636 Notices respecting New Books. 



briefly treated as an example o£ the participation of ions in 

 chemical reactions. Some lines of experimental investiga- 

 tion are indicated in the paper which it is intended to 

 follow up. 



In conclusion the author wishes to thank Dr. J W. 

 Nicholson and Mr. H. B. Hartley for encouragement and 

 interest in this paper and for helpful advice with regard to 

 preparation for publication. 



Balliol College. 

 Nov. 10, 1921. 



LXXIV. Notices respecting New Books. 



A Treatise on the Integral Calculus. By Joseph Edwaeds, M.A., 

 Principal of Queen's College, London. Vol. I. 907 pages. 

 (Macmillan, 1921 ; price 50 shillings.) 



r pHIS work when complete will challenge competition with 

 -*- Bertrand's Calcul integral, in size and scope. And the price 

 will make us all reflect, gone up about fivefold by comparison with 

 the pre-war era. 



Chapter I leads off in the manner to be anticipated in the 

 modern treatise, with a review of fundamental metaphysical con- 

 ceptions of difficulties the beginner has not yet encountered, and 

 best kept out of his sight as long as possible. 



The author does not settle down in his stride till Chapter II, 

 where it is a comfort to find that the old-fashioned procedure is 

 tolerated of treating Integration as Anti-Differentiation, as leading 

 most rapidly to the applications to give reality to the subject. 



Practice is required here as much as in the scale practice of 

 the musician, and this elementary practice is best carried out in 

 the viva voce catechetical instruction of a small class, of two or 

 three ; in this way the beginner acquires confidence in his initial 

 judgment of the first steps, and can be made to apply them at 

 once to some well chosen elementary applications, and state his 

 result in words. The instructor will be inspired by this treatise 

 in his hand, equivalent of the corresponding German volume by 

 Stegemann. 



Eeal progress has been made in the foreign language when the 

 ear seizes the whole phrase and does not dwell on the separate 

 word. The musician does not read the separate notes of the 

 score, but plays the whole musical phrase, ignoring a misprint. 



So too iu the Integral Calculus : the object is to see at a glance 

 the nature of the integral, and the class to which it belongs. 



A rapid method is described here, p. 179, where the integral is 



sought as a function of the integrand, as in jsec.r<ir=ch~ sec a?, 

 called integration without preparation. 



