the Vibration of Light and the Plane of Polarization. 191 



opposite kind as c changes sign, that is, according as the earth 

 approaches the star or recedes from it. Nevertheless Arago, with 

 the most accurate instruments, was unable to detect any such 

 displacement. Fresnel, in a letter to Arago* explained this 

 negative result on the hypothesis that the elasticity of rether is 

 the same in all bodies, but that its density is proportional to the 

 square of the index of refi action j and it is not easy to see how 

 the fact can be accounted for in any other way. This, at least, 

 as is well known, was the hypothesis which was adopted by that 

 physicist to explain the different velocity of light in different 

 media, and which stands in necessary connexion with the doc- 

 trine that rether vibrates perpendicularly to the plane of polari- 

 zation. The confirmation, therefore, which the above hypothesis 

 receives in FresnePs essay extends also to the doctrine in question. 

 I may perhaps hope to assist in disseminating an acquaintance 

 with the interesting demonstration given by Fresnel, by substi- 

 tuting a simple geometrical proof for the algebraical one which 

 he makes use of. 



Let L L' be a pencil of light a 



incident perpendicularly on the 

 first surface A C of a glass prism, 

 andsuppose it to issuefrom a star 

 from which the earth is moving 

 directly away. It will then pro- 

 ceed without deviation as far as 

 P M. For the sake of simplicity, 

 instead of the earth moving and 

 the rether remaining at rest, sup- 

 pose the earth to be at rest and 

 the surrounding sether to move 



with the velocity C in the opposite direction. The density 

 of the aether within the prism being, then, to that without, as A 



to 1, its rate of motion in the prism will be -~; since the par- 

 ticles of aether, which are at the surface A C at any epoch, must 

 travel a unit of length from it in the same time' that it takes 



those to the depth -^ in the prism to issue from it, so as to 



occupy in vacuo a stratum of space a linear unit deep. If, then, 

 w; denote the velocity of light, n the index of refraction, the wave 

 of light PM, which begins to leave the prism at M, will move 



from P to N with the velocity -- ^ 



A' 



and if the time it takes 



Ann. de Chiin. el de riiys. 1818, vol. ix. p. 5(i. 



