REVIEWS 



MATHEMATICS 



Applied Calculus. By F. F. P. Bisacre, M.A., B.Sc. [Pp. xv + 446, 

 with 5 plates.] (London : Blackie & Son, 1921. Price 10s. 6d. net.) 



This book is intended to provide an introductory course in the calculus for 

 the use of students of natural and applied science whose knowledge of 

 mathematics is slight, and it is an interesting refutation of the idea that an 

 elementary treatment is inconsistent with mathematical rigour. Whether 

 or no the students will appreciate the pains the author has evidently taken 

 in this respect is another matter. 



The book is full of " modern instances " which are entertaining even 

 when their introduction does not seem to increase the clarity of the exposi- 

 tion. An interesting and novel feature is the series of biographical notes on 

 and portraits of mathematicians and scientific men whose work is referred 

 to in the text. 



The book is written by a mathematician and shows a lamentable lack 

 of appreciation of what is involved in physical measurement. In estimating 

 the total error in calculating the mass of a ring whose density is known only 

 to I part in 30, the author finds it necessary to add istVt " because n is not 

 known accurately." Starting with the side of a cube measured to 7 significant 

 figures, he proceeds to calculate, with what he calls " accuracy," the area of 

 a face to 13, and the volume to 19 figures. He reduces these to 7 figures 

 each, not because the remaining figures mean nothing at all, but because 

 " we do not need 19 significant figures for any practical purpose." It seems 

 quite inexcusable that a book intended for students of science should not have 

 been submitted in proof to someone who would have purged it of such 

 examples of one of the most deeply-rooted misconceptions with which the 

 teacher of physics has to contend. 



The type of the book is excellent and the diagrams are good. The price 

 is not excessive. 



G. A. Sutherland. 



Cours complet de Mathematiques sp6ciales. Par J. Haag. Tome II, 

 Geometric. (Pp. vii + 662.] (Paris : Gauthier-ViUars & Cie, 1921. 

 Price 65 fr.) 



This book covers familiar ground, the elements of analytical and differential 

 geometry, and presents few novelties in the way of matter or of treatment. 

 Practical utility being the guiding principle, the discussion of conies and 

 quadrics is relatively condensed and is postponed to the latter part of the 

 volume ; on the other hand, differential geometry is treated in more detail 

 than is usual in an elementary work. The great drawback to the book is 

 its prolixity, which causes its enormous size and its enormous price. The 



author has a curious dislike for the ordinary formula, involving ^, for the 



curvature of a plane curve. 



F. P. W. 

 IS4 



