36 



quencies w^ and coo- If the sj'stem is undisturbed all coefficients Ctj, tj will be zero, 

 except Cj.D and Cp.^. When, however, the system is perturbed, for instance by an 

 arbitral'}' small central force, there will in the Fourier expressions for the dis- 

 placements of the particle, in addition to the main terms corresponding to the 

 fundamental frequencies co^ and w.-,, appear a number of small terms corresponding 

 to frequencies given by r^w-^^^ r^m^ where r^ and r2 are entire numbers which may 

 be positive as well as negative. On the present theory we shall therefore expect 

 that in the presence of the perturbing force there will appear small probabilities 

 for new transitions which will give rise to radiations analogous to the socalled 

 harmonics and combination tones in acoustics, just as it should be expected on the 

 ordinary theorj' of radiation where a direct connection between the emitted radia- 

 tion and the motion of the system is assumed. Another example of more direct 

 phj-sical application is afforded by the effect of an external homogeneous electric 

 field in producing new spectral lines. In this case the potential of the perturbing 

 force is a linear function of the coordinates of the particles and, whatever is the 

 nature of the original system, it follows directh' from the general theory of per- 

 turbations that the frequencj' of any additional term in the expression for the perturbed 

 motion, which is of the same order of magnitude as the external force, must corres- 

 pond to the .sum or difference of two frequencies of the harmonic vibrations into 

 which the original motion can be resolved. With applications of these considerations 

 we will meet in Part II in connection with the discussion of Sommerfeld's theorj' 

 of the fine structure of the hydrogen lines and in Part III in connection with the 

 problem of the appearance of new series in the spectra of other elements under the 

 influence of intense external electric fields. 



As mentioned we cannot without a more detailed theory of the mechanism of trans- 

 ition between stationary states obtain quantitative information as regards the general 

 question of the intensities of the different lines of the spectrum of a conditionally 

 periodic system given by (26), except in the limit where the n's are large numbers, 

 or in such special cases where for all values of the constants «j, ... as certain 

 coefficients Ct-^,...t^ in (31; are equal to zero. From considerations of analogy, how- 

 ever, we must expect that it will be possible also in the general case to obtain an 

 estimate of the intensities of the different lines in the spectrum by comparing 

 the intensity of a given line, corresponding to a transition between two stationary 

 states characterised by the numbers n\, • ■ ■ n^ and n", ■ ■ ■ n"^ respectively, with the 

 intensities of the radiations of frequencies w^ {n\ — n") + • - - +f" ("' — "') to be ex- 

 pected on ordinary electrodynamics from the motions in these states: although of 

 course this estimate becomes more uncertain the smaller the A'alues for the n's are. 

 As it will be seen from the applications mentioned in the following Parts this is 

 supported in a general way bj- comparison with the observations. 



Færdig fra Trykkeriet d. 27. April 191S. 



