216 Dr. R. A. Houstoun on 



The index of refraction is given by 



where c is the velocity of light in vacuo. 



Now n=z27rc/\, where A is the wave-length in vacuo. It 

 will be found, by differentiating (5) with respect to A and 

 making the necessary substitutions, that 



/t _l_ /tX _____ 2 (6 ) 



Suppose now that the refracting medium is moving through 

 the aether with velocity v, in the direction in which the light- 

 wave is travelling. Our co-ordinate axes are fixed in the 

 aether. We assume that the light-wave is given by 



y =cos n(t— x /V). 



Since there is no damping, rj is in phase with ?/, and is pro- 

 portional to the same cosine. Equations (2) and (3) still 

 hold, but in equation (2) now 



dt ~&t 3a?' 



Previously the 3/Ba; term was zero. This is the only 

 difference between moving and stationary media. For one 

 definite particle of the " virtual " aether 



5i--rs- Hence jH^w 



Substitute now in (2) and (4), and we obtain 



[/ ? +/ J _ .(i_ v /V)VU3* 2 ~ B^ 2 ' 



Hence 1_ 1 r , Ml-g/V) 8 1 ... 



V 2 El P+ k-a{l-v/V) 2 n 2 y * # * {i) 



This is absolutely true, no matter what the size of v/Y is. 

 Assume that v/Y is small, and the equation reduces to 



V 2 ET + /:-c™ 2 V (/c-<m 2 ) 2 J 



"c 2 L VV /* /*dAJ' 

 Invert and take the root of both sides, remembering that v/Y 



