Theory of Matter and on Radiation. 203 



The mean radiation from the gas per second per free ion is 



1 f T 1 — e~y T 



Tl R ^ = E o T • 



•^ o ' 



When the damping y is very small, as for the vibrations of 

 high class, the last factor is practically unity and the radiation 

 is R . When the damping is large, as for vibrations of low 



class, the last factor is nearly -7™ and the radiation is nearly 



7I 



R /yT, that is E /T. Thus the relative intensity of waves of 



high class and small radiation depends mainly on the relative 



radiation, calculated in § 9. The relative intensity of waves 



of low class and large radiation depends mainly on their 



relative initial energy, calculated in § 11. 



The damping, 7, is given by 7= -p : for E we may take 



the maximum kinetic energy of § 11, which is ^-o"u 2 5 



T> / 2 W 



thus 7= — s- ^-™ This may also be written 



' 7r 2 2 m(^/a>j 2 



§ 13. We shall now try to form an estimate of the values 

 of 7T for vibrations of different classes, in order to decide for 

 which of these classes the intensity of the waves emitted is 

 determined by the initial radiation, or by the initial energy. 



In § 8 we saw that a vibration of class k produces a series 

 of harmonic waves, whose frequencies are q + kco + snco. The 



71 



strongest of these, for k between +-, is given by s = Q; this 



alone will be considered, because the others are extremely 

 weak in proportion. If \ be the corresponding wave-length, 

 we have 



hence qfi , - _ 2-rrp 



&) A 



For frequencies within the limits of the spectrum -^ is 



08 . ^ 



very small ; hence — is very nearly equal to — k/3. There- 

 fore for waves of corresponding frequency we find 

 „ T= -T R 



7 TtX'nnp' /rV =" 



