120 The Lumniiferous Medium, 



and therefore (neglecting second-order terms in w/c] 



A 



sin A^B^D c - w cos 81 _ c w w ^ 



- : ~ ~ "f- *" COo Ol 



sin ^ Ci c t c Ci 



Ct-W- 



Denoting by 8 the value of 81 when w is zero, we have 



sin (i -8) c 

 sin i d 



Subtracting this equation from the preceding, we have 



8 -Si _ w 

 sin c 



Now the telescope by which the emergent wave-front B\ D 

 is received is itself being carried forward by the earth's motion; 

 and we must therefore apply the usual correction for aberration 

 in order to find the apparent direction of the emergent ray. But 

 this correction is w sin 8/c, and precisely counteracts the effect 

 which has been calculated as due to the motion of the prism. 

 So finally we see that the motion of the earth has no first-order 

 influence on the refraction of light from the stars. 



Fresnel inferred from his formula that if observations were 

 made with a telescope filled with water, the aberration would be 

 unaffected by the presence of the water a result which was 

 verified by Airy* in 1871. He showed, moreover, that the 

 apparent positions of terrestrial objects, carried along with the 

 observer, are not displaced by the earth's motion ; that experi- 

 ments in refraction and interference are not influenced by any 

 motion which is common to the source, apparatus, and observer ; 

 and that light travels between given points of a moving material 

 system by the path of least time. These predictions have also been 

 confirmed by observation: Kespighif in 1861, and Hoek+ in 1868, 

 experimenting with a telescope filled with water and a terrestrial 

 source of light, found that no effect was produced on the 

 phenomena of reflexion and refraction by altering the orienta- 



* Proc. Roy. Soc., xx, p. 35. t Mem. Accad. Sci. Bologna, ii, p. 279. 



I Ast. Nach., Ixxiii, p. 193. 



