Mechanism of Radiation. 445 



contain the factor e im<p , we see that the aggregate radiation 

 is nil. 



The amount of the latter will also be proportional to a 

 factor e im Q, and the radiation will be nil except in the case of 

 m= +1. 



In the case of m — 1, the radiation is such as would be 

 emitted by a single particle describing an orbit in the 

 equatorial plane. To investigate this orbit it is only necessary 

 to notice that the values of u, v, iv at every point will depend 

 on <f> and t only through the factor e^Q+P^. Hence the 

 equivalent displacement will depend on <p and t through 

 the same factor, and will therefore be that of a particle 

 describing a circle in the equatorial plane, the direction being 

 that of increasing or decreasing according as m has the 

 value — 1 or +1. 



Hence the polarization of the lines m= — 1, 0, +1 can be 

 accounted for in the manner in which they have already been 

 accounted for by Larmor upon the supposition that the 

 radiation is emitted by a single ion vibrating in a spherically 

 symmetrical field of force. On the other hand, our theory 

 does not compel us to expect that every line will be separated 

 into a triplet, or that the separation will be of constant 

 amount. 



§ 32. It must be remembered that our examination of the 

 polarization is subject to two corrections : one arising from 

 the finite radius of the atom (which was neglected in com- 

 parison with the wave-length), and the other from the discrete 

 structure of the actual atom. For this reason we cannot 

 expect the polarization of the lines to be absolutely complete, 

 and the lines for which m has values other than or + 1 

 will not actually be invisible, although since the total 

 radiation arises solely from two small corrections, they will 

 probably be very faint. 



The polarization of the side-lines of a triplet shows that the 

 equivalent single ion must be supposed to be of negative 

 sign. It is of interest to notice that on the present theory 

 this does not indicate that the light is emitted solely by 

 negative ions, but only that the vibrations of the negative 

 ions contribute more to the radiation of the particular periods 

 in question than do the positive ions (see § 2ti). 



The Influence of the Translation and Rotation of the Atom. 



§ 33. There is a purely kinematical result of the trans- 

 lational motion of the atom, which shows itself in the well- 

 known Doppler effect, and consequent broadening of the 



