On Fresnel's Theory of the Aberration of Light. 77 



-tt. in a direction contrary to that of the earth's real motion. 



P 



On account of the smallness of the coefficient of aberration, 



we may also neglect the square of the. ratio of the earth's ve- 

 locity to that of light ; and if we resolve the earth's velocity in 

 different directions, we may consider the effect of each resolved 

 part separately. 



In the nintfi volume of the Comptes Rendus of the Academy 

 of Sciences, p. 774, there is a short notice of a memoir by M. 

 Babinet, giving an account of an experiment which seemed to 

 present a difficulty in its explanation. M. Babinet found that 

 when two pieces of glass of equal thickness were placed across 

 two streams of light which interfered and exhibited fringes, in 

 such a manner that one piece was traversed by the light in the 

 direction of the earth's motion, and the other in the contrary 

 direction, the fringes were not in the least displaced. This 

 result, as M. Babinet asserts, is contrary to the theory of aber- 

 ration contained in a memoir read by him before the Aca- 

 demy in 1829, as well as to the other received theories on the 

 subject. I have not been able to meet with this memoir, but 

 it is easy to show that the result of M. Babinet's experiment 

 is in perfect accordance with Fresnel's theory. 



Let T be the thickness of one of the glass plates, V the ve- 

 locity of propagation of light in vacuum, supposing the aether 



at rest. Then — would be the velocity with which light would 



P 

 traverse the glass if the aether were at rest ; but the aether 



v 

 moving with a velocity —# the light traverses the glass with a 

 P 



V v 

 velocity — + — , and therefore in a time 



But if the glass were away, the light, travelling with a velo- 

 city V + v, would pass over the space T in the time 



T + (V±v) = ±(l+%). 



T 



Hence the retardation, expressed in time, =((/.— 1 ) ^, the 



same as if the earth were at rest. But in this case no effect 

 would be produced on the fringes, and therefore none will be 

 produced in the actual case. 



I shall now show that, according to Fresnel's theory, the 

 laws of reflexion and refraction in singly refracting media are 



