NA TORE 



[May 5. 1892 



he has so many that they block each other's path " is 

 practically to abandon the position which has been pain- 

 fully and slowly gained by those who have thought and 

 written on instinct. Instinct is a definite and special 

 manifestation of innate tendency : here the innate ten- 

 dency is not manifested in this definite and special way, 

 but is thwarted. To call both manifestation and non- 

 manifestation alike instinct is, in our view, a retrograde 

 step, which we regret that a psychologist of Prof. James's 

 insight and influence should have taken. 



We cannot, however, leave the book with a note of 

 dissent ; for we find far more in this text-book to agree 

 with than to dissent from. Whether we agree or dissent, 

 we always find Prof. James full of stimulating thought ; 

 and we advise all who are interested in psychology to 

 read at least the chapters on " Habit," " The Stream of 

 Consciousness," and " The Self," if they read no more. 



C. Ll. M. 



DYNAMICS OF ROTATION. 

 Dynamics of Rotation : an Elementary Introduction to 



Rigid Dynamics. By A. M. Worthington. Pp. 155. 



(London : Longmans, Green, and Co., 1892.) 

 Spinning Tops. By John Perry. Pp. 136. (London: 



Society for Promoting Christian Knowledge, 1890.) 



THE persistence of spinning tops and of running 

 bicycles in rearing themselves erect are common 

 examples of a wide class of dynamical phenomena which 

 are influenced or governed by the presence of rapidly 

 rotating parts, and which have a prominent place in all 

 departments of physical science, from the relations of the 

 systems of the stars down to molecular actions. 



In formal treatises on abstract dynamics we are accus- 

 tomed to find the properties of freely rotating systems 

 relegated to an advanced part of the development of the 

 subject, and expounded with all the powerful help which 

 mathematical analysis can afford. If we are to have a 

 complete theory of the circumstances which determine 

 the stability and transformations of rotational motions, 

 this analytical aid is none too extensive. But there is 

 another mode of approaching a physical subject, which 

 consists in learning from observation and properly varied 

 experiment what are the phenomena that are persistent 

 and stable, and then applying known dynamical principles 

 to the elucidation of the properties of the motions thus 

 known in fact to exist — a problem which need not in those 

 simpler cases which are fundamental require any great 

 amount of analytical knowledge. 



As an additional reason for the customary abstract 

 development of dynamics, there may perhaps be counted 

 the historical fact that the questions that were of para- 

 mount importance when dynamical principles concerning 

 extended systems of bodies were being evolved, related to 

 the orbital and axial motions of the heavenly bodies, and 

 their reconciliation with the law of universal gravitation. 

 The absence of frictional resistances, and the long dura- 

 tion and delicacy of astronomical observations, had led to 

 a minute knowledge of the motions of the solar system, 

 which taxed all the resources of Clairaut, D'Alembert, 

 Laplace, and Lagrange, to verify and explain. 



Many of the dynamical principles which are now 

 NO. I I 75, VOL. 46] 



treated as elementary and fundamental were thus come 

 upon in special analytical investigations relating to 

 physical astronomy. It was, for example, in this way 

 that the principle of the conservation of angular momen- 

 tum for the solar system was discovered by Laplace, and 

 then generalized to a system with any kind of internal 

 connections which is not subject to forces from outside it. 

 How far a general principle of this kind, when divested 

 of its analytical dress, enables us to see into the general 

 causes of things is well known. A striking illustration is 

 the ap?rcu of Prof. James Thomson, that when once the 

 trade winds have been explained as a consequence of the 

 earth's rotation, they involve of necessity the existence 

 also of anti-trades or south-west winds in the temperate 

 zone ; for if the trades blew by themselves their friction 

 against the earth would always be acting round in the 

 same direction, and therefore would tend to stop the 

 earth's rotation, not by wholly destroying its motion, but 

 by transferring its angular momentum undiminished to 

 the atmosphere, where it would continually accumulate. 

 This simple remark thus shows that the trades blowing 

 to the equator must be compensated by anti-trades blow- 

 ing from it ; and therefore also explains the existence of 

 a region of high barometer between them. It will also 

 occur to memory how much J. Purser, W. Thomson, and 

 specially G. H. Darwin, have establis hed in the tidal 

 evolution of the earth-moon system, by studying the 

 possibilities of development that are allowed subject to 

 the conservation of its angular momentum and the 

 degradation of its energy. 



It has been reserved for our own half-century to bring 

 out the wealth of general dynamical ideas that is con- 

 tained in the magnificent analytical presentation by 

 Lagrange of the results of the application of the laws of 

 motion to systems of bodies, the number of variables or 

 co-ordinates being of necessity (for analytical purposes) 

 restricted to the number of degrees of freedom, and every- 

 thing turning out to be expressible in terms of one funda- 

 mental function — the energy of the system. It will be 

 apparent, on looking through Prof. Cay ley's Reports on 

 Dynamics to the British Association, how much the pro- 

 gress of this department of abstract dynamics was 

 indebted to the necessities of astronomy. That science 

 presented a problem which was in one sense quite 

 definite and precise, on account of the smallness of the 

 planetary masses, but which nevertheless required a 

 minute explanation of the perturbations to which the 

 planetary bodies are subjected owing to their mutual 

 actions. The methods which proved comprehensive and 

 efficient for this purpose also showed themselves, when 

 they were examined from a more general standpoint, to 

 reveal principles of a far-reaching character, that applied 

 to dynamical systems however complicated. The final 

 stage of analytical development was reached when the 

 keen perception of Sir W. R. Hamilton saw that the 

 whole subject could be removed from special considera- 

 tions of space and time, and attached to the purely 

 analytical treatment of a single varying action function ; 

 and the commentary of Jacobi showed precisely how to 

 pass from this general differential analysis to the solutions 

 of special dynamical questions. 



At the present time there seems to be no danger of the 

 interruption of prt)gress by too close an adherence to the 



