88 



the same direction as that of the magnetic force which ■would arise from the motion 

 of the electron according to ordinary electrodynamics. 



From the considerations in § 2 it follows now in the first place that, with 

 neglect of small quantities proportional to the square of the external forces, f^fE-j- ^m 

 wUl remain constant during the perturbations within a time interval, sufficiently 

 long for the perturbing forces to produce a considerable change in the shape and 

 position of the orbit of the electron; i. e. in a time interval of the same order as 

 oix, if /, just as in s 2, denotes a small quantity of the same order as the ratio 

 between the external forces acting on the electron and the attraction from the nucleus. 

 From a consideration analogous to that given in S 2, we may further conclude that, 

 in the stationary states of the perturbed system, the quantity '/'=?fe-j" fn may 

 be taken equal to the additional energy of the system due to the presence of the 

 external fields. In fact, let us imagine that these fields are slowly established at a 

 uniform rate within a time interval from ; ^ to f ^ '_>. where <> is a quantity 

 of the same order as <' >.. For the total alteration in the inner energ}' of the system 

 during this process we get then, with neglect of small quantities proportional to /.-, 



J*«i 





where the first term represents the work done on the system by the slowly in- 

 creasing external electric forces, while the second term represents the work per- 

 formed by the induced electric forces which accompany the variation in the in- 

 tensité' of the magnetic field. By partial integration of the first term, we get from 

 this equation, with the approximation under consideration, 



('»* ,'•■' r-^ 



(85) 



Now the expression on the left side of this equation is equal to the change in the 

 total energy." of the system due to the establishment of the external field. Since the 

 expression on the right side is seen to be a small quantity of the same order as 

 /«i, it foUow's therefore from (85» in the first place that the secular variations of 

 a,, Oj, ß,. ,^3 during the increase of the fields -will, just as in the case considered 

 in .§ 2 (see page 47), be given by a set of equations of the same form as (46), where 



W is replaced by -9] and where again a- may be considered as a constant. Also in 



the present case it follows therefore that '/' will remain constant during the establish- 

 ment of the external fields, and we see consequently that the expression on the 

 right side of (85j will be simply equal to '/'; a result which, with reference to the 

 principle of the mechanical transformability of the stationarj" states, leads to the 



