﻿580 Spectrum Lines with Constant Frequency-Difference . 



In a paper shortly to be published I have shown that the 

 only vibrations of this type which can give rise to spectrum- 

 lines of sufficient intensity to be observed, are those for which 

 k + sn + s'n' has one of the values 0, +1. Of these, the 

 strongest are given by small values of k-\-sn. We must 

 therefore find integral values *of s, s' which shall satisfy the 

 equations 



k + m + s*ri = Q 9 + 1. 



n 

 Convert — into a continued fraction, and let the last 

 n 

 p 

 convergent be r y, so that Tn — Qn' = +1. We find 

 H 



s = + hV +j Jen, / = + kQ —j hi (j an integer) 



for the first case, and similar expressions for the other two. 

 The corresponding frequency is for the first case 



q + kQn'fo — ft/) +jknn'(<D—(o r ). 



In other words, the vibrations emitted in consequence of 

 the interaction of the two rings form groups with the 

 constant frequency-difference knn{(o — ft/). The strongest 

 of these, corresponding to Jc = 0, k= +1, ... have the differ- 

 ences 0, ±ovn / (co — «'), .... The application is obvious to 

 Prof. Wood's result, as well as to the groups of lines of 

 constant frequency-difference found by Kayser and Runge 

 in the spectra of Sn, Pb, As, Sb, Bi. At the same time it does 

 not lead to an explanation of these results ; for in the first 

 place it has still to be shown that the factors C, B, A, which 

 enter into the amplitude of the vibration, can, by a suitable 

 choice of the structures and relative positions of the rings, 

 be given values which will account for the observed intensities 

 of the vibrations ; and secondly, the lines observed by 

 Prof. Wood show frequency-differences which vary somewhat 

 with the frequency. The investigation of the values of C, B, A 

 will prove a very difficult one, and it is impossible to foresee 

 the result. The deviations from constant frequency-difference 

 may possibly be due to the fact that the controlling field of 

 the rings is altered by the neighbourhood of molecules of 

 sodium other than that to which the rings belong. 



Yours faithfully, 

 University College of Wales, Gr. A. ScHOTT. 



Aberystwyth, 

 Nov. 6, 1906. 



