[ 238 i 



XXVII. A Comparison of the Electric Theory of Light and 

 Sir William Thomson's Theory of a Quasi-labile ^ther. 



By J. WiLLAKD GiBBS*. 



AEEMAEKABLE paper bj Sir William Thomson, in 

 the November number of the Philosophical Magazine, 

 has opened a new vista in the possibilities of the theory of an 

 elastic sether. Since the general theory of elasticity gives 

 three waves characterized by different directions of displace- 

 ment for a single wave-plane, while the phenomena of optics 

 show but two, the first point in accommodating any theory to 

 observation is to get rid (absolutely or sensibly) of the third 

 wave. For this end it has been common to make the sether 

 incompressible, or, as it is sometimes expressed, to make the 

 velocity of the third wave infinite. The velocity of the wave 

 of compression becomes, in fact, infinite as the compressibility 

 vanishes. Of course it has not escaped the notice of physi- 

 cists 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 invol- 

 ving an unstable state of the medium. The condition of 

 incompressibility, absolute or approximate, has therefore ap- 

 peared 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 ^'' 'pro- 

 vided we either suppose the medium to extend all through hound- 

 less space, or give it a fixed containing-vessel as its boundary.'' 

 This renders possible a very simple theory of light^ which tias 

 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 seolotropic 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 J. 



* From the American Journal of Science for February 1889. 



t 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 Eefraction and the Dispersion of Colours," in the June number 

 of the Amer. Journ. Sci., was written. The conclusions of that paper, 

 except so far as respects the dispersion of colours, will not apply to the 

 new theorJ^ 



J Sir William Thomson, loc. cit. R. T. Glazebrook, Phil. Mag. 

 December 1888. 



