( 9) 



Whence 



Replacing h by a -}- .>> we may write approximately 



or 



1 



n = a + y(«± l/»M--^') (14) 



According' to (13) to these fVeqiieiicies correspond two values of 

 the complex amplitude q 



.s ± l/r^T'^ 



Q=^ (1^) 



r 



9. We shall again consider three special cases. 

 Case I. Electric tield zero, hence s = 0. 



Using (14) and (15) we find for the motion in the plane of XT 

 n ^ a ± ^ r , q = ± /, 

 equations discussed in § 6 above. 



Case 11. Magnetic field absent, r=0. 



Now, by (14) and (15), if the upper signs are taken 



71 = a -]- 5 = A , q — cc^ 

 representing rectilinear vibrations parallel to O V. 

 If the lower signs are used 



n =■ a , Y — ^1 

 meaning rectilinear vibrations parallel to OX. 



10. Case 111. Electric field vertical and magnetic field horizontal. 

 This case is slightly less simple. 



Let us write a = i (l^r'^ -j- 5" — ■ s) and let r be positive. 

 Taking the upper sign in (14) and (15), then 



n = a 4- i(« + ^?~+^= 6 -j- è i^r' -j- s^— s) = 6 J- a. 

 6 being a positive quantity. The coeflicient of / in 



q=i 



r 



is positive and > 1. This represents an elliptic vibration in the plane 

 of A^ }', the axes being parallel to OX and OY, the major axis 

 parallel to OY. The motion of the electron is right-handed. 



