August 15, 1907] 



A'.^ rURE 



379 



tinuous medium, and this line of discussion brings us 

 very close to tiie electron theory. What the author 

 has reallv done is to apply the method of exhaustion 

 to mechanical theories of the electromagnetic medium, 

 and he finds that when atomic theories of the ether 

 are taken into account the number of possible hypo- 

 theses is very large. Perhaps, as the author points 

 out, no mechanical theory may be found to be capable 

 of e.xplaining satisfactorily all the phenomena of 

 nature. The subject-matter of the present book is 

 certainly only a very small fraction of all that might 

 be written on mechanical theories of the ether, and 

 probably no physicist would regard the arguments as 

 conclusive except so far as they show that certain 

 hypotheses are insufficient to account for the results 

 of experience. But at the same time, if the book does 

 nothing else, it shows that clearer and more definite 

 ideas of existing electromagnetic theories may be 

 obtained by an attempt to exhaust and classify the 

 different possibilities which present themselves. 



It is in connection with irreversible phenomena that 

 mechanical theories present the greatest difficulties. 

 As a consequence, the kinetic theory of gases has not 

 received much attention from physicists very recently. 

 But Dr. Jager points out in the preface to his book 

 that meanwhile an atomic theory of electricity has 

 been built up, bringing us back to the fundamental 

 notions of the kinetic theory of gases. The present 

 book contains a good outline of those applications of 

 the kinetic theory which are most easily understood. 

 Under this heading we include the error law of distri- 

 bution with special reference to spherical molecules; 

 the virial theorem, a brief account of Boltzmann's 

 minimum theorem without examination of its diffi- 

 culties, and a discussion of applications to viscosity 

 and other convection phenomena. This book is a verv 

 good introduction to place in the hands of the student 

 of physics whose time is very limited, but he must 

 remember that there is a great deal more to be said 

 about the kinetic theory than meets the eye in these 

 pages. 



Whether "Theoretical Mechanics" is properly de- 

 scribed as a branch of physics or of applied mathe- 

 matics is a matter of opinion. But the ever-increasing 

 part played by mechanical theories in the study of 

 physical phenomena is suflicient justification for Prof. 

 Jeans 's book. It is becoming every year more and 

 more difficult for the science student to keep pace 

 with the demands made on his time by modern de- 

 velopments of physics, and a book which starts with 

 the laws of motion and leads the reader up to 

 Lagrange's equations, all in the compass of a single 

 volume, is certain to prove a great boon to a large 

 class of students. In his preface Prof. Jeans dis- 

 cusses the reasons for carrying the subject so far 

 as the study of generalised coordinates, but in view 

 of the fact that Lagrange's equations are freely used 

 in treatises on electricity — for example, in discussing 

 the effects of mutual and self-induction in electric 

 circuits — no defence of their inclusion in the present 

 volume seems to be needed. In the chapter on motion 

 of rigid bodies we should like to have seen a little 

 NO. 1972, VOL. ^6] 



more about " uniplanar " motion. This would enable 

 the student to obtain a much more tangible and- 

 definite conception of the meaning of a moment of 

 inertia than is possible when he is rushed on at once 

 to Euler's equations. Moreover, the proof of 

 these equations is unnecessarily cumbersome and 

 difficult for the beginner, and space could easily 

 be saved by simplifying it. The equations of § 250 

 for moving axes, when generalised for any vector, 

 such as angular momentum, immediately lead to 

 Euler's equations. Instead of doing this. Prof. 

 Jeans gives what is nothing more than an alternative 

 proof of the vector differentiation formulae, as applied 

 to angular velocity in §252, and after all this trouble 

 the student has learnt nothing about the fundamental 

 principle involved in both applications. 



Returning to the earlier chapters, Prof. Jeans makes 

 an attempt in chapter iii. to prove the parallelogram of 

 forces by the now usually discarded dynamical method. 

 He escapes the fallacies of the old books in connection 

 with the parallelogram of velocities, but is led into 

 the usual nor. seqiiilur in assuming that the accelera- 

 tion which the forces produce when acting simul- 

 taneously must be compounded of the accelerations 

 which they would produce if acting singly. In con- 

 nection with his proof of the property that any motion 

 of a rigid body is compounded of a motion of transla- 

 tion and one of rotation, he defines rotation as motion 

 with one point fixed; the subsequent paragraph, 

 headed " A.xis of Rotation," is so extraordinary that 

 it is best reproduced here in full. It runs as 

 follows : — 



" In a motion of rotation, let P be the point which 

 remains fixed. Take any plane A through P and let 

 B be the position of the plane A after the rotation has 

 occurred. These two planes both pass through P, and 

 must therefore intersect in some line PO passing 

 through P. This line is called the axis of rotation. 

 The rotation can be imagined as a turning about an 

 imaginary pivot running along the axis of rotation." 



The absurdity of this statement is evident if we 

 suppose that the chosen plane A does not contain 

 the axis of rotation. 



The book is freely illustrated by examples. Many 

 of these are very useful, but others are calculated to 

 inculcate very extraordinary ideas in the mind of the 

 reader. For example, on p. 68 we have an impossible 

 figure of a nut-cracker, neither the nut nor the cracker 

 being in equilibrium. The ladder in the next 

 example is free from this objection, but it contains a 

 superfluity of trigonometry which is hardly justified 

 by the preface. The question can be solved by 

 geometry with half the work. On p. 194 is given a 

 construction for placing a chute in such a position 

 that the time of sliding from a ship's side on to a pier 

 may be as short as possible. If any reader were to 

 put the matter to a practical test, he would certainly 

 not get the same result, even if he got the objects 

 to slide at all. The correct construction is obtained 

 bv placing the chute along a chord of a certain 

 circle touching the ship's side, but the tangent 

 to this circle at the point where it meets the pier 



