﻿712 Dr. L. Silberstein on Radiation from an 



nearly with H^., i. e. with H 2l (Balmer's m = 21 ; H a is H 3 ), 

 X 28 with H 23 , and X^ very nearly with H 31 , the last observed 

 line of the hydrogen series. In a word, from i = 2Q or so 

 the formula (4) is " getting out of step," with the above 

 constants that is. The reason of the superabundance of 

 theoretical lines is, of course, the choice of 7 just behind 

 the last observed line H 31 , which is certainly before the 

 convergence-point of the series (15'1 A.U. before X B ). 

 Owing to this circumstance the theoretical lines begin 

 to crowd, as it were, too early. This is one defect of 

 Table I. Another, more serious, defect is that the above 

 constants 7, a, k give, for i = l and i = 2, 



\! = -6267, X 2 = -4839, 



whereas the first tw r o hydrogen lines are (to four figures) 



H a = -6563, H3 = -4861, 



so that o the corresponding differences are A = —-296 (!) and 

 — 22 A.U. They have, therefore, not been incorporated 

 into Table I. In fact, the constants used in that table have 

 been calculated without any regard to H a , Hg. (And i 

 the reader tries to determine a. and k from these 

 two rebellious lines, so as to make them fit exactly, or 

 nearly so, he will at once spoil the rest of the series, from 

 X 3 till the end.) But apart from these two defects, the 

 agreement of the two columns of Table I., and more 

 especially for i=3 till e = 13*, seems remarkable. Notice 

 that the decreasing intensities of the successive lines, as 

 expressed by (2), and not given in the table, may serve as a 

 supplementary corroboration of the formulae here proposed. 



In Table II., in which 7 is very little smaller than in 

 the preceding table, the constants k Q , « have been deter- 

 mined from postulating X 4 = H^, X 5 = H e . Hence the 

 absence of A for these two lines, calculated only for the 

 sake of control. But the exceedingly close agreement 

 of X 6 , X 7 , X 8 , X 9 with H^, etc., seems very remarkable. The 

 results for X 1? X 2 are as bad as in the first case, but the 

 agreement for the remaining part of the series is, in general, 

 more close. 



The coordination of the theoretical and observed X's 



* The lines being here less crowded than in the lower part of the 

 table, there is little probability for the agreement being a "chance- 

 agreement. " 



