XXXIX. A Theory of the Transmission of Light through Transparent Media, 

 and of Double Refraction, on the Hypothesis of XJndulations. By the 

 Rev. J. Challis, I\I.A., Plumian Professor of Astronomy and Experimental 

 Philosophy in the University of Cambridge. 



[Read May 17, 1847-] 



In a former communication to this Society, I ventured to advance a new Theory of the 

 Polarization of Light, founded on a Mathematical Theory of Luminous Rays. (^Cambridge 

 Philosophical Trans act io7is. Vol. viii. Part in. pp. 36l, and 371.) As the Theory was not then 

 applied to the phfenomena of Double Refraction, I propose in this Paper to attempt to give it 

 that extension. The course of the reasoning will require a general consideration of the transmission 

 of light through transparent media. I shall therefore commence with this part of the subject. 



1. It will be assumed that the sether is of the same uniform density and elasticity within 

 any transparent medium as it is 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 aetherial 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 will also be supposed that the mean effect of the presence of the atoms is to 

 produce an apparent diminution of the elasticity of the fether, the motion in all other respects 

 being the same as in free space. Let a = the velocity of propagation without the medium, 



and — = that within. Then, p being the density in a line of rectilinear propagation, at a point 



2 1 



distant by x from the origin, the effective accelerative force = ; . —'— . If there were no 



fi' pdat 



a^dp 



retarding effect of the atoms, the accelerative force would be -S- . Hence, the accelerative 



° pdai 



force of the retardation (/?) is equal to a" I 1 ; J — j- . For this force another expression may 



be obtained by the following considerations. If u be the velocity of the sether at the time t at 

 the point whose co-ordinate is .■», we have by known equations, 



V = — Nap. log. p = (j> i — t — aA 



Now the accelerative force of the retardation at a given point must vary conjointly as the 

 number of atoms in a given space, that is, as the density of the medium, and as the effective 

 accelerative force of the aether at that point. Hence, K being a certain constant, and h the density 

 of the medium, 



R = - Kl [-^\ = — Kh — very nearly. 

 \dtj dt ^ •' 



