Displacement of Spectral Lines produced by Pressure. 563 



It is now necessary to consider the quantities L x L 2 in 

 equation (9). On the assumption we have made in the 

 calculation that the displacements a^, a 2 i; o£ the electron B 

 were due to a steady electric force, it is easy to show that 



L 1 = 2\ s =- j , where K is the specific inductive capacity 



of the surrounding medium when there are v molecules per 

 unit volume. As a matter of fact, the displacements aif, a£ 

 are produced by a periodic force of time t. If we neglect 

 the initial disturbance at B of period corresponding to \ s , the 

 coefficients a 1 a 2 will be given by equation (5) provided 

 \ s is replaced by \ s /1—t 2 /t 2 . Under these circumstances it 

 can easily be shown that 



Lt = S X * -£z± . . . ( io) 



where fi is the refractive index of the medium for light of 

 the wave-length emitted. It seems permissible to disregard 

 the initial disturbance on account of the difference in period. 

 It will only produce a broadening not a shift of the line. 



The quantity L 2 is evidently the value of £(y s , 2 J 



taken over the molecule B. Unless r is in the neighbourhood 

 of t s one of the natural periods of the B molecules L 2 will be 

 of the order L^/h, where n is the number of mobile electrons 

 in the molecule. The ratio of the two terms in equation (9) 



1-26L! 1-26 (yu 2 -l) 



tina? '6'2irnv oi 6 



(ii) 



Taking the case of air as the surrounding medium we have 

 I* 2 — 1 = 5*9 x 10 -4 when v = 4xl0 19 . According to J. J. 

 Thomson's most recent estimate n will be of the order of 

 twice the ratio of the density of the gas to that of hydrogen. 

 This at any rate can be taken with safety as a lower limit 

 to n. Putting ?2 = 29 and taking 1'5 X 10 -8 {half the radius 

 of the sphere of molecular action) for a we find that the 

 ratio is very nearly =2 x 10~ 3 . In the neighbourhood or an 

 absorption-band of one of the B molecules one of the terms 



\J1 — I — ) would be great compared with the others. In this 



case a superior limit to the ratio would be obtained by putting 

 n=l in equation (11). Even in this case the second term is 

 comparatively unimportant. 



