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SCIENCE 



[N. S. Vol. XXVIII. No. 709 



company are fitted by temperament or by 

 education to take up with success tbe work 

 of pure engineering. A recent classifica- 

 tion of the graduates of Sibley College, 

 Cornell University, shows that about half 

 are in occupations which require no ad- 

 vanced mathematics and it is probable 

 that many of the 36 per cent, classed as 

 mechanical and electrical engineers seldom 

 go beyond the rules of arithmetic. Hence 

 a goodly proportion of engineering gradu- 

 ates do not need to be mathematical ex- 

 perts. Their mathematical studies need 

 not aim to produce experts, but should 

 have as a principal object the mathematical 

 training which is a most efficient kind of 

 training in an engineering course. On the 

 other hand, the engineers who will have 

 practical use for the higher mathematics 

 will find their ability as engineers is in a 

 large measure determined by their ability 

 as mathematicians. 



Second, the question, what kinds of 

 mathematics does the engineer need? is 

 closely related to the class of work he is 

 to do. In general a great deal of engineer- 

 ing work is done with much less use of 

 higher mathematics than most professors 

 probably imagine; and furthermore, it 

 may be remarked, with much less than 

 could profitably be employed. Engineers 

 are apt to use ordinarily the mathematical 

 methods with which they are most familiar 

 and which will bring the result with the 

 least effort. One man employs calculus, 

 another draws a diagTam, another writes 

 out formulge, while another gets his results 

 by mental arithmetic. The object is to get 

 the result. 



The fundamental idea that mathematics 

 is something for the engineer to use finds 

 many illustrative analogies in ordinary 

 tools. Adaptation is the first requisite. 

 Tools should be suited to the work to be 

 done. An expensive machine tool with its 

 refined adjustments is quite unnecessary 



for executing a piece of work which can 

 be done with sufficient accuracy by a few 

 minutes' application of a file. An ordi- 

 nary calculating slide rule is infinitely 

 better than a table of seven-piece logar- 

 ithms in every-day work. 



On the other hand, it is particularly 

 wasteful to attempt to execute a difficult 

 and intricate piece of work with inade- 

 quate tools. But more important than the 

 tool is the skiU of the man who uses it. 

 A skillful workman can accomplish results 

 with a few simple tools which others can 

 not get with the most elaborate special 

 equipment. 



Third, therefore, skill in the use of 

 mathematics is the really essential thing. 

 A judicious use of arithmetic with a little 

 algebra or a simple diagram often leads 

 to more satisfactory results than others 

 secure through elaborate processes involv- 

 ing lengthy equations and complicated 

 operations. In the latter, erroi's are liable 

 to occur, the common-sense import of the 

 problem is apt to be overlooked, assump- 

 tions may be made to facilitate calculations 

 which are physically unwarranted as one 

 loses sight of the physical problem in the 

 intricacy of the mathematical solution. 

 Abstract mathematical studies, if pursued 

 as a kind of intellectual calisthenics, may 

 produce a pure mathematician, but they 

 may unfit a man for practical engineering. 

 A mathematician is not necessarily an 

 engineer ; nor is an elocutionist necessarily 

 a good lecturer, nor is a tool expert a suc- 

 cessful manufacturer. 



Matliematics is used in engineering to 

 express the quantitative relations of na1> 

 ural phenomena. The mathematician de- 

 lights in the relations: he divorces them 

 from the phenomena and gives them ab- 

 stract expression, while the engineer is con- 

 cerned with the natural phenomena; he 

 demands the physical conception; the me- 



