I^rOiidcuinp of Spectral Lines. 539 



Let : = d when f is zero. Tlieii we oet 







Now a, ?>, and d are the linear vek^cities of the ])articl 

 before the waves start, and they will be in general small 

 compared with Yq. 



We should get the usual Doppler effect by taking account 

 of all velocities, and this we need not discuss. Independently 

 of this, we see that the period of the scattered light will be 

 increased by 



or the wave-length will be increased by 



2Yo7ny 



Thus, instead of homogeneous light, there will be a portion 

 of lio'ht scattered by the free-charged particles, and the 

 wave-length of this portion will be longer than the wave- 

 length of the original light. The intensity of the scattered 

 light will be proportional to the number of free-charged 

 particles which are present in the vicinity of the luminous 

 source. Probably this will not show as a new line, but by 

 complication with the Doppler effect we shall get only un- 

 symmetrical broadening to the red. 



Xq^ is a measure of the intensity of the original light, so 

 that the broadening will increase with increasing intensity 

 of the original radiations. We may thus expect very different 

 amounts of broadening, not only in different lines, but also in 

 different forms and intensity of the electric discharge. 



Other things being equal, the increased breadth will be 

 proportional to the cube of the wave-length. 



It thus seems to me that we have a reasonable explanation 

 of at least part of the observed broadening, and the formula 

 possesses considerable power of adaptability to the different 

 circumstances which determine the particular line in question. 



So far, however, the theory leaves the question of broad- 

 ening towards the violet unexplained. iSTow I think the 

 charged negative particles may contribute to this in the 

 following way. The continual stream of charged particles 

 w^hich goes on in the electrical discharge means that a local 

 magnetic field of perhaps considerable strength will be set up 

 in the immediate vicinity of the luminous source. 



The phenomena will thus be complicated by the Zeeman 

 effect. Now Zeeman has observed a lack of svmmetry of the 



