the Michelson Interference Experiment. 155 



1 lie angle <f> does not enter into this formula. The light 

 consumes the same time to go from S to S x and back to S, 

 however the apparatus of Michelson is set relative to the 

 direction o£ the earth's translation. Especially the same 

 time T is consumed from S to Si and back to S as from S to 

 S 2 and back to S. As we have further assumed the fre- 

 quency to be the same for nil light-rays emitted from S, 

 the number of wave-lengths will bn the same to and fro 

 between 8 and S x as between 8 and S 2 , however the arrange- 

 ment is set. No displacement of the interference-bands 

 can therefore appear by the Michelson experiment, however 

 the apparatus is swung with respect to the direction of 

 translation. 



It is still to be proved that no error has been committed 

 by substituting the velocity c along SSx for the velocity of 



light c , along SSx', forming an angle <£' with the 



direction of translation. We find 



v » -••=,» [l-J(l+rin«#)] 



r v 2 / \~\ 



= c 2 1— T J1 -|- (sin 0cos Acp— cos <£ sin Ac/>) 2 j , 



A</> being =<j> — $>' = Sx SSx' (fig- 1)- Projecting S 2 on 

 SSx' to the point P (fig. 1), we obtain 



S 1 P = r£ 1 cos I — — <b' \ = vt 1 sm <j)' = l sin A</>. 



Hence 



. . , vti sin 6' 

 sin A $ = r 



" I v 



*x is to be sure <2 -, and consequently |sinA<£j<2-. 



The difference between the two angles <$> and <$>' is therefore 



v 



of the order - =10~ 4 . c* and <y will consequently differ 



c . . v 



only in terms of the third order with respect to -. The time 



t 2 will, with the same accuracy, be the same replacing the 

 velocity along Sx 7 S" by c^. 



3. Adopting this hypothesis, we meet with no contra- 

 diction if we determine the time by means of light-signals 



