﻿The Hon. J. W. Strutt on Double Refraction. 519 



r being the actual radius of the primary, and p its density divided 

 by that of the satellite ; so that the radius of the smallest orbit 

 for the latter will be 2*4547r v/p. On comparing the results in 

 the last paragraph with (12), (13), and (14), it will be seen that 

 the heterogeneous composition of a planet would be attended 

 with a far less change in the results in the present investigations 

 than in those usually given for the figure of worlds, supposing 

 the deviation from a true sphere to arise from the sole action of 

 centrifugal force. 



Cincinnati, March 24, 1871. 



LXV. On Double Refraction. By the Hon. J. W. Strutt, 

 Fellow of Trinity College, Cambridge*. 



IN a former paper f I have shown that, of the various hypo- 

 theses which might be made to explain the diminished ve- 

 locity of light in transparent matter, only one can be reconciled 

 with the observed laws regulating the intensity of polarized 

 light scattered in different directions from an assemblage of par- 

 ticles whose diameters do not exceed a small fraction of the wave- 

 length. We are forced to suppose that the difference between 

 media which is the cause of refraction is a dynamical and not a 

 statical difference, that the rigidity or force with which the 

 sether resists distortion is absolutely invariable. In this view 

 there is nothing novel. Fresnel distinctly adopts it in the in- 

 vestigation of his celebrated formulae for the intensities of re- 

 flected light ) and, what is more important, Green's rigorous 

 mechanical theory of reflections % is based on the same assump- 

 tion. Cauchy also, to whom much of the credit really due to 

 Green has been transferred, starts from the principle of conti- 

 nuity of movement, which asserts that in the passage from one 

 medium to another there is no break in the continuity of the 

 values, either of the displacements or of their differential coeffi- 

 cients. I believe that Cauchy has nowhere explained the ground 

 or significance of his principle ; but it is easy to see that to as- 

 sume the continuity of strain is equivalent to asserting a com- 

 plete continuity of statical properties, so that, as has been pointed 

 out by Haughton§, Cauchy's theory is essentially the same as 

 Green's. 



On the other hand, MacCullagh and Neumann have founded 

 their investigations of reflection on the hypothesis that the dif- 

 ference between media is statical and not dynamical. There is, 



* Communicated by the Author, 

 t Phil. Mag. for June 1871, p. 447- 

 \ Camb. Phil. Trans. 1838, or Green's ' Math. Papers.' 

 § Phil. Mag. S.4.vol. vi.p.81. 

 2M2 



