312 Mr. H. Eamage. The Spectra of Potassium, etc. [May 14, 



The convergence points of the series as deduced in different ways 

 are given in the following table : — 



Element. 



Prom above formulae. 



By cal- 

 culation 



from 

 observed 



lines. 



From 

 formula 



for 

 principal 



series.* 



Numbers 

 calculated 



Rvdberg. 



First 

 series. 



second 

 series. 



Mean of 

 two series. 



Potassium (1) 

 „ (2) 

 Rubidium (1) 



» (2) 

 Caesium (1) 



(2) 



21953-9 

 22011-7 

 20861-8 

 21098-2 

 19677-2 

 20224-8 



219680 

 22025-8 

 20868-3 

 211063 

 19674-2 

 20228-0 



21960-95 



22018*75 



20865-65 



21102-25 



19675-7 



20226-4 



Mean. 

 21960 

 22018 

 20865 

 22101 

 19672 

 20226 



21969-4 

 22024-3 

 20868-6 

 211123 

 J 96867 

 202342 



21955-46 

 22013-31 

 20869-15 

 21098-83 



The numbers in the sixth column were obtained by the law, dis- 

 covered by Eydberg and independently by Schuster, which connects 

 the principal and subordinate series : the convergence points of the 

 subordinate series are given by the differences between the convergence 

 points and first lines (for which m = 1) of the principal series. One 

 set of the numbers was obtained from the expression 



No 



(1 + 1 -19126 + 0- 00103 W) 2 5 

 and the other set from the expression 



No 



(1 + 1-19126 + 0-00103 W+182 W 2 x40~ 8 ) 2 ' 



The figures in this column agree best with those of the second subordi- 

 nate series in the third column • and it will be remarked as confirming 

 the closer connection between the principal and second subordinate 

 series, that the results calculated for the latter series of rubidium 

 differ by about nine units, whereas those given by the formula for the 

 principal series differ by about 27 -5 units from the observed numbers. 

 The connection between the first subordinate series and the atomic 

 mass is apparently simpler than between the other two series and the 

 atomic mass. 



The numbers in the last column were taken from Rydberg's paper, f 

 He calculated them by means of an empirical formula, from the 

 observed lines. 



All the strong lines, and nearly all the weak lines which have been 

 observed in the flame and arc spectra of these elements, are included 

 in the three harmonic series of lines. The empirical formulas given 

 show that the differences in the corresponding series depend wholly on 

 the atomic masses of the three elements. 



* Author, loc. cit. 



f ' Paris Congress Reports,' vol. 2, p. 212, 1900. 



