814 Prof. H. A. Wilson on the Relative 



motion of the aether will not affect the spectroscopic determi- 

 nation of the velocity of stars in the line of sight. Suppose 

 a telescope at the earth's * surface is kept directed towards 

 a star, then it will suffice to show that the number of light- 

 waves arriving per second at the image A of the star in the 

 telescope is not affected appreciably by the motion of the 

 aether, or by the variations in the motion due to the earth's 

 rotation. Consider a point P fixed relatively to the tele- 

 scope, and on its axis produced so far away that the aether at 

 P is undisturbed by the earth. The number (n) of waves 

 from the star passing P per second will be given by Doppler's 

 principle, allowing of course for the motions of both P and 

 the star. The number (n') of waves arriving per second at 

 the image A in the telescope will be equal to n minus the rate 

 of increase of the number (r) of waves between P and A. 



This number is 1 ds/\ where X is the wave-length at ds. If 



v e is constant, the number of waves passing any point between 

 P and A is n, and 



n\ = c/fi + v m (l - 1/yLt 2 ) 4- v e /fi 2 ; 



so that 



r = n I - 



The rate of variation of this when v e varies is approximately 



£GJ» 



Thus , dr (.Id 



71 ' = 71— TT 



dt 



Since we are now taking the earth to be moving with 

 velocity v and the aether at a great distance to be at rest, we 

 have 



-K 1 - ?£<*■-**>} 



Consequently 

 so that 



<p= — COS0. 



<£ P = and <)) A = vacGsQ; 

 , /., , va . „d6\ 



n= „V + _ sme _- 



The greatest value of a sin -7- is equal io the velocity of 



the earth's surface due to its daily rotation, while v/c is about 



* This way of treating the problem is due to H. A. Lorentz (' Theory 

 of Electrons '), who applies it to the case where the aether is regarded as 

 stagnant. 



