SPECTRAL LINES 443 



not dealing with statistical or averaged effects, but considering 

 a single vibrator, some hypothesis must be made as to the 

 molecular constitution of the medium. This was done by Sir 

 Joseph Larmor, 1 who considered a spherical vibrator of radius 

 a, which acts as a simple Hertzian oscillator, and replaced the 

 surrounding gas by a medium of specific inductive capacity K, 

 assumed continuous, but extending only up to a distance ka 

 from the centre of the vibrator. Since the electric field of such 

 a vibrator varies, as regards distance, according to the inverse 

 cube law, the static energy in the field outside and up to a 

 distance r from the centre of the oscillator, supposed alone in 

 free aether, is proportional to 



/: 



r~ 6 . 47rr*dr or — rex"* 



and so, in the case considered, since where the specific inductive 

 capacity is K, the electrical energy is altered as compared with 

 a vacuum in the ratio K~ l , it is evident that the total static energy 

 is altered in the ratio 



a- 3 - (ka)~ 3 (i - K- 1 ) to a" 3 



and since the frequency is increased as the square root of this 

 ratio, it follows that 



d\ 1 K - 1 



X ~ 2k 3 ' K 



The value of K which occurs in this equation is not the 

 specific inductive capacity as determined by ordinary static ex- 

 periments, but the value appropriate to light waves of a frequency 

 corresponding to the wave length X, and by the electromagnetic 

 theory of light is defined by means of the relation K = /t 2 , in 

 which [J,, a function of the wave length, is the refractive index 

 of the gas for the wave length X. Thus Larmor's theory gives 

 a displacement of amount dX where 



dx 1 u? - 1 



X 2k» * /i* 



Using the value of fi for air at normal temperature and 

 pressure, and the observed values of dX/X, Larmor obtained k=8, 

 and concluded that the dielectric influence of the surrounding 

 medium is a vera causa of the right order of magnitude. It 

 seems more reasonable, however, to use the value of /x corre- 



1 Astroph. Journ. 26, p. 120, 1907. 



