1'AKT II. 1'OI-AK MAGNETIC PI IENOMKN A AND TERRELLA EXPERIMENTS. CHAP. VI. 689 



, being a positive root in the equation 



Mich is obtained from (IV) by putting v = 1 , and ' = 

 If (V) is to be possible for real , then of necessity 



Let us now look at the function 



We obtain 



& 



dr~ 



If we put u = - -f- v- -J ., , then it = for r = t\, according to (VI). But further 



dn _ _ , dv _,_ AM dv '_ 'ivlM _ ft fl ^ _j_ IM (p fl ^\ _ 2vt.M 



dr r- a 



imembering that 



Consequently ^> for r<O',, and then also ~ ^> for r<^r^, and consequently 



for r = r, > s for r = /- , 



Mich is at variance with (VII). 



It is thus quite generally proved that the partible cannot from within approach a boundary-circle 

 I a positive orbit-direction. 



It might now be imagined that the ejected particle first changed from out-going to in-going motion, 

 ; d approached a boundary-circle from without. 



We can here distinguish between two cases. 



Case i. The direction of the path of the particle is positive at the moment the change to in-going 

 ntion takes place. 



dy 



In this case v must remain positive along the entire in-going path. From the expression for -~ 



i has been seen that y cannot become 0, unless . '0. If y became negative somewhere along the 



i-going path, it must then, owing to the continuity, as its value at the change is 1, also become for 

 ne or more values of r, and among these there must be a greatest value r 1 . Then of necessity, how- 



< er, for r = > A , 



'J > and i- = , 

 dr 



Mich is impossible. 



