[ 337 ] 



XXXVI. Atomic Number and Frequency Differences in 

 Spectral Series. By Herbert Bell *. 



IT is a well-known law t that in the visible spectrum the 

 wave-number differences v between the components of 

 a doublet series, and the differences v x , v 2 between the com- 

 ponents of a triplet series vary from element to element 

 in such a way that, for the same family (column of the 

 Mendelejeft table), the v's are roughly proportional to 

 the squares of the atomic weights. We have, for example, 

 in Baiy's ' Spectroscopy,' p. 624, the following table J where 

 the argument is 1000 v (or v 1 )/(atomic weight) 2 : — 



Na 32-3 



Mg 68S 



Al 152-8 



14-5 



K 37-8 



Ca 66*1 



Ga 168-6 



S 17-7 



Rb 32-3 



Sr 51*5 



In 172-1 



Sel6-6 



Cs 31-6 



Ba 46-8 



Tl 187-0 





If the law were accurate the arguments in the several 

 columns would be constant. Perhaps the most thorough 

 discussions from this point of view have been given by 

 Rudorf § and Hicks || . 



An attempt was made by Runge and Preclit % to show 

 that the outstanding discrepancies in the above table, 

 e.g. the case of thallium, are removed by assuming a 

 different law. They stated that the logarithm of v is linaar 

 in terms of the logarithms of the atomic weights. We shall 

 have to refer to its correctness later. 



Since Moseley's** discovery that the square root of the 

 frequencies of the X-ray series is linear in terms of 

 the atomic number, for all elements, more attention has 

 naturally been turned to it than to atomic weight. In 

 particular, Runge and Precht's method was modified in 

 this direction by Ives and Stuhlmanjt with a decided im- 

 provement especially in the case of potassium. Their paper 

 contains no constants for the straight lines so that the 

 agreement is only graphically demonstrated. 



* Communicated by the Author. 

 + Due to Kayser and Runge, and Rydberg. 

 X Due to Rvdberg, Intern. Reports, ii. p. 217 (Paris, 1900). 

 % Zt. Phys." Chetnie, 1. p. 100 (1904). 



|| See e.g. Phil. Trans. A. ccx. (1910), ccxii. (1912), ccxiii. (1913), 

 ccxvii. (1917). 



II Phil. Mag. v. p. 476 (1903). 



** Phil. Mag. xxvii. p. 703 (1914). 



tt Phys. Rev. v. p. 703 (1915). 



