146 Prof. J. R. Rydberg on the Ordinals of the 



Then we have 



a(N 2 ~N 1 )=r 2 -r 1 , 



and r 2 — ri 



and can in this way calculate a series of approximate values 

 of a, independent of the absolute values of N. 



Having taken the mean of these values of a I have calcu- 



v 



lated the values of - or N— C, and found that in all six 

 a 



series these numbers, and consequently also the values of 

 (N always being an integer), approach very nearly to whole 

 or half units. 



I have then assumed that the values of N— C end exactly 

 on *0 or *5, and on inverting the reckoning have calculated 



-vr p or a for every line in the spectra. If the formula of 



Mr. Moseley is exact, we shall then find a constant value 

 of a in every series. 



On using the N -values of my system the values of C will 

 follow directly on taking for any one element the difference 

 N — (N — C). These values of C are given at the heads of 

 the columns a (N — C). As our N- values are 2 units greater 

 than Moseley's, our C-values will also be greater, As we 

 shall see, the six lines form three pairs Ka and K/? ; La and 

 L/3; Ly and L<£, of which the C-value of the first line in 

 every pair contains 3, the second 3" 5 as a factor. I have 

 designated the corresponding a-values by a ly b l9 a 2 , b 2 , and 

 a 3 , b 3 in the three pairs. 



In the following tables the above-mentioned reckoning is 

 given for all the six series, with the exception of the later 

 part of L/3, where the lines seem not to belong to the same 

 series as the first ones, but to have been interchanged 

 in some way. The last 5 lines (Ta to An) , given by Moseley 

 for L/3, I have carried over to the series L<£, where their 

 wave-lengths answer tolerably well. Probably there will 

 be more lines in the high-frequency spectra than those 

 hitherto measured or published. 



As we see, the a-values in the different series are nearly 

 constant. Greater deviations occur only at the beginning 

 and at the end of the series, in Ka for the two first and for 

 the 3 (7) last elements; in K/3 for the two first only. In La 

 there are some greater values at the ends of the series, but 

 the differences are of no consequence. Ly and L(/> show 



