Suppletnent to '"Nature^' May 5, 1904 



current on the conducting" boundaries tliat are sensibly 

 elTective as regards the internal state of each element, 

 and Jheir mutual influences are adjusted in times which 

 are in any case inappreciable in an estimate of the 

 times required for transmitting- eiTects along the 

 cylinder. For wider cvlinders or shorter waves, the 

 U'ebcrian formula of Kirchhoff gives a result differing 

 from the velocity of radiation, of which Maxwell was 

 of course well aware, while Lord Kelvin's approxi- 

 mate treatment is no longer applicable. We now 

 know that, to transform the \^'eber-Kirchhoff formulae 

 into those of the modern electron theory, it is only 

 necessary, in the integral expressions for the vector 

 potential of the current and the scalar potential of the 

 charges, to consider each element as propagated 

 through space with the velocity of radiation instead 

 of being transmitted instantaneously. 



One of the great historical difficulties in optical 

 theon,', above referred to, was that of embracing the 

 phenomena of propagation in crystals and of reflection 

 from transparent bodies within the dynamics of 

 ordinary elastic solid media. This problem was 

 resolutely attacked by Green nearly sixty years ago 

 with a brilliant but unsuccessful result, and no success 

 in adapting his analysis was achieved by anyone 

 else until some three years after the Baltimore lectures 

 were delivered. Then Lord Kelvin produced his 

 theory of an elastic medium with finite rigidity but 

 perfectly labile as regards compression, and character- 

 istically illustrated it by material structures, such as 

 a mass of foam in vacuo, which resist distortion but 

 are insensitive to shrinkage of volume. If lumin- 

 iferous media were elastically like this, the necessity 

 of continuity of displacement normal to a reflecting 

 interface would no longer press upon the theory, for 

 the two media would stretch locally in the direction 

 of the normal without reaction on the other stresses, 

 just as much as might be required. And it was 

 promptly pointed out by Glazebrook that the arrange- 

 ment which thus allowed Fresnel's laws for reflection 

 was also competent to explain propagation in crystals 

 by the simple expedient of making the inertia asolo- 

 tropic, while the lability as regards compression is 

 again all that is wanted to obtain the ascertained laws 

 of MacCullagh's theory (Lord Kelvin's rotational 

 aether) or the electric theory for crystalline reflection. 

 In fact, one advantage accruing with the electric theory 

 is that it dissects the accepted and unique formal 

 analysis of propagation of light into a series of linear 

 relations between various vectors, each of which has 

 a distinctive name and quality ; and according as we 

 take one or other of these vectors to represent a dis- 

 placement of an elastic medium, we have the various 

 mechanical theories of Fresnel, MacCullagh, and 

 Sarrau and Boussinesq, differing in the tvpes of inter- 

 facial continuity that they require, but algebraically 

 the same; the exact duality between the systems of 

 Fresnel and Sarrau is in this way open to direct in- 

 spection. Such, then, was Lord Kelvin's solution of 

 1887, in which all media were taken to be labile as 

 regards compression, the type which Green had re- 

 jected under the idea that it was intrinsically unstable ; 

 this classical objection Lord Kelvin at once removed 

 NO. 1 801, VOL. 70] 



bv the illutninating remark that the medium only re- 

 quired to be held fixed at an outer boundary to prevent 

 anv internal collapse. There was something un- 

 natural about this, as its author admitted, and it now 

 appears that an aether so constituted would still absorb- 

 much condensational energy from vibrators ; but here 

 in iqo4 comes the further crucial remark that only one 

 of the two media need be thus labile in order to confer 

 the requisite freedom for reflection without interference 

 from compressional waves; the aether itself may re- 

 main incompressible, as Green took it to be, but the 

 interaction of aether and molecules in every material 

 bodv is to be such as always to make it labile or in- 

 elastic for compressional disturbance. It need not,, 

 however, be absolutely labile if Fresnel's laws are to 

 be satisfied onlv within experimental limits. .\nd 

 here the remarkable peculiarity of highly refractive 

 substances like diamond, the " adamantine property "' 

 discovered bv .\iry, which replaces an abrupt change 

 of phase in passing the polarising angle by a gradual 

 though rapid one, comes into consideration ; if only 

 the velocity of propagation of the condensational wave 

 in material media is a small complex quantity, the 

 complexity will introduce just the gradual change of 

 phase that is required in order to include that property. 

 Moreover, if this velocity is a pure imaginary, there 

 will be no loss of energy involved ; this happens for a 

 granular or discrete medium whenever there are- 

 periods of free internal vibrations among its con- 

 stituent granules that are longer than the period of 

 the waves under consideration. If we cannot include- 

 the adamantine property as introduced in this wa)^ 

 through total reflection for compressional waves, no- 

 resource is known except that of gradual transition 

 at the surface; this Lord Rayleigh has shown to be 

 the main cause for water, as careful cleansing of the- 

 surface almost entirely removes the phenomenon. 



In this chain of simple, yet brilliant and attractive, 

 ideas. Lord Kelvin has gradually forged a reconcili- 

 ation between fact and theory that would probably 

 have been received with universal acclaim thirty years- 

 ago. Nowadays, as regards most people, the need 

 has ceased to be so strongly felt ; for better for worse 

 most of us are now wedded to the electric theory of 

 light, the creation of Lord Kelvin's most famous dis- 

 ciple, which forms a consistent scheme of the relations- 

 of electricity and radiation, perfectly definite and un- 

 ambiguous with the large simplicity of nature itself, 

 that has led into no essential contradiction with fact,, 

 though it has manv times predicted phenomena of the 

 most essential and fundamental kinds. 



Not that there is any difference of opinion as to the 

 value of the electric theory. Lord Kelvin would 

 doubtless agree that, as a new mode of grouping of 

 the relations, it has placed them in a most fruitful 

 light, and shown the directions of natural develop- 

 ment. He would perhaps say that it is a successful 

 description rather than an explanation, and he would 

 probably desire to modify the terms of the description 

 in order to bring it closer to the train of dynamical 

 ideas in which he would search for the explanation. 

 And here we are at the parting of the ways. Is it 

 incumbent on us to treat the »ther as strictlv akirr 



