PROCEEDINGS 



CAMBRIDGE PHILOSOPHICAL SOCIETY. 



May 17, 1847. 



A Theory of the Transmission of Light through Transparent 

 Media, and of Double Refraction, on the Hypothesis of Undula- 

 tions. By Professor Challis. 



The object of the author in this, as in two preceding communica- 

 tions on Luminous Rays and on the Polarization of Light'*, is, to esta- 

 blish the modulatory theory of light on hydrodynamical principles, 

 by means of a system of ray-vibrations, the motions in which are 

 mathematically deduced from hydrodynamical equations. In ap- 

 plying these views to the transmission of light through transparent 

 media, it is assumed that the aether is of the same uniform density 

 and elasticity within any transparent medium as without ; and that 

 the diminished rate of propagation in the medium is owing to the 

 obstacle which its atoms oppose to the free motion of the sethereal 

 particles. Considering the proximity of the atoms to each other, 

 and that the retarding effect of each atom at a given instant extends 

 through many multiples of its linear dimensions, it is presumed that 

 the mean retardation, though resulting from the presence of discrete 

 atoms, may be regarded as continuous. It is also supposed that 

 the mean effect of the presence of the atoms is to produce an appa- 

 rent diminution of the elasticity of the either, the motion in all other 

 respects being the same as in free space. By the application of 

 these principles, it is first shown that the surface of elasticity, that is, 

 the surface whose radius vector drawn in any given direction repre- 

 sents the elasticity in that direction, is in general an ellipsoid. This 

 being ascertained, the velocity o£&ray in any given direction is inves- 

 tigated ; and the result is, that the surface whose radius vectors 

 drawn in any given direction represent the velocities of propagation 

 of two oppositely polarized rays in that direction, is precisely the 

 wave-surface in Fresnel's theory of double refraction. 



March 6, 1848. 



A Mathematical Theory of Luminous Vibrations. By Professor 

 Challis. 



This paper is intended to be supplementary to three former com- 



* See Lond. Ed. and Dubl. Phil. Mag. vol. xxx. p. 365. 

 No. VI. — Proceedings of the Cambridge Phil. Soc. 



