Notices respecting New Books. 445 



the absorption is mainly concerned with the organizing 

 effect of the electric force in the incident radiation fields, 

 the emission is more concerned with the disorganizing col- 

 lisions, and it is only in the case of very slow alternations 

 that a balance between the two has time to be established 

 before the one or the other is modified by the altering field 

 or by the collisions. 

 The University, Sheffield, 

 Jan. 4th, '1915. 



XL VI. Notices respecting New Books. 



Calculus Made Easy : Being a very -simplest Introduction to those 

 beautiful Methods of Reckoning which are generally called by the 

 terrifying Names of the Differential and the Integral Calculus. 

 By F.R.S. Second Edition, enlarged. MacmiJlan & Co., 

 Ltd., 1914. Pp. xii + 265. Price2.s-.net. 

 n^HE motto of this little book is : " What one fool can do, 

 -^ another can." It makes, in fact, some portions of the Calculus 

 ' ; easy," and, putting aside all claims of modern rigour, it can be 

 said that the facilitation attained has been achieved without 

 serious sacrifices of correctness. Also there is no doubt that the 

 book has been and will be useful to some classes of beginners. 

 But one thing is to be regret' ed : the author has diligently inter- 

 calated at every step such words and notions as "dodges," "tricks," 

 " pitfalls," "triumphs," &c, and used throughout a corresponding 

 style of exposition, to such a degree, that the reader, having gone 

 through all the little chapters, will most likely experience the 

 feeling of having conquered some hostile camp (where " trade- 

 secrets" have been kept in custody by the caste of " professional 

 mathematicians") instead of enjoying the acquired knowledge of 

 a really beautiful domain of human thought. Faraday, Tyndull,and 

 Clifford more especially, have taught us that almost everything 

 can be popularized in the good sense of the word, i. e. without 

 being unjust to the more subtle sides of the subject and without 

 leaving on it the brutal stamp of practical human concerns. 

 Frenchmen express this requirement shortly by distinguishing 

 " popularization " from " vulgarization." 



In spite of the author's warning (cf. " Epilogue and Apologue ") 

 there are in the book not many " most grievous and deplorable 

 errors," and the few that the reviewer has remarked will certainly 

 do no harm to the beginner. They will simply pass unobserved. 

 But such a statement as one reads on p. 204, viz.: — 



"If the figure of the solid be expressed by the function 

 /(.r, y, r), then the whole solid will have the volume-integral, 



volume = ft \f(v, y, -) . dx . dy . dz," 

 will certainly require a careful correction in a future edition. 

 Again, remarks such as that concerning \a~ x *dx, on p. 200, seem 

 rather misleading and, to say the least, unnecessary. 



