﻿722 Dr. H. Stanley Allen on an 



several recorded results. According to Hicks * both fi and « 

 depend on the atomic weight or atomic volume of: the 

 element, ot/fi being a pure number and equal to 0*21520. 

 Birge f points out that the coefficients in the formula of 

 Bitz increase with increasing atomic weight, being propor- 

 tional to the atomic volume in the case of sodium, potassium, 

 rubidium, and caesium. 



Several investigators have drawn attention to relations 

 between frequencies and atomic weights, Bamage and 

 Marshall Watts in particular having obtained relationships 

 involving the square of the atomic weight. This of course 

 implies that the constants in the spectral formulae depend 

 upon the atomic weight of the element in question. 



Hicks finds that the change necessary in the value of jjl to 

 account for the observed differences in the frequencies of 

 doublets and triplets can be expressed in terms of a quantity 

 which he calls the * oun ' depending on the square of the 

 atomic weight. 



Further arguments may be drawn from the " combination 

 principle of Bitz.''' The formula of Bitz may be written 



= A N 



U [ m + yU ,-j-/3(A-«)] 2 ' 



which is usually abbreviated as 



n=A— O, p, /3). 



The values of fi and of j3 differ in different " sequences/' 

 and Bitz shows that frequencies corresponding to definite 

 lines can be obtained by taking the difference between 

 various sequences. 



In the case of a principal sequence //, may have two values 

 fi x and fi 2 , the corresponding values of yS being /3 X and j3 2 . 

 Bitz proves that other lines may be obtained by taking 

 (m, fAi—ft 2 , fii—fa) as a sequence. In the case of the triplets 

 of the alkaline earths, differences such as fi 1 — /3 2 for the 

 principal series are the same as the corresponding differences 

 calculated from the diffuse series, so that evidence of a new 

 combination exists here. 



According to the simple form of the theory put forward in 

 my former paper, /3 is proportional to the magnetic moment 

 of the core. From this point of view, it is not difficult to 

 understand how we can get combinations such as A— /3 2 , 

 regarding the core as composed of positively and negatively 

 electrified particles in orbital motion. 



* Hicks, Phil. Trans, vol. ccx. p. 85 (1910) : vol. ccxii. p. 33 (1912) ; 

 vol. ccxiii. p. 323 (1913). J 



t Birge, Astrophys. Journ. vol. xxxii. p. 112 (1910). 



