INORGANIC EVOLUTION. 



[CHAP. 



Formula for Calculating Series. 



Kayser and Eunge. 



Bydberg. 



where 

 <or 



A = ware-length 



= wave frequency) 



n = 3, 4,5, . . 



A, B, C = constants calculated for 

 each series. 



The constants for the principal series 

 tire different from those used in the 

 subordinate series. 



For sub-series of every element the 

 constant A is nearly identical. For all 

 series of all elements the constant B does 

 not vary by more than 22 per cent. 

 This constant B corresponds to Byd- 

 berg's NO. 



n = n n 



where 



n wave frequency 

 m = 1, 2, 3, . . . 

 NO = 109721'G (a constant ap- 

 plicable to all series 

 of every element) 



J characteristic constants 



M 1 varying with each series. 



In the above formula, when m = oo , 



n = n ; or n is the limit which the 



number of waves n approaches when m 



is infinite. 



The value of N is assumed by Eyd- 

 berg to be constant, as it varies only 

 slightly, and this variation may be due 

 to uncertain data. 



he worked. There was no common constant similar to this used by 

 Kayser and Eunge, but they found that some of their constants varied 

 little from element to element. In that way they not only obtained 

 the first term of a series, but the whole series throughout the entire 

 length of the spectrum, and where observations had been made in the 

 case of the different elements they could of course check their calcu- 

 lations by the actual observations so made, and see how the theory 

 seemed to be justified as the work was extended. The first line in a 

 .series must be considered to be comparable to a fundamental note in 

 music. It represents really the longest light wave in the same way 

 that the fundamental note in music represents the longest sound 

 wave. Both series of results, obtained in the way I have described 

 by Kayser and Runge and by Eydberg, show us that, in many cases, 

 we may be almost certain to obtain from the higgledy-piggledy arrange 

 ment of the lines in the spectrum of any one substance two or three 

 beautiful regular series like those already shown in the case of 

 the cleveite gases. There is a little difference in the nomenclature 

 employed by the investigators to whom I have referred, as shown in 

 the annexed table. 



