Electric and Magnetic Fields on Spectral Lines. 509 



stationary states corresponding to different values for n. 

 We must assume that the mechanism of emission cannot be 

 described in detail on the basis of the ordinary electro- 

 dynamics. However, it is known that it is possible on the 

 latter theory to account satisfactorily for the phenomena of 

 radiation in the region of slow vibrations. If our point of 

 view is sound, we should therefore expect to find in this 

 region some connexion between the present theory and the 

 ordinary ideas of electrodynamics. 



From (7) we see that u> n vanishes for large values of n y 

 and that at the same time the ratio w„/co„ +1 tends to unity. 

 On the present theory the frequency of the radiation emitted 

 by the transition from the (n+l)th to the nth stationary 



state is equal to -(A n+1 — A«). When n is large, tlrs 



lc/A 

 approaches to j -rr» On the ordinary electrodynamics we 



should expect the frequency of the radiation to be equal to 

 the frequency of revolution, and consequently it is to be 

 anticipated that for large values of n 



dA 



dn 



- =ha), 



(8) 



Introducing the values for A n and co n . given by (5) and (7), 

 we see that n disappears from this equation, and that the 

 condition of identity is 



27rVmM 

 A 3 (M-r-m) [ } 



From direct observations we have K = 3*290 . 10 15 . Intro- 

 ducing recent values for e, m, and h *, we get for the 

 expression on the right side of (9) 3'26 . 10 15 . The agree- 

 ment is inside the limit of experimental errors in the deter- 

 mination of e, m, and h ; and we may therefore conclude that 

 the connexion sought between the present considerations and 

 the ordinary electrodynamics actually exists. 



From (7) and (9) we get 



2irV-roM 47rVmM a n*/* a (M + »») 



W n 



nVi^M + m/ 



<9»i = 



n 8 A*(M + wO J 



2a n — 



'27T-( 



M 



(10) 



For n = l, corresponding to the normal state of the atom, 

 we set 2<2 = l'l . 10 -8 ; a value of the same order of mao- 

 nitude as the values for the diameters of atoms calculated on 



* Phil. Mag-, loc. cit. p. 487. 

 Phil. Mag. S. G. Vol. 27. No. 159. March 1914, 2 M 



