

PART II. I'OI.AR MAG.NKTIC PHENOMENA AND TERRELLA EXPERIMENTS. CHAP VI. 69! 



The above-found expression for y now holds good, of course, whatever value r a and er may have; 

 other words, we can quite imagine an arbitrary point in the path as the point of commencement. We 

 uy then write r, instead of r n , and or, instead of a , and obtain 



f t.M 



sin o, - ^1 ** 



J *"i 



If the particle then approaches, by the positive way, a boundary-circle with radius r,, then of 

 i cessity 



/ F*iM 



g- *rj (*(-,) sin , '- ,M 



V J r, If* 



> being a positive root in the equation 



='' + ^ + ^1 = . 

 r 



If we put 



v obtain 



z for r = r., <^ s for r =;-, , 



n matter how little greater r, is than ;., ; but then 



(VIII) f>0 



dr 



(< values of r= ;-., + , where i is a positive quantity that can be chosen as small as desired. 

 We found further that 



du n 



As f(r) along the in-going path is negative, we cannot here, as before, conclude that the value of 

 must be negative. But if the function f(r] is assumed to be such that 



, - <T for r = i\ , 



dr 



tl a, as n for r== t\ , 



it <^ for r = r, -|- e , 



\v -re i has the same signification as before. Then too, however, 



-T- < for r = r a -f , 

 c/r 



ai this is at variance with (VIII). 



Hence it follows that the negatively-charged particle cannot approach a boundary-circle from without 



ar the positive way, unless 



dn 



for r = r, . 



dr 

 On the other hand we can prove that if, for r = r 2 , 



,t = and dl . ' > . 



f/A' 



th particle can, from without and the positive way, approach a boundary-circle with r t as radius. 



