Nov. 5, 18S5] 



NA TURE 



19 



^olid tlieory are considered — De St. Venant, Sarraii, Lorenz. 

 Stokes, Lord Rayleigh, Kirchhoff, and others. 



The third section is devoted to theories in which the mutual 

 action between the matter molecules of the transparent body and 

 the ether is considered as the main cause of refraction, dispersion, 

 and other phenomena. 



The chief workers in this field seem to be Boussinesq, 

 Sellmeier, Helmholtz, Lommel, Ketteler, Voigt, and, in his 

 lectures at Baltimore, Sir W. Thomson. 



The fourth and last section deals with the electro-magnetic 

 theory of Maxwell, and the developments it has received from 

 the hands of Helmholtz, fl. A. Lorentz, Fitzgerald, J. J. 

 Thomson, Rowland, and Glazebrook. 



The report is devoted strictly to general optical themes. This 

 has been required by the necessities of both space and time, 

 and, as a consequence, the optical papers of many most dis- 

 tinguished workers, such as Fizeau, Janiin, and Quincke, are 

 hardly noticed, e.xcept in so far as the results at which they have 

 arrived bear on some point or other of the general theory. 

 There is ample room for a report dealing with optics from an 

 experimental standpoint which should airange and compare the 

 conclusions of various experimenters on debated points. 



Turning, then, to the sections in order : in the second section, 

 which deals with the elastic-solid theory, the optical properties 

 of media are considered on the hypothesis that they arise entirely 

 from differences in the rigidity or in the density of the ether in 

 these media. 



While the development of this theory has taught us much, we 

 are driven to conclude that the fundamental hypothesis will not 

 account for all the optical phenomena. 



The papers of Stokes on diffraction, of L. Lorenz and Lord 

 Rayleigh on refraction and the scattering of light by small 

 particles, have proved conclusively that we must look to differ- 

 ence of density, or of apparent density, in the media to explain 

 the phenomena, and not, as was suggested by MacCullagh and 

 Neumann, to difference of rigidity. 



With this conclusion Fresnel's hypothesis that the direction 

 of vibration in polarised light is normal to the plane of polarisa- 

 tion is necessarily connected. 



On the other hand, the only strict elastic-solid theory of 

 double I'efraction is that of Green, and according to it, if we 

 suppose the medium initially free from stress, the direction of 

 vibration lies in the plane of polarisation, and even this conclu- 

 sion is only arrived at by supposing certain arbitrary relations 

 between the coefficients. 



These two conclusions, then, of the elastic-solid theory are 

 hopelessly at variance. It is true that, by supposing the medium 

 initially to be in a state of stress. Green arrived at a second theory 

 in agreement with his theory of reflection, but this agreement is 

 gained by the introduction of a second set of arbitrary relations. 



In connection with this point I should mention that it seems 

 to me that Green's theory of reflection can be reconciled with 

 experiment by adopting the suggestions of Lord Rayleigh as to 

 the refractive index of the media for the normal waves. 



The elastic-solid theory also fails to explain anomalous dis- 

 persion and metallic reflection. Cauchy's expressions for the 

 mathematical analysis of the latter agree with experiment ; but 

 then they require that iT- should be complex quantity with 

 its real part negative, and this involves the instability of the 

 medium as regards the problem of ordinary dispersion. Cauchy's 

 theory has been advanced by the writings of Sarrau ; while the 

 investigations of Ketteler have shown that a formula of the 

 form— 



A' h* 

 agrees very closely with experiment. 



.Stokes has given us an explanation of aberration by showing 

 us that we may suppose the ear:li to move through space and 

 carry the surrounding ether with it, the ether at some distance 

 fro a it being at rest ; provided that the motion thus produced 

 in the ether be irrotational, all the known phenomena of aberra- 

 tion will follow. And he has further shown us that any small 

 tendency to variation from such irrotational motion will call into 

 action the rigidity of the ether, and be propagated into space 

 with the velocity of light. According to the views developed in 

 these papers of Prof. .Stokes, the ether may be treated as a 

 perfect fluid for the large motions produced in it by the motion 

 of the earth ; while at the same time it has rigidity, and obeys 

 the equations of an elastic-solid for such small motions as are 

 involved in the passage of a wave of light. 



liT 



dw 



According to the views dealt with in the second section, the 

 ether is of the same density and rigidity in all transparent media. 

 For such media, however, its motions are affected by the pre- 

 sence of the molecules of the medium. Some of the energy of 

 the incident light may be used up in setting these matter-molecules 

 into motion. The amount required for this depends on the 

 nature and properties of the matter-molecules, and hence is 

 different for different media and for waves of different length. 

 This gives rise to reflection and refraction. 



There are indications in the writings of Fresnel that he looked 

 to some explanation himself, but it seems to be to^Boussinesq 

 that we owe the first real development of the theory. 



He forms the equation of motion of the ether and matter 

 combined on the supposition that the forces on the matter arising 

 from the direct action of surrounding matter are owing to the 

 smallness of the displacements negligible. He then supposes 

 that the matter displacement t'may be expanded in terms of the 

 ether displacements « and its differential coefficients, and finally 

 arrives at equations of the form 



{p +^/)'^ = B^"-t, + C'^-^, &c. 



where 



5 du 



dx dy az 

 B and C involve the period, p is the density of the ether, and p ' 

 of the matter ; and hence dispersion is accounted for. Double 

 refraction is explained by supposing .4 to be a function of the 

 direction, while B and C remain constant ; and for this reasons 

 are given, and it is shown that on certain other hypotheses this 

 leads to Fresnel's theory. This theory deals also with the 

 phenomena of elliptic polarisation in quartz, and of aberr.ation. 



In Boussinesq's theoi-y the motions of the matter particles are 

 neglected, except in so far as they act on the ether and modify 

 its motion. Sellmeier was the first to see that reflection and 

 refraction would be profoundly modified in the cases in which 

 the free period of the matter particles agrees with that of the 

 incident light, and when, therefore, the energy in that light is 

 absorbed in setting the matter into motion. His work was 

 continued by Helmholtz, Lommel, Ketteler, Voigt, and Sir 

 W. Thomson. 



The equations of motion employed by all these writers are the 

 following : 



Jll'^ X VA + X', 

 df 



.d-U _ 

 df- 



In these equations X represents the force on the ether, in the 

 element of volume considered, arising from the surrounding 

 ether ; X', from any external impressed forces ; and A, from 

 the matter ; while K-, »', and A, are the same for the matter. 

 According to all X = X' = o. We must also have A + A = o. 

 The difference in the theories consists in the different forms 

 given to A. 



Sellmeier, Thomson, and Helmholtz put A = 0- {u - U). 



Lommel puts A =^ $'^ ^ {11 - U). The results of Ketteler's 

 theory are, except in one small and, I venture to think, non-essen- 

 tial point, identical with those found by putting A = $'- —-^ 

 ^ dt' 



{11 - U) (Ketteler obtains his equations in a different form 

 from the above). Voigt investigates the general form possible 

 for A consistent with the propagation of a plane wave and the 

 conservation of energy. He finds 

 ,0 rf" . _ ., d- 



_-— = Sf + A + ^ . 



-■i = 



-taking waves travelling 



; put- 



..i^+^ d.^ 

 For the v.alue of .^'.all the aulhi 

 parallel to = — 



while Voigt adds the term -^. For » all Init Voigt and Thom- 

 son write — 



Thomson objects to the term — as involving a viscous ex- 

 penditure of energy. Voigt argues, with Boussinesq that in 



