362 



NATURE 



[Fkbruarv 14, 1895 



in the ordinary way as the real part of (B — i C)<^f' 

 where » = s' - • , and p = g-iy. The value of / is here 

 misprinted y-\-iq. The author then proceeds to find 

 solutiins for the case of an indefinitely extended 

 dielectric, and throwing the equations into the form 



that is introducing the vector-potential, he goes on to 

 solve the resulting equations for X, Y, Z. Two solutions 

 are obtained of the form 



f = - A \[^'^dxdyd= 



where («) may have either of the values u', u' , given by 

 li -/ (jr'.y, z\ t), u = f {y,y, z, t - Ar). Here u' is 

 the value of the ^--component of the current at the point 

 (y.y, s") at time /, u" the value of the same component 

 at the same point at a time previous by the interval 

 required for the lij;ht to travel from (.»', j, z) to {x' , y' , s'), 

 r being the distance between these two points. The j 

 latter solution is, of course, adapted to the case of pro- 

 pagation in space with velocity i. A. It is exemplified by 

 application to the complete solution of Lodge's spherical 

 vibrator. This, in the assumed absence of radia'.ion of 

 energy and frictional damping out of the electrical vibra- 

 tion, may be regarded, for points external to the sphere, as 

 simply a time-periodic electric doublet; for its electrifica- 

 tion may be imagined produced by the relative displace- 

 ment through a small distance of two uniform sphcrica 

 volume distributions, each of which acts as if its whole 

 charge were situated at its centre. But the existence of 

 radiation very materially afi"ccts the result, for if r be the 

 distance of any point from the centre of the vibrator, a 

 the radius of the sphere, ^ a function which gives the 

 electric forces by the equations 



X = a-y^bx^z, Y = d^^jfldySz, 

 Z = - A=a>/a/- + d^-^/3z\ 



the direction of the axis of the vibrator being that of r 

 then 



n,= \Se e cos -_^V " A^ 



rlta - t\ia\ 



■JfZe e 



- SI'C' - A^) 



This expressio.1 is interesting as showing exactly the 

 damping due to radiation in this case ; that due to fric- 

 tional generation of heat is neglected. As i/A is the 

 velocity of lij,'ht, it will be seen that the radiation damping 

 is exceedingly rapid. Thii illustrates the difficulty of 

 " maintaining " electric oscillations ; and has an important 

 blaring on the interpretation of results obtained with- 

 resonators which are damped slowly as compared with 

 the exciters. 



Of course, the damping in complicated cases can be 

 found when the total flow of energy through a spherical 

 surface of large radius, surrounding the vibrator, can be 

 computed by Poynttng's theorem. Thus it is possible to 

 construct a more accurate solution for points distant from 

 the vibrator, than that given by the supposition of no 

 damping, by thu* calculating approximately the expon- 

 ential factor, and we can go on by successive approxima- 

 tion if need be. 



The results obtained by Hen with regard to the period 

 and the damping out of the vibrations of his exciter were 

 NO. 1320. VOL. 51] 



tested, of course, by his resonator ; and we have, in 

 chapter iv. of M. Poincaro's work, an excellent account 

 of the mathematics of resonince, so far as here required, 

 and of the propagation of electric waves along wires, 

 illustrated by reference to the experiments of Sarasin and 

 De la Rive, Blondlot, and others. Many of these have 

 reference to the variation of the current with distance 

 from the end of the wire, at which, of course, reflections 

 took place. The theory, for example, of Mr. D. E. Jone> 

 experiments, in which a thermo-electric couple was usctl 

 to measure the heating effect at different distances from 

 the end of a long wire, is worked out ; and the results, 

 when compared with those of the experiments, are found 

 to agree. 



Chapters follow on Propagation in Air, and Applica- 

 tions of Theory. In the latter, M. Poincarc refers, among 

 other things, to the results of the very important 

 experiments of Bjerknes, on waves received by re- 

 sonators of ditil'erent metals ; that is, their difterent rates 

 of damping, and the depths to which the currents 

 penetrate into the metal as measured by the thickness 

 (to take an example) of copper, which must be deposited 

 on an iron resonator in order that it may behave like 

 one of solid copper. 



These three chapters have a very important bearing on 

 the question of multiple resonince, to which M. Poincare 

 has himself devoted special attention, and form, perhaps, 

 the most valuable part of the work. 



Lastly, the book deals with such applications of 

 electrical oscillations as the determination of specific 

 inductive capacities, the reflection and refraction of 

 electric waves, and ends with a study of Hertz's 

 '• Memoir on the Fund.imental l-'qu.itions of Electro- 

 dynamics for Moving Bodies." 



The mathematical discussions are, as we liave indi- 

 cated, throughout lucid and very frequently elegant. 

 The facility with which an app.\rently intractable 

 problem is taken hold of, and a few more or less 

 elementary considerations made to yield an approximate 

 solution or result, is very remarkable. We could have 

 wished for a somewhat mote physical treatment of the 

 subject ; but to those whose physical ideas have had some 

 training with regard to these matters, M. Poincarc's trea- 

 tise cannot but be ofgre.it service, as supplying what no 

 doubt was its obj:cl, a review of the princip.il results 

 obtained in this field of research compared with theory, 

 as far as possible by the only sure test, that of calculation. 



A. Gr.W. 



r//E BOOK OF THE ROSE. 

 The Book of the Rose. By the Rev. A. Eoster-Melliar, 

 M.A., Rector of Sproughton, Sufl'olk. Pp. 33'). 29 

 illustrations. (London: Macmillan and Co., 1894.) 



MR. MELLIAR is well known among horticulturists 

 as a successful grower and exhibitor of roses, and 

 his book is what he wished it to be — the rose considered 

 as a flower, with full dct.iils for its practical culture for 

 amateurs, from the beginning to the end. Art is his text 

 all through. He has very little to say about the botany 

 of the rose, its geographical distribution, the origin of 

 the numerous races of garden roses as distinguished from 

 their wild progenitors, the fourteen chapters of his book 



