NA TURE 



?6i 



THURSDAY, FEBRUARY 14, 1S95. 



ELECTRIC OSCILLATIONS. 

 Les Oscillations ]-'.lcctriques. Par H. Poincarc, Membre 

 de rinstitut, Redigees par M. Ch. Maurain. (Paris : 

 Georges Carrd, 1894.) 



WE have already noticed at some length M. Poin- 

 card's works on Electricity et Optique, and given 

 an account of his views regarding Maxwell's theories, 

 and his mode of presenting the subject in the light of 

 Hertz's researches. The present work discusses more 

 particularly the subject of Electric Oscillations, and 

 includes comparatively little of the more abstract treat- 

 ment of electrical theory to be found in the others. We 

 have in it a veiy instructive and well-timed n'stinn' 

 of a good deal of the later work on the subject, with 

 mathematical investigations of many points arising in 

 connection with the various experimental researches 

 referred to, which are of great value. 



In a short preliminary statement of the theory under- 

 lying the Hertzian e.xpcriments, M. Poincarc' adopts, to 

 a certain ettent, the mode of presentation used by Hertz 

 himself. The two reciprocal sets of equations also made 

 by Heaviiide the starting-point of his researches, and 

 called by him the circuital equations, are made by 

 Hertz the basis of everything. Thus if L, M, N, X, Y, Z 

 be the components of the magnetic and electric forces, 

 ^l and f the " coefficients of magnetic and electric induc- 

 tion,'' and A the reciprocal of the velocity of light, the 

 equations are 



/aL aM ^^xi^T- 3Y ax az aY_a>:\ 



\bt' Hi' ilt) \by ds dz dx' d.v By)' 



n. t sx ,, „^ \ /dM. a.v 



&c. 



, a^ dy 



where u, v, \v are the components of conduction current 

 at .r,/, .?. When ?<, 7^, a' = o, one set of equations can 

 thus be formed from the other set by interchange of 

 L, M, N with X, Y, Z, and fi with -6. The electric 

 energy is f (X--|-Y-+Z-)/ St, and the magnetic energy 

 fi (L--|-M-+N-)'87r, each taken per unit of volume of the 

 medium. 



The units of force are so chosen that /i and f are both 

 unity for vacuum, that is, for ether. Hence the intro- 

 duction of A m the equations above. It is required to 

 make the dimensions of both sides alike. We must con- 

 fess that we much prefer the idea contained, though not 

 clearly expressed, in Maxwell's treatise, of regard- 

 ing jjL and Iv as quantities dependent on the physical 

 properties of the medium, and such that the velocity 

 of light in the medium is i \/ /i K. There can be no 

 question of the enormous advantage of thus proceeding, 

 it avoids the obvious absurdity of giving in a general 

 system of measurement founded on the units of length, 

 mass, and time, two different sets of dimensions to the 

 same quantity according as it is measured electro- 

 statically or electromagnetically. Further, if this were 

 recognised, the serious difficulty which besets students, 

 when they find that what is defined or explained as a 

 mere ratio is unity, or the reciprocal of the square of the 

 velocity of light, according to the system of units adopted, 

 would entirely disappear. The discussion which took 

 NO. J 3 20. VOL. 51] 



place in 1882 regarding the dimensions of magnetic pole 

 in electrostatic units, gave illustrations of the confusion 

 and misconception to which neglect of the dimensional 

 relation between /i and K can give rise in the mind of 

 even a master of physical science. 



Let ^i„,K„, or better, /i,,,*,,, be the inductive capacities 

 ( magnetic and electric) of ether, ja,K, those of any other 

 substance, then /x >i„, kk,-, will be the magnetic and 

 electric permeabilities of the medium, and will be mere 

 ratios. The magnetic permeability will then be as 

 Lord Kelvin originally defined it, the ratio of two magnetic 

 forces, of the magnetic force defined electromagnetically 

 (in a crevasse across the direction of magnetisation) to 

 the magnetic force according to the polar definition (in 

 a narrow cylindrical hollow parallel to the magnetisation), 

 and our ideas will no longer be liable to obfuscation in an 

 important fundamental matter. 



M. Poincarc derives the second set of equations stated 

 above from the first set and the principle of conservation 

 of energy, using for the total energy per unit of volume 

 the sum of the expressions quoted above. The theoretical 

 basis consists thus of (i) the experimental fact that the 

 line-integral of electric force round a circuit is equal to 

 the time-rate of variation of the total magnetic induction 

 through the circuit, which gives the first set of equations : 

 (2) the expressions for the magnetic and electric energies; 

 and (3) the theorem that the work spent in heat per unit 

 of volume per unit of time is 'X!i-\-\'v-\-Z7t.'. The ex- 

 pressions for the energies are thus taken as fundamental. 

 The result does not, however, depend on zny supposition 

 as to exact localisation of the energy ; all that is involved 

 is the expression of the energy as an integral extended 

 through the whole field. 



This is not the same as the process of Hertz, and it is 

 not clear that it possesses any advantage over that 

 method. In fact, Hertz's foundation is the two sets of 

 reciprocal equations, which are first postulated, then 

 shown to be consistent with observed phenomena. Thus 

 the whole structure rests on the equations, and Hertz is 

 but little, if at all, concerned with the dynamical explan- 

 ation of electromagnetic phenomena. This, on the 

 other hand. Maxwell is continually ; and one of the 

 most remarkable chapters of his book is that in 

 which he applies the method of Lagrange to give a 

 dynamical basis to the theory of induction and electro- 

 magnetic action. This was a natural outcome of the 

 other process, which he followed, of establishing his 

 equations as far as possible directly from the experi- 

 mental facts, and connecting them by a strong web of 

 dyn;imical theory. It does not seem likely, moreover, 

 that the minds of many of those who are eagerly seeking 

 for some more intimate knowledge of electromagnetic 

 action will be content with anything but a dynamical 

 explanation of electrical phenomena, and one which shall 

 elucidate, in some measure at least, the relation of the 

 ether to ordinary matter, and the reason for the 

 existence of the ponderomotive forces exerted in the 

 electromagnetic field. 



In chapter iii. M. Poincarc proceeds to the theoretical 

 study of Hertzian oscillations, and discusses in the first 

 instance the solution of the differential equations for the 

 case of conductors situated in a dielectric. The first 

 part of this does not calf for special remark. X is taken 



R 



