﻿710 Dr. L. Silberstein on Radiation from an 



where a, ft, 7; are constants, which will have to be deter- 

 mined, for each individual spectrum, on the ground of 

 experience, such as the dispersive properties of molar lumps 

 of the substance in question or the characteristic features of 

 the spectrum itself. But we need not enter here upon 

 details of this kind. 



The purpose of the present note is shortly to report on 

 certain results already obtained by means of (1) in the 

 simplest case of the dispersion-law (3), viz. for *e = l. 

 Then 



*=-+t^ < 3 «> 



If k be the static value of Jc, that is, for an invariable 

 impressed force, or for \/<y=oo, we have a + /3 = Je . 

 Introducing (3 a) into the full formula (1), I obtain, for 

 the wave-lengths of the successive spectrum-lines, 



v-i(^)*tf('tS)'-3r- • <*> 



where ui (*=i, 2, 3, . . .) are the successive roots of the 

 transcendental equation mentioned' above *. The relative 

 intensities of the "lines" are given by (2), and since 

 K 2 >Kj, K 3 >K 2 , etc., the successive lines become not only 

 fainter but also sharper. The values of the successive roots, 

 u ii u 2-> etc., increase indefinitely, so that the lines become 

 more and more crowded from the red towards the violet end 

 of the spectrum, and, by (4), 



Xcc — y (5) 



Thus, the lines constitute a series having its convergence-point 

 at A, = 7. 



These being exactly the characteristic features of the 

 so-called "first'"' hydrogen spectrum f, it seemed interesting 

 to try to determine the constants a, ft 7 (and the order of 

 magnitude of K), so as to represent the beautiful series 

 of that gas by the formula (4). My calculations, which 

 now extend over many days, are not yet completed. The 

 following tables contain some of the results of my first 

 attempts. In each of these tables, the first column contains 

 the order-number (i) of the root ; the second column, 

 \i calculated by means of (4), in microns ; the third, the 



* Owing- to the large values of K , and, a fortiori, of KX, X >y, 

 this transcendental equation becomes — -1 =0, where g(u) = sin ulu. 



-cosu. u y^) 



t Which, in its essence, is also shown by aluminium and thallium. 



