﻿42 Dr. H. Stanley Allen on the 



If v denote the frequency of: vibration, v = Nc, where c is 

 the velocity of light, and the formula may be written 



^(l-i) 



where v has the value 3*29 x 10 15 sec. -1 . Bohr's theory 

 identifies v with 27r 2 >»<? 4 //r 3 , the numerical agreement between 

 the two quantities being remarkable. 



complicated formulae have been proposed. The typical 

 Rydberg series is of the form 



N=N ( / -4 



^) 2 r 



\ (1 + ^u) 2 (m + 



where /x and jjl are fractions. This may conveniently be 

 written 



K=N 4ii?-A} 



Rydberg states that the true formula should be given by 



writing for D some function of m + a, say m + lu-\ — . In 



° r J m ■+- fju 



commenting on this Hicks makes the following significant 

 statement : — 



"If a series is represented by J) = m + a-j a slight 



1 J r- m + ^ r> 



alteration will represent it equally well by putting D a 

 continued fraction, viz. 



I-. a 



D=m-fyL6+ - 



in other words, 



a. 

 m+fi+ — — — 



No N r /J'(m + A- , \ m 4- fi] 2 



or N = A — B{a/( w 2 + 2« m + &) —(?»+«)<■ 2 ^ 



which looks quite different, and points to the frequencies- 

 depending on the roots of a quadratic" t- 



* Curtis (Proc. Roy. Soc. vol. xc. p. 605, 1914) finds that the results 

 for hydrogen may be represented by a modified Rydberg formula. 



t Hicks, Phil. Trans, vol. ccx. p. 85 (1910)/ The notation of ths 

 original has been slightly modified. 



