554 



SCIENCE 



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



ric, are almost always of the simpler 

 sorts; in fact, as compared with algebra 

 employed, they are very easy. Difficult 

 differentiations occur rarely, while the trig- 

 onometric are usually limited to combina- 

 tions involving sines and cosines. 



Tafa/s -4Ci(/rjei - P/Z/e/v/jf/a/ 



throughout. The duty of the mathemati- 

 cian is clear here, but rigor should in every 

 case add to clearness of concept. 



The subject of maxima and minima is 

 handled without the aid of the second de- 

 rivative, the nature of the problem and 

 result being sufficient in almost every ca.se 



Tbfah - 4Coi/rje3 -Me^ra/ 



Appro/i. 



P/afe3 ) 



The use of differentials almost invariably 

 brings in the notion of infinitesimals, and 

 it is in this connection that the instructor 

 of mathematics in preparing the future 

 engineer can do an excellent work in giving 

 clear notions of the differential, which 

 need in no wise antagonize the use of the 

 infinitesimal. 



The engineering texts are certainly ad- 

 dicted to a rather loose use of the notion 

 of the derivative curves corresponding to 

 the elastic curve for concentrated load- 

 ings. A common tangent to these elastic 

 curves at points of discontinuity of the 

 derivative curves is frequently mentioned, 

 and quite erroneously. 



Increments and differentials are often 

 used quite synonymously, limits are rarely 

 mentioned, though understood to exist 



for the determination of the complete solu- 

 tion. Maxima and minima are often found 

 when no first derivative is equated to zero ; 

 in fact, many cases arise where the notions 

 exist quite sub rosa, because rigid conditions 

 for maxima and minima can, of necessity, 

 exist but approximately. Relative maxima 

 and minima are emphasized and lead to a 

 term such as maximum maximorum. It 

 might be well for the instructor of mathe- 

 matics to emphasize this feature more in 

 his teaching. Maxima and minima are 

 often solved from the standpoint of algebra 

 and trigonometry. 



The series found are usually simple in 

 construction and the question of their con- 

 vergence is mentioned in but a single text. 



The integrals used in almost all cases 

 arise as a consequence of the summation 



