232 



SCIENCE 



[N. S. Vol. XXXIV. No. 



trigonometric expressions than by the 

 methods of the calculus, and but little at- 

 tention is paid to the sign of the second 

 derivative in determining the nature of 

 the same. The conditions of the problem 

 are, in general, sufficient to determine the 

 nature of the result on solving the equation 

 obtained by putting dy/dx^^Q. 



Series where used are assumed to be con- 

 vergent, or at least their convergence is 

 not questioned. They are generally simple 

 types. 



Many approximations occur in engineer- 

 ing practise, while those listed seem to be 

 few in number. However, none was 

 counted except the approximations of the 

 calculus. Among such we might mention 

 1/r^d^y/dx^, which is used in a ease 

 where, as stated, "dy/dx is small." 



The symbol of summation 2 is used often 

 and we find many a case of "near integra- 

 tion." The great importance placed on the 

 formulation and evaluation of the definite 

 integral is everywhere evident and many 

 areas are found where no definite integral 

 is expressed and where it is absolutely 

 essential to keep in mind the relation be- 

 tween the two. In this connection we 

 wish to mention the universal use of indi- 

 cator diagrams, and the frequent mention 

 of the planimeter used in determining 

 areas approximately — a point of view 

 which should be kept in mind when the 

 subject of definite integrals is being con- 

 sidered in the class-room. 



In connection with the integrations 

 found it seemed that at times the con- 

 stants multiplying the integral were by far 

 the most important part of the expression. 

 Instructors of calculus might with profit at 

 times allow their students to make their 

 own choice of such constants, which should 

 be placed on the outside of the integral 

 sign before evaluating the definite integral. 

 The term moment of inertia seems to mean 



two things to two different classes of engi- 

 neers. The engineer dealing with static 

 problems will have almost exclusively to 

 do with moments of inertia of sections, 

 while one working with problems bringing 

 in dynamics will think of what in one case 

 is called the "equatorial moment." The 

 two points of view should receive equal 

 attention in any course on the calculus. 



Concerning the differential equations 

 used and their solutions it may be said 

 that those used were of the simpler types 

 usually included in an elementary treatise 

 on ordinary differential equations. How- 

 ever, it seems to me that their solutions 

 must at times have been far above the head 

 of the average engineer, unless he had 

 given the subject special attention after 

 completing his university course in engi- 

 neering. The recommendation of the com- 

 mittee on engineering mathematics is to the 

 point, and should be carefully considered 

 by the instructor of calculus. It agrees 

 with results as found in practise. 



A further study of the mathematics used 

 by the practising engineer will reveal other 

 conditions in every way similar to those 

 existing in the undergraduate technical 

 course. The algebra and trigonometry 

 used are heavy as compared with the cal- 

 culus; naturally they are used much 

 oftener. 



If we look for things characteristic of 

 the engineer we easily find that numerical 

 results, correct to a certain decimal place, 

 are common and that much stress is placed 

 on accurate computation. Much care is 

 bestowed on the drawings and illustrations, 

 and constant attention is given to the scale 

 of the same. This is necessary in check- 

 ing up. Much use is made of indicator 

 diagrams and the planimeter is used to 

 obtain or check up on areas. At least one 

 of the journals makes a considerable use of 

 the first and second derivative curves and 



