﻿based on Free Electrons. 



1095 



or 



I 2 p 2 0>'\p2+P4) 



9e 2 

 16 



(P2 + Pih 



>»2P 2 M 2 (P>2-Pi) = ~ Jg (P2—P±)i 



n hl >W(0 2 -0 4 )=^(0 2 -0 4 ). 



(30) 



Terms linear in p having been omitted on the inertia side, 

 the above gives main terms in the value of p 2 . The first of 

 the real periods, numerical value p=71'2 s/ — 1, will be 

 found to agree with the result of § 25 for purely radinl 

 oscillation. 



For 2 and 0± the values are exponential, and as the 

 exponent may have either sign, there is a clear case of 

 instability in respect to oscillations of tangential character 

 in special connexion with the motion of electrons. 



For oscillations in a direction z perpendicular to the plane 

 of the orbit, we have 



tt / 9_ (~1 ~3)" (~2~ Z 4J 



16a 2 3 2(a 1 2 + <)^ 

 [(*-Jr0 , + («i-O , +(*i-**) , + C*-**) , !l. 



) (31) 



48\/3 16 



+ tV [ (~i - H) 2 + (*i - ~4) 2 + (*« ~Hf + (zs-ztf] . 



The order of equations being only half that for motion in 

 the plane, we may dispense with the special method ; the 

 types are then given by 



., _ €»&-;,) ,\2z l -z 2 -z i ) 1 



mi ~ l ~^Wl ~8 'I 



,„ - e 2 (**sd e*( 2* 2 - gl - % ) f 

 "*= 8 8 J 



Subtracting forms for Zj and z 3 , 



(32) 



mip 2 (o 2 • 



