 seem true when we recall that instruction 

 in these two lines forms the principal 

 mathematical element of the second and 

 third years of the ordinary technical course 

 and that the calculus itself is probably the 

 most powerful and wonderful tool for in- 



