72 



/3 



\9^ 



«)°. f = const. (1*) 



Denoting tlie components parallel lo the .r, y and r-axis of the angular niomentuni of the 

 electron round the nucleus, considered as a vector, by Px, Py and Pr, we have next 



PI. + Pfi + P? = {1 — e'-)[2-ma-a,f, P^ = co n st. (2*) 



Since the angular momentum is perpendicular to the plane of the orbit, we have further 



$Px^r^Py-{-;P, = 0. (3*) 



Nov,- VC have for the mean values of the rates of variation of Px and Py with the time 



JJ Px 7-T U Pq J-. i- . .^ 



^ör=eF,, --^ = -eh,. (4*) 



From this we get. differentiating 1*) and '2*) with respect to the time, and remembering that a 

 and Ol remain constant during the perturbations, 



fg|+^g| = -K^(p.^f + Pu ^) = -eFK^{y,Px-SPy), (5*) 



where j, _ 3_ 



i-maw 



On the other hand we have, differentiating (3*) and introducing (4*), 



m_ Dr, 



Dt ' ^ Dt 



/'..^!-P.^Ï=0, 



which together with (5*) gives 



DS_„^^,^ Djo 



jj^ — .. .. .y. ^^ — eFK-Px, 

 from which we get, bj- means of (4*), 



the solution of which is 



4^= 2tcos2-(o;^a), 5j = S3cos2-(of + B), (7*) 



where 21, a, S and 6 are constants, and where, introducing 6*\ we have 



_eF,K _ 3eF 



8î:rmacu' 



(8*) 



During the perturbations the electrical centre will thus perform 

 slow harmonic vibrations perpendicular to the direction of the 

 electric force, with a frequency which is proportional to the intensity of the 

 electric field, but, for a given value of F, quite independent of the initial shape of 

 the orbit and its position relative to the direction of the field. For the value of 

 this frequency' in the multitude of states of the perturbed system, for which the' 

 mean value of the inner energj' is equal to the energy £„ in a stationary state of 

 the undisturbed system corresponding to a given value of n, we get from the above 

 calculation, introducing for a and w the values of a„ and con given by (41), 



