556 



SCIENCE 



[N. S. Vol. XXX. No. 773 



eially from the standpoint of their inter- 

 pretation, is a feature of the M.E. and E.B. 

 courses. 



Plates 6 and 7 seem to indicate that the 

 M.E. course requires a more general use 



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of the principles of the integral calculus 

 than the C.E. course. 



If we look for such articles as the evalua- 

 tion of indeterminate forms, complicated 

 integrals to be broken up into partial frac- 

 tions before integrating, long reduction 

 formulas, fancy substitutions, forms of re- 

 mainders, order of contact, envelopes, sub- 

 tangents and the like, we won't find them. 

 Many curves are used and should be studied 

 more for their properties than they are, one 

 reason why they are not being the fact that 

 the equations of so many of the curves 

 which arise can at best be found only em- 

 pirically. 



It might seem that the matter of approxi- 

 mations is neglected in the enumeration be- 

 cause of the fact that so many approxima- 

 tions must necessarily occur in engineering 

 practise ; but in the list of those enumerated 

 none were included which did not have a 

 strong flavor of the calculus, which fact ex- 



cluded many often listed under the head of 

 approximate integrations, such as the use 

 of Simpson's rule and the like. 



Can we learn any general lessons from 

 the results of the investigation? Easily. 

 It is apparent to even the casual observer 

 that the subject which stands out most 

 prominently is that of the formulation of 

 the definite integral with its limits. Here 

 it is a question of whether or not the stu- 

 dent can think mathematically, whether he 

 is alive to the situation and grasps the 

 problem before him, and whether he can 

 express existing conditions in mathematical 

 language. He should know the funda- 

 mental principle of the integral calculus 

 well, and should have a check on his work 

 wherever possible. A planimeter should 

 find its place in the same class-room with 

 the slide rule, and both should be used as 

 early as possible for checking up results. 



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It is not sufficient to have theory only, for 

 engineering by its very nature calls for 

 results. The notions of the calculus are 

 not iTsed blindly, each has its specific ap- 



