318 Kxinz — Electromagnetic Emission Theory of Light. 



§ 3. The Doppler effect. 



Let a source of light be moving with velocity v along a 

 line AO, emitting disturbances of frequeney n in all direc- 

 tions ; the velocity of propagation will be ecpial to c + v ; after 

 one second the first disturbance emitted in A will reach the 

 observer in O. If we start counting the time in the moment 

 in which the source is in A, then in ^= 1 the source will be 

 in B and emit the ?ith disturbance. This disturbance will reach 



the observer after a time t = . Hence the observer receives 



c + u 



n disturbances in the time interval , or ?i' disturbances per 



unit time : 





e 





c -\-v 





n' 

 n ~ 



/c + v\ n' X' = c + v 

 \ c J nX = c 



X' c + v n 

 X ~ c ' n' ~ 



or the wave length remains unchanged. . 



In the case of sound we have : 



AA. _ « 

 X ~ T 



and this formula is also used in spectroscopy for the determina- 

 tion of the velocity of stars. 



The principle of relativity leads to the expression : 



i 



V' 



«_ — n'X'=nX 



c 



while the emission theory here sketched gives the result ; 



n' c+v 



On the other hand, the principle of relativity maintains that 

 the velocity of light is always the same, c, whatever be the 

 velocity of the source or of the observer. The electromagnetic 

 emission theory holds that the velocity of light given out by a 



