130 J.W. Gibbs — Comparison of the Electric Theory of 



course it has not escaped the notice of physicists that we may 

 also get rid of the third wave by making its velocity zero, as 

 may be done by giving certain values to the constants which 

 express the elastic properties of the medium, but such values 

 have appeared impossible, as involving an unstable state of the 

 medium. The condition of incompressibility, absolute or ap- 

 proximate, has therefore appeared necessary.* This question 

 of instability has now, however, been subjected to a more 

 searching examination, with the result that the instability does 

 not really exist "provided, we either suppose the medium to ex- 

 tend all through boundless space, or give it a fixed containing 

 vessel as its boundary." This renders possible a very simple 

 theory of light, which has been shown to give Fresnel's laws 

 for the intensities of reflected and refracted light and for 

 double refraction, so far as concerns the phenomena which 

 can be directly observed. The displacement in an aeolotropic 

 medium is in the same plane passing through the wave-normal 

 as was supposed by Fresnel, but its position in that plane is 

 different, being perpendicular to the ray instead of to the 

 wave-normal, f 



It is the object of this paper to compare this new theory 

 with the electric theory of light. In the limiting cases, that 

 is, when we regard the velocity of the missing wave in the 

 elastic theory as zero, and in the electric theory as infinite, we 

 shall find a remarkable correspondence between the two theo- 

 ries, the motions of monochromatic light within isotropic or 

 aeolotropic media of any degree of transparency or opacity, 

 and at the boundary between two such media, being repre- 

 sented by equations absolutely identical, except that the sym- 

 bols which denote displacement in one theory denote force in 

 the other, and vice versd.\ In order to exhibit this corre- 

 spondence completely and clearly, it is necessary that the fun- 

 damental principles of the two theories should be treated with 

 the same generality, and, so far as possible, by the same method. 

 The immediate consequences of the Dew theory will therefore 

 be deduced with the same generality and essentially by the 

 same method "which has been used with reference to the electric 

 theory in a former volume of this Journal (vol. xxv, p. 107). 



* It was under this impression that the paper entitled "A Comparison of the 

 Elastic and the Electric Theories of Light with respect to the Law of Double re- 

 fraction and the dispersion of colors," in the June number of this Journal, was 

 written. The conclusions of that paper, except so far as respects the dispersion 

 of colors, will not apply to the new theory. 



f Sir William Thomson, loc. citat. R. T. Glazebrook, Phil. Mag., December, 

 18S8. 



X In giving us a new interpretation of the equations of the electric theory, the 

 author of the new theory has in fact enriched the mathematical theory of physics 

 with something which may be compared to the celebrated principle of duality in 

 geometry. 



