38 



As explained in Part I, there will in general be no simple connection between 

 the motion of a system in the stationary states and the spectrum emitted during 

 transitions between these stales; such a connection, however, must be expected to 

 exist in the limit where the motions in successive stationary states differ compara- 

 tively little from each other. In the present case this connection claims in the first 

 place that the frequency of revolution tends to zero for increasing n. According to 

 (36) and (37) we may therefore pul the value of W in the n"' stationary state equal to 



lih 



W„ = ^. (38) 



Moreover, since (35) can be written in the form 



.-("■-") '''aï- 



it is seen to be a necessary condition that the frequency of revolution for large 

 values of n is asymptotically given by • 



W„ CNJ jT , (39) 



if we wish that the frequency of the radiation emitted during a transition between 

 two stationary states, for which the numbers n' and n" are large compared with 

 their difference n' — n", shall tend to coincide with one of the frequencies of the 

 spectrum which on ordinary electrodynamics would be emitted from the system in 

 these states. But from (37) and (38) it will be seen that (39) claims the fulfilment 



ot the relation 



_ 2-'N'emm _ 2n'N'e^m 



hHM^m) ~ h^l^m/M)- ^ -' 



As shown in previous papei-s, this relation is actually found to be fulfilled 

 within the limit of experimental errors if we put N = 1 and for e, m, and li in- 

 troduce the values deduced from measurements on other phenomena; a result 

 which may be considered as affording a strong support, for the validity of the 

 general principles discussed in Part I, as well as for the reality of the atomic model 

 under consideration. Further it was found that, if in formula (35) for the hydrogen 

 spectrum the constant K is replaced by a constant which is four times larger, this 

 formula represents to a high degree of approximation the frequencies of the lines of a 

 spectrum emitted by helium, when this gas is subject to a condensed discharge. This 

 was to be expected on Rutherford's theory, according to which a neutral helium 

 atom contains two electrons and a nucleus of a charge twice that of the nucleus 

 of the hydrogen atom. A helium atom from which one electron is removed will 

 thus form a dynamical system perfectly similar to a neutral hydrogen atom, and 

 may therefore be expected to emit a spectrum represented by (35) if in (40) we put 

 N = 2. Moreover a closer comparison of the helium spectrum under consideration 



