x.] THE "SERIES" EVIDENCE. 87 



gen lines could be calculated with wonderful accuracy. The formula 

 is as follows : 



rt-2 



x = A -^-i> 



n- - 4 



in which A is the wave-length in vacuo of' the line to be calculated, A 

 constant common for all the lines, and n one of the series of numbers 

 from 3 to 15. 



The constant A, according to Cornu's measurements, is 3645*42 

 Angstrom units, or, using Ames' more correct value, 3647*20 Angstrom 

 units. 



Simultaneously with Balmer's discovery, Cornu* pointed out that 

 the lines of aluminium and thallium, which are readily reversible, bear 

 a definite relation to those of hydrogen, while at a later date Des- 

 landresf published a formula from which could be calculated the wave- 

 lengths of the lines composing the bands of numerous elements. 



The above brief history brings us down to the year 1887, in 

 which Kayser and RungeJ began their series of minute investigations 

 dealing with a great number of elements. It was also about this time 

 that Rydberg commenced to take up the subject. 



The work of Kayser, Runge ami Rydberg. 



I will state generally the ground over which their work has ex- 

 tended. They have attacked the question mathematically from 

 different standpoints. In the following table (p. 88) I give th& 

 formula employed by Kayser and Runge, and that employed by 

 Rydberg. 



The formulae are not by any means identical, but both deal with 

 wave-frequency, that is to say, the number of waves in a given unit 

 of length. Both Kayser and Runge, and Rydberg employ certain 

 signs to represent the successive integers which have to be used to- 

 define certain of their terms, and in addition to this we get certain 

 constants which are calculated for each series. The most interesting 

 consideration from this point of view is that Rydberg found that 

 there was one constant which he could use in order to search for the- 

 series of lines in the spectra of all the chemical elements with which 



* Complex rendu.1 (1885), vol. c, p. 1181. 



t Ibid. (188G), vol. ciii, p. 375; (1887), vol. civ, p. 972. 



"t "TJeber die Spectren der Elemente," Alhandlungen d. K. Alcad. Berlin,. 

 1888, 1889, 3890, 1891, 1892, 1893. 



SvensJca Vetenslcat. Akad. Handlingar, Stockholm (1890), vol. xxiii No. 11;. 

 Wied. Annalen (1893), vol. 1, p. 629 ; (1894), vol. lii, p. 119. 



