OCTOBEB 22, 1909] 



SCIENCE 



555 



process, as would naturally be expected, 

 and the integral is most frequently that of 

 a power of the variable or function. 

 Double and triple integrals occur but 

 rarely, not but what they could be used 



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much oftener— but they aren't. The inte- 

 grals found are simple and the trigonomet- 

 ric are u-sually limited to combinations of 

 sines and cosines. 



The symbol of summation occurs fre- 

 quently, while the limit of the same Ls 

 rarely mentioned. 



The constant of integration quite often 

 composes the greater part of the indefinite 

 integral, in both size and importance. 



Calculus notions, such as moment of 

 inertia, centroid and radius of gyration, oc- 

 cur so frequently that there are portions 

 of certain courses which u.se very little else 

 in the way of calculus. The question may 

 be raised as to whether these should be 

 classified as principles of the calculus or of 

 mechanics, and the answer to this is that 

 the various texts in the technical subjects 

 assume that the student has learned them 

 in the studj- of the calculus as a prerequi- 

 site. 



The principle of mean value as used to 



find mean pressures, forces, etc., is re- 

 stricted to the M.E. and E.E. courses. 



The limits of the definite integrals used 

 are generally quite apparent from the na- 

 ture of the problem. The mathematician 

 may well learn a lesson here in the art of 

 making his problems both practical and 

 concrete. 



A comparison of Plates 4 and 5 will 

 show that the matter of partial differentia- 

 tion is one in which the mechanical engi- 

 neer alone seems to be interested. In this 

 connection it might also be mentioned that 

 the principle of exact or inexact differen- 

 tials, otherwise known as the integrability 

 condition, plays quite an important and 

 definite part in certain discussions, and 

 that it is deserving of more attention than 

 it receives at the hands of the authors of 

 texts in the calculus. 



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It will also be seen that the subject of 

 angular velocities and accelerations should 

 receive more attention than is usually given 

 to it. 



The study of differential equations, espe- 



