On Illumination and Polarization in Transparent Substances. 221 



potential energy of the elastic stress of unity of mass of the body 

 at constant temperature ; then 



dV 

 = Jchyp.logT + x(«r) + -^-j - . . {<iv) 



and the corresponding form of the general equation of thermo- 

 dynamics is as follows : — 



dQ={Jc + T^{T)}dr + rd.-~ (21) 



§ 12. Conclusion. — In conclusion, then, it appears that the 

 special suppositions, as to matters of detail, introduced into the 

 hypothesis of molecular vortices in the paper of 1849-50 are 

 not essential to the deduction from that hypothesis of the princi- 

 ples of thermodynamics, but that such matters of detail may be 

 left open to be determined by future investigations. 



XXVIII. On Illumination and Polarization in Transparent Sub- 

 stances. By L. Soret. 



My DEAR Tyndall, Geneva, Jan. 24, 1870. 



I HAVE been somewhat long in replying to your kind letter 

 of the 5th of December ; numerous occupations have pre- 

 vented me from communicating to you my idea of how, by the pre- 

 sence of particles diffused in a transparent medium, we may theo- 

 retically explain the various phenomena of illumination and of 

 polarization which are observed when a pencil of light passes 

 through a transparent substance. I am far from believing that 

 my theory is not open to objection, and I should be at no loss to 

 criticise it myself and to raise doubts in respect of it. You know, 

 moreover, how many delicate points are involved in all that 

 concerns the theory of reflection. I think, nevertheless, that 

 my views on this subject will not be uninteresting to you. 



Let us see, then, how we can account for the action exerted 

 by these particles. 



I. The first hypothesis would be to assume that the vibratory 

 motion of the aether is communicated to those minute parti- 

 cles which occur in the path of the pencil of light pretty much 

 as sound-vibrations in air are communicated to solids, such as 

 strings or membranes. The corpuscles would thus become cen- 

 tres of disturbance, sending in all directions vibrations of the 

 same kind as those which constitute the pencil of light ; if, more 

 especially, this pencil were polarized, the waves emitted by the 

 particles would consist of rectilinear vibrations parallel to the 

 incident vibrations. The explanation of the phenomenon would 



