Theory of Radiation. 245 



Hence tan 2 = 2; 



hnv 2 — \/Mmecot- . </> 



1 



°4 



or since h — — - v^lme' 



\/2 



\/2 • 



Thus since |mr is the kinetic energy and (p the frequency 

 of the steady motion, we see that the steady motion of the 

 corpuscle is such that the kinetic energy is proportional to 

 the frequency. 



We can easily show that if the corpuscle is disturbed 

 from the state of steady motion, and if r + p, tan -1 \/2 + 3, 

 where p and 3 are small, are the values of p and 3 in the 

 disturbed motion, then 



-g-o. 



or the frequency of the vibration about the steady motion is 

 v'2 times the frequency of the steady motion, and both are 

 proportional to the kinetic energy of the corpuscle in its 

 steady motion. 



By altering the distance of the corpuscle from the centre 

 of the doublet always keeping tan 6 = 2, we can make the 

 frequency for steady motion any thing we please, the kinetic 

 energy will always be proportional to the frequency. 



Hence, if the atoms contain doublets, it is probable that 

 in a certain number of cases these doublets will have cor- 

 puscles circulating round them, in some atoms the distance 

 of the corpuscles from the doublet will have one value, in 

 others another, and these differences in the distances will 

 give rise to steady motions with different periods. Thus in 

 a body made up of an enormous number of atoms, there are 

 systems consisting of a doublet and a corpuscle in steady 

 motion, the frequency of the motion having all values, the 

 kinetic energy of this motion bears a constant ratio to the 

 frequency, the frequency being independent of the kind of 

 atom in which the steady motion takes place. What will be 

 the behaviour of such a body when an electric wave of 

 definite frequency passes through it ? The electric forces 

 in the wave might do work upon the doublet, twisting its 

 axis so as to alter the angle it makes with the radius to the 



