﻿The Hon. J. W. Strutt on Double Refraction. 521 



be considered worthy of his great genius ; but it is well known 

 that as a rigorous mechanical theory it will not bear criticism. 

 Nor do the attempts that have been made to improve upon it 

 carry the mark of truth. On this point I refer to the excellent 

 report on double refraction by Professor Stokes in the British 

 Association's Report for 1862, and will only say that the ana- 

 logy between the vibrations of the sether and those which may 

 take place in solids, so striking as long as we confine ourselves 

 to ordinary media, seems to break down when we pass on to 

 consider the case of crystals. For Green has shown that the 

 elasticity of a crystallized medium depends in general on twenty- 

 one constants*, while the phenomena of double refraction in 

 biaxal crystals involve only six. It is true that, by assumptions 

 more or less arbitrary, the redundant constants may be got rid 

 of, and the result manipulated so as to agree very well with ob- 

 servation ; but no one, I suppose, would consider a theory arrived 

 at in such a manner altogether satisfactory. At any rate this 

 is not the opinion of Professor Stokes, who says that in his be- 

 lief the true theory of double refraction is yet to be found. 



We have, then, to consider this question : Can double refrac- 

 tion be explained if the statical properties of the sether are inde- 

 pendent of the associated matter ? Can we suppose that the 

 density within a crystal is a function of the direction of vibra- 

 tion ? I answer, yes. The absurdity is apparent only, and dis- 

 appears on more attentive examination. As I am conscious the 

 position is one that will need all the light that can be thrown 

 upon it, I think it well to give an illustration of a comparatively 

 simple character which occurred to me at an early stage of this 

 inquiry, and which was of great use in showing me in a general 

 way the possibility of the kind of explanation I was in search of. 



Let a solid body, such as an ellipsoid, be so supported in 

 space that its centre of inertia is free to move in any direction, 

 but is urged by springs or otherwise towards a certain fixed 

 point with a force symmetrical all round and proportional to 

 the displacement. The arrangement may be supposed to be 

 such that the body always retains its parallelism. Under these 

 circumstances, a vibration may be performed in any direction, 

 and its period is the same in all cases. If the inertia of the body 

 be increased, the only result can be that the motion will become 

 more sluggish and the period longer. Here we have the ana- 

 logue of singly refracting media. But now suppose that instead 

 of moving in free space the body is immersed in a fluid of sen- 

 sible density. According to known theorems in hydrodyna- 

 mics f, the inertia of the fluid adds itself to the inertia of the 



* See also Thomson and Tait's ' Natural Philosophy/ vol. i. p. 708. 

 t Thomson and Tait, p. 262. 



