59 



343 



already involved in the assumption that the different initial states, corresponding 

 lo one and the same stationary state of the simplified hydrogen atom, are of equal 

 occurrence in the luminous gas. Moreover the uncertainty involved in the estimate of 

 the intensities from the density of the image of the components on the photographic 

 plate is so large that, with intensities of the electric force of the order of magni- 

 tude used in Stark's experiments, a possible dependency of the relative intensities 

 of the components on the intensity of the force cannot be brought to light 

 ex})erimentally. It may in this connection be of interest to remark that for states 

 for which 1^ = the amplitudes of the vibrations of frequency Vj^tu^^ ~ t^o)^-]- t^oj-^ 

 occurring in the motion of the system will, also if the first and higher powers of 

 the electric force are taken into account, still be equal to zero if r.^ is ditîerent from 

 zero (compare § 3, page 25), while in general the amplitudes of the vibrations of 

 frequency Vj^Wy -\- t^m^, where Tj = r,, will be small quantities proportional to the 

 intensity of this force in states for which /j ^ /.,. 



Another point which we have disregarded in the calculations in § 3 is 

 the influence which the modifications in the laws of mechanics, claimed by the 

 theory of relativity, have on the motion of the electron. This influence will be 

 treated in detail in the paper mentioned in the beginning of § 4. Here it may only 

 be remarked that this influence will consist partly in a small effect on the frequen- 

 cies of the Stark effect components, partly in a small change in the relative inten- 

 sities of these components. Thus the components will, on account of the relativity 

 modifications, be displaced from the positions determined by (111) by small quantities 

 of the same order as "'/c- where v is the velocity of the electron and c the velocity 

 of light, in such a way that the symmetry of the Stark effect will be disturbed. 

 The intensity of the electric field applied in Stark's experiments is, however, so 

 large that such a dissymmetry cannot be detected. Further the effect of the relativity 

 modifications on the values of the amplitudes of the harmonic vibrations, in which 

 the motion of the electron can be resolved, will consist in the addition of small 

 terms of the same order as c-F. Especially, in a state of the atom for which 

 /, = 4, the amplitudes of the vibrations of frequencies r^w^-'r z.^w^, where = r.^, 

 will no more be equal to zero but equal to a small quantity of this order'). 

 Components corresponding to transitions of the type (^a a c ^ b b c) must therefore 

 be expected to appear with an intensity of the same order as ("■ c-f)^ This might 

 probably explain the appearance of the component corresponding to (112 — 002) in 

 Hß, mentioned in the above; this explanation is seen to claim that the intensity 

 of the component under consideration decreases for increasing intensity of the 

 electric field-). 



') The appearance of tliese vibrations of new frequencies in the states under consideration is 

 analogous to the appearance of vibrations with new frequencies and of amplitudes which are of the 

 same order as f^<^li>- in the problem treated in § 4. 



■ On Stahk s photographs of the Stark effect of Hß for a field of 28 500 Volt cM the relative 

 intensity of this component seems actually to be much stronger than on the photograph corresponding 

 to a field of 74 000 Volt cM. 



44- 



