54Q SCIENCE PROGRESS 



of the plane and quadric surfaces in three dimensions. It really matters little 

 whether stress is laid upon analytic geometry or upon algebra ; the important 

 fact is that the two subjects should not be divorced, and their union in this book 

 is welcome. 



Algebra is for the student often a collection of loosely jointed subjects : in this 

 book he will learn at least the true place of some algebaric forms. The chapter 

 on complex numbers is out of place ; it forms part of another set of ideas, and its 

 presence suggests difficulties in connection with geometry which are not discussed. 

 It seems a pity also that the authors did not assume a knowledge in the reader of 

 differentiation of algebraic functions. One result of modern changes for the 

 better in teaching is that such a course is now possible ; timid authors who 

 cater for the old and the new schools of teaching retard a wise and progres- 

 sive movement. The discussion of algebraic curves, short as it is, is a step in the 

 right direction ; it would have been better to have continued it further and 

 given a discussion of asymptotes and singular points. Room for this extra 

 could have been found by the omission of Part II. of the chapter of which Part I. 

 is algebraic curves ; the treatment of transcendental curves is in no way 

 germane to the general lines of thought of the book ; these curves are introduced 

 apparently to satisfy that most insatiable of all readers — the practical man. 



The book is well written, clearly illustrated, and will be of great service to the 

 large class of students who find in mathematical books on analytical geometry too 

 much and too little. 



C. 



An Elementary Treatment of the Theory of Spinning Tops and Gyroscopic 

 Motion. By Harold Crabtree, M.A. Second Edition. [Pp. xv + 193, 

 with illustrations.] (London : Longmans, Green & Co., 1914. Price 

 js. 6d. net.) 



This is the second edition of a very attractive book, and is considerably larger 

 than the first edition, which appeared in 1909. 



The most notable additions are discussions on the motion of the Gyro-compass 

 and on the rising of a Spinning Top. After elementary explanations in the first 

 part of the book, these two subjects are treated with considerable mathematical 

 detail in two appendices of twenty-eight and fourteen pages respectively. In 

 the former is given an adaptation of Schuler's investigation, while in the latter 

 the results of Jellet and Gallop are obtained. Other additions are sections on 

 the recently invented mono-rail car of Schilowsky, on the swerving of a " sliced " 

 golf ball, and on the drifting of projectiles, together with two plates and an index 

 to the whole. The sections on Brennan's mono-rail car have been altered. 



The matter has been arranged with great care and presented with clearness, 

 while all parts of the book are illustrated by numerous and excellent diagrams. 



A special feature is the repeated discussion of the same problem from different 

 points of view. This should tend to promote a fuller understanding of the subject 

 by that class of readers for whom the first edition was said to be intended— viz. 

 the abler mathematicians at our public schools and first-year undergraduates at 

 the universities. As the book now stands, however, it is only the first part that 

 need, or perhaps can, be regarded as intended for such a class of readers, as 

 many of the subjects treated are not found in the text-books on Rigid Dynamics 

 usually used by more advanced mathematical students, while the latter part 

 contains mathematics which is beyond the average first-year undergraduate. 



