NOTICES OF BOOKS. v 



more particularly for readers who have had very little Mathematical 

 training, but that he also has in view readers who already know a good 

 deal about the Calculus, but are unable to apply their knowledge in 

 practical Engineering problems : " A man learns to use the Calculus 

 as he learns to use the chisel and file on actual concrete bits of work, 

 and it is on this idea that I act in teaching the use of Calculus to 

 Engineers ". 



The powerful tools of the Calculus are put into the hands of the 

 reader, and he is shown to what use the}- may be turned in the solution 

 of Engineering problems. 



The first chapter of more than 150 pages is devoted to the study of 

 x". The use of squared paper is explained, and a set of exercises on 

 graphing are given : also the method of investigating whether any 



•■11 U ax 



empirical law such as y = — -, or kv" = constant, connects two van- 



bx + c 



ables.v, j', of which sets of simultaneous values have been experimentally 

 determined. By means of numerical illustrations the idea of a limit is 

 clearly shown, and the absolute accuracy of a differential coefficient as a 

 rate-measurer brought home thoroughly to the mind of the reader. The 

 arithmetical method of finding approximately the acceleration at differ- 

 ent points of a moving body whose positions at close intervals have been 

 observed, is illustrated in a table. 



The integration of 



x m dx is immediately defined as the inverse of 



differentiation, and here perhaps it might have been well to have shown 

 b F\x) dx = F(b) - F{a) . 



at length that 



a 



Partial differentiation, maxima and minima, and tangents and nor- 

 mals to a curve are briefly explained, and then areas of closed curves, 

 lengths of curves, volumes of surfaces and moments of inertia are dealt 

 with, and a large number of illustrative problems on the bending o 

 beams, the flow of liquids, magnetism, and thermodynamics, are dis- 

 cussed, nearly all of which require no further knowledge of the Calculus 

 than the differentiation and integration of a ". 



Chapter ii. deals with the compound interest law and harmonic 

 functions, that is with problems involving the functions e x and sin ax, a 

 quantity whose rate of increase is proportional to itself being said to 

 follow the compound interest law. Here again numerical illustrations 

 of the value of the differential coefficients are recommended to the con- 

 sideration of the reader, and many electrical and mechanical problems 

 are discussed. Fourier's theorem is stated, and its practical application 

 is explained. On the subject of vibrations a very instructive numerical 

 example of a linear differential equation with constant coefficients is 

 worked out at length. 



Chapter iii. is called " Academic Exercises,'' and contains in brief 

 some of the usual elementary portions of the ordinary treatises on 

 Differential and Integral Calculus and Differential Equations. Elliptic 



