On the Spectra of the Alkalies. 261 



Different combinations of numerals will of course require 

 different values for a solution, but these are easily determined by 

 deducting their square numbers and multiplying the differences 

 respectively. 



I shall refer to the three constants by calling x the root, 

 because it is identical in value to Balmer's constant; y the ampli- 

 tude, because its square root gives the final number of the series; 

 and z the excentricity, as it determines the shape of the curve. 



To ascertain the numerals of a series generally requires 

 repeated trials. If z turns out negative, of course the numerals 

 are wrongly chosen, but even in the case of its acquiring a 

 positive value, the final test applied consists in working out 

 the values and to select the numerals, that accord best with the 

 experimental values. I have thus been forced to change the 

 numerals, as given by Kaiser and Runge, in many instances. 



A second difficulty is offered by the degree of exactness of the 

 experimental values. The latter have been supplied by Kaiser 

 and Runge, Liveing and Dewar, Lecoq do Boisbeaudran and 

 Snow, and they do not always accord well. But even the values 

 of one observer may greatly differ in exactness and may cause 

 considerable discrepancies, which will show themselves most 

 markedly in the red and ultrared rays. 



Only a few lines do not seem to fit into any series. These 

 lines are all of a slight intensity, they differ sometimes in aspect 

 from the other lines or are omitted by other observers. I there- 

 fore conclude them to be due to impurities. 



Several' series of the same metal may be united either by the 

 same root or the same excentricity or by both combined. In 

 the Table of Wave Lengths I have bracketed those values. 



The spectrum lines of each alkali metal seem to form two 

 groups, divided by a large gap or interval, and appear to form 

 two octaves, differentiated by their amplitudes especially. These 

 gaps proceed towards the red with increasing atomic weight. 



During the progress of my work T have been assisted by Mr. 

 R. L. J. Ellery, late Director of the Melbourne Observatory, 

 who aided me in solving difficult algebraical questions, and 

 by Mr. W. Sutherland, the author of important works on 

 molecular physics. To these gentlemen I hereby offer my 

 grateful acknowledgment. 



