an Electric Source, and Line Spectra. 797 



spectral lines Xi, say, X/ and X/'. To these latter we shall 

 refer shortly as the i-th lines. Similarly for any number of 

 convergence-points. The relevant combination of dispersion 



constants, /3 Z =— ^ might conveniently be called the intensity 



it 

 of the i-th convergence-point. 



The simplest typical Dispersion, and the Balmer Law. 



Postponing the fuller discussion of the cases of two and 

 more y's, let us consider the simplest case in which there is 

 but one convergence-point. Then the dispersion formula 

 (44), with (45), becomes 



/ l • J> W fAA V 



and therefore the equation of the spectrum, 

 b:y 2 (X 2 -y 2 ) = u*, 



7 2 +-^, i-l, 2, 3,. ..oo. • . . (47) 



*•«• x.2 2 , P 



We shall call this infinity of lines, converging towards 

 A,=7, a simple series of lines. Its relationship to those series 



CO 



known from spectroscopic experience w r ill be shown presently. 

 It will be remembered that ^ = 4*4934, u 2 = 7'7253, &c, 

 so that the second term in (47) decreases rapidly with the 

 increasing ordinal number of the lines. 



The most characteristic feature of a series of lines is 

 doubtless its convergence-point itself and its immediate 

 neighbourhood. For, apart from other reasons, this feature 

 remains unaffected by the simultaneous existence of other 

 convergence-points. It is therefore natural to inquire first 

 of all into the properties of the simple series \47), especially 

 when Xi approaches 7. We have, rigorously, 



Now, for high values of i, that is for u? large as compared 

 with fy'7 4 , we have, neglecting terms with 1/u 4 , etc., 



i-\\}-»h} <"->' 



By (27), Second Paper, 



*-[* ' L >2 (2i + l)7r 3^(21 + J W ■***•' * 



