574 Prof. 0. W. KichardsoD on a Theory of the 



force outside the atom A due to the doublets in B. By con- 

 siderations similar to those already brought forward, the force 

 at the 5th electron in A will be less than this in some ratio y' s . 

 For the case of the dielectric sphere y = y' = 3//c-\-2, but 

 there is no reason why this equality should subsist in general. 

 A repetition of the method of calculation of § 3, to the 

 accuracy of the first term in expression (9), shows that 

 it is necessary to multiply L : by 7*7/. For this to be the 

 correct explanation of the discrepancy between the calculated 

 and observed values, it is necessary that the average value 

 of 7 s y/ should be of the order of 1/10 or 1/80 according to 

 which of the values of a on p. 56 6 we take to be the more 

 reasonable. This would require the specific inductive capacity 

 of the atom to be of order either 7 or 25, the average 

 values of 7 being 1/3 or 1/9. The experimental results on 

 dispersion do not appear to contradict the possibility of values 

 of 7 in the neighbourhood of either of the above numbers. 

 It is evident that the coefficient 7 will depend on the structure 

 of the atom and the orientation of the vibrating electron in 

 it. On this account the pressure- shift for different elements 

 might reasonably be expected to be a periodic function of 

 the atomic weight [as the valency relations require atomic 

 structure in general to be such a function] and also to possess 

 different values for different series of lines of the same 

 element. It will be noticed that a similar periodicity might 

 be expected to arise if the discrepancy were due to the orbital 

 motions of the electrons previously considered. 



Relations of this kind have been discovered experimentally*, 

 but our present knowledge of atomic structure is too slight 

 to be used to test this hypothesis. It is idle therefore to 

 pursue this part of the subject further, but it is hoped that 

 what has been said is sufficient to show that interference by 

 other electrons is in all probability at least a partial cause of 

 the smallness of the observed shift compared with that calcu- 

 lated on the simpler theory. 



§ 7. An Alternative Theory. 



A different theory of the pressure shift of spectral lines 

 has been given by Humphreys f, who supposes that the effect 

 is caused by the mutual magnetic perturbations of the atoms. 

 On this view the pressure shift is allied to the Zeeman effect. 

 The following considerations appear to show that the effects 



* Humphreys, Astropliys. Journal, vol. vi. p. 169 (1897). 

 t Astrophys. Journ. vol. xxiii. p. 233. 



