REVIEWS 



MATHEMATICS 



A Treatise on Gyrostatics and Rotational Motion : Theory and Applications. 



By Andrew Gray, F.R.S., Professor of Natural Philosophy in the Univer- 

 sity of Glasgow. [Pp. xx + 530.] (London: Macmillan & Co., Ltd., 1918. 

 Price 42s. net.) 



Especially in recent years, the theory and applications of gyrostatic action have 

 occupied the minds of many people. This is due, to a large extent, to the import- 

 ance of inventions depending on gyrostatic principles, such as torpedoes, which is 

 even greater in the time of war than in times of peace. This very thorough and 

 systematic treatise, which is very finely produced by the publishers, is of great 

 value both to students and to would-be inventors. There is much about this book 

 that will be very attractive to those who have tendencies opposed to the traditional 

 " academic " ideals. The aim of the present work is " to refer, as far as possible, 

 each gyrostatic problem directly to first principles, and to derive the solutions by 

 steps which could be interpreted at every stage of progress " (p. v). 



After an introductory account of many striking gyrostatic phenomena, the 

 chapters (II-XXIII) deal in succession with dynamical principles ; elementary 

 discussion of gyrostatic action ; systems of co-ordinates and their relations, and 

 " space-cone " and " body-cone " ; the simpler theory of tops and gyrostats ; 

 further discussion of the rise and fall of a top when the precession is not zero ; 

 gyrostats and various physical applications of gyrostats ; vibrating systems of 

 gyrostats, and suggestions of gyrostatic explanation of properties of matter ; the 

 motion of chains of gyrostatic links, and magneto-optic rotation ; the earth as a 

 top, precession and rotation, and gyrostatic theory of the motion of the nodes of 

 the moon's orbit ; the free precession of the earth : further discussion ; calculation 

 of the path of the axis of a top by elliptic integrals ; liquid gyrostats, and mis- 

 cellaneous investigations (such as the motion of a projectile) ; effects of air-friction 

 and pressure, and boomerangs ; the spherical pendulum, and motion of a particle 

 on a surface of revolution ; dynamics of a moving frame containing a fly-wheel ; 

 motion of an unsymmetrical top ; the rising of a symmetrical top supported on a 

 horizontal surface ; general dynamics of gyrostatic and cyclic systems ; theory of 

 gyrostatic domination ; geometrical representation of the motion of a top ; analogy 

 between a bent rod and the motion of a top, and the whirling of shafts, chains, 

 etc. ; and examples of gyrostatic action and rotational motion. 



Of the book we may say, in general, that, like very many other books published 

 in this country, vector ideas and traditional co-ordinate methods are used (cf., for 

 example, p. 408). " As a rule the method employed has been one of calculating 

 rates of, growth of angular momentum for different axes, which amounts to a 

 reduction to practice of vector ideas, and which I devised nearly twenty years ago 

 for use in my own teaching and dynamical work" (p. vi). It seems rather a pity 

 that the extraordinary simplification introduced by Grassmann's methods should 

 be ignored. Also, when discussing non-holonomous systems in Chapter XIV, it 

 is unfortunate that no notice should have been taken (as there might have been on 



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