146 



NA TURE 



[December 14, 1S93 



points out that if oi is less than n, the current is opposed 

 to the electromotive force of the disk, and that therefore 

 in this case " the chemical action is the source of the 

 current instead of being an effect of it ; and the disk by 

 its rotation produces mechanical effect as an electro- 

 magnetic engine" (or, as we now call it, a motor) "in- 

 stead of requiring work to be spent upon it to keep it 

 pioving as a magneto-electric machine." If y be the 

 current flowing, F the intensity of the field in which the 

 disk revolves, r the radius of the disk, R the resistance 

 of the circuit, W the rate at which work is done by the 

 current en the engine, M' the rate at which energy is 

 spent by the battery, then the results — 



7 = -2^(-"- - '^), 



or 



n 

 are given, and it is pointed out that the fraction of the 

 '• entire duty of the consumption which is actually per- 

 formed by the engine is equal to co/n." The ratio w/n is 

 the ratio of the back electromotive force of the motor to 

 the total electromotive force of the generator, and is 

 therefore the law of efficiency stated above in the words 

 of M. Witz. 



The examples worked out in the book are many of 

 them highly instructive, and, so far as we can judge from 

 the examination of a selected few, seem clearly and 

 correctly dealt with. They are not merely numerical, but 

 include in most cases the deduction from general 

 theorems of formulas for particular cases, which are then 

 illustrated by numerical problems in which results are 

 expressed in C G.S. units. The value of these problems 

 is enhanced by the fact that they are, as we have said 

 for the most part actual problems which have turned up 

 in experimental or practical work. The subjects thus 

 elucidated include magnetism, electrostatics, steady flow 

 of electricity, electro-magnetism, dynamos, motors, and 

 the distribution and transmission of electric energy. 

 There can be no doubt that the book will prove very 

 useful to teachers and students. Its only fault is that it 

 leaves nothing for the student himself to do. A moderate 

 number of unworked examples, on which he might test 

 his grip of the subject, and power of applying principles, 

 would have been very valuable. It is undesirable to spend 

 very much time in solving mere arithmetical or algebraic 

 conundrums, but enough must be done to acquire a fair 

 amount of readiness and expertness of calculation ; and 

 of the great benefit derived from working out numerical 

 examples of physical principles, there can be no doubt. 

 We think, therefore, the author would do well to supply 

 material for this in a future edition. A. Gray. 



BESANT-S DYNAMICS. 

 A Treatise on Dynamics. By W. H. Besant. (Cam- 

 bridge : Deighton, Bell, and Co., 1893;) 

 'T^HIS popular text-book has now reached a second 

 J- edition, and contains several additions which have 

 increased its size from 334 to 448 pages. A new chapter 

 has been added on disturbed elliptic motion, which 

 shows how the elements of an elliptic orbit are aftected 

 NO. 1259, VOL. 49] 



by small disturbances in the same plane. This chapter 

 will serve as a useful introduction to the planetary 

 theory, since the limitation of the problem to two- 

 dimensional motion enables various difficulties, which 

 arise from taking into account the longitude of the node 

 and the inclination of the orbit, to be got rid of. The 

 principle, upon which the method of the variation of the 

 elements is based, is one to which students should be 

 introduced at an early stage ; but unless some simplifica- 

 tion is made, the analysis becomes rather complicated. 

 We are inclined to suggest that this chapter might be 

 extended in a future edition. 



The last chapter of the first edition has been amplified 

 into two, the first of which deals with motion in three 

 dimensions, whilst the second discusses several im- 

 portant problems relating to the motion of tops, discs, 

 gyroicopes, &c. ; and the book concludes with a new 

 chapter on Lagrange's equations, together with several 

 applications illustrating their use. To discuss any of 

 the higher developments of this branch of the subject, 

 including the Hamiltonian transformation, and the mixed 

 transformation which in 1887 was for the first time given 

 in a complete form by the author of this review, would 

 probably be thought beyond the scope of an ele- 

 mentary work ; but it would be well to bring out more 

 pointedly the fact that the kinetic energy of a dynamical 

 system can be expressed in several different forms, and 

 that when employing Lagrange's equations there is only 

 one form which it is permissible to use, viz. the La- 

 grangian form, in which the kinetic energy is expressed 

 as a homogeneous quadratic function of velocities which 

 are the time-variations of coordinates. Mistakes are 

 frequently made upon this point ; and it is most neces- 

 sary to impress upon the minds of students that La- 

 grange's equations are double-edged tools, which are apt 

 to cut the fingers of those who unskilfully handle them. 



Dr. Besant has used the word phoroiiomy in the place 

 oi kinematics, and he has stated his reasons for so doing 

 in a letter published in Nature, lAIarch 17, 1892. The 

 word appears to be a good one, and has the merit of 

 being classical, and not Teutonic ; but notwithstanding 

 occasional fiights into the regions of radicalism, the in- 

 grained conservatism of the English mind is so strong 

 that it is by no means certain whether phoronomy will 

 supplant a word which has long held the field. 



One of the most satisfactory features of the work is that 

 Dr. Besant has drawn marked attention to the principle 

 of momentum. This principle is in some respects a 

 more fundamental one than the principle of the con- 

 servation of mechanical energy ; for the former principle 

 is true in the case of viscous systems in which there is a 

 conversion of mechanical energy into heat, whilst the 

 latter does not hold good when internal friction or vis- 

 cosity exists. The principle of linear momentum can 

 be shown to be a direct consequence of Newton's second 

 and third Laws of Motion ; but doubts have been enter- 

 tained whether the principle of angular momentum can 

 be deduced from Newton's Laws without the aid of an 

 additional hypothesis. The question, however, is far too 

 recondite a one to be discussed in a review. 



It is possible that some of those whom a recent corre- 

 spondent in Nature has described as "the slug and the 

 bug school '' may object to the large amount of problems 



