PART II. POLAR MAGNKTIC PHENOMENA AND TERRELLA EXPERIMENTS. CHAP. VI. 707 



hence 



r n\ ^^ 



id consequently 

 r, if preferred, 



3 4n 

 1 2 



Thus on the whole / "1 must satisfy the following inequalities: 



n V^ -f 1 < / 2 (and / 2 < -f |/2 -f- 1 , which is satisfied according to (b)) 



1 



2<0 / 2> 



1 2w 



Now if n satisfies (e), it is evident that /, in an infinite number of ways, can be so determined 

 i at these last inequalities are satisfied. Then, however, the relations (a), (b), (c) and (d) are also satisfied, 

 ; d we can consequently find positive values of ;, v a , (.1, i? and M 2 , which satisfy equations (i) and (2). 

 hder suitable conditions therefore, the particle can approach an arbitrary circle, of which the radius r 

 stislies the inequalities 



Let us, upon the assumption that gravitation dominates the effect of electric force (case III), see 

 1 \v the radii of the boundary-circles depend upon the relation between charge and mass, or, in other 

 \>rds, upon the quantity /. 



The necessary and sufficient condition for the approach of a particle to a boundary-circle, is the 

 snultaneous satisfaction of the following relations: 



If we confine ourselves to a consideration of those values of n that are i- 1 -f- y 2 , (a) is satisfied, 

 a i (b) is satisfied, provided (c) is. The three conditions (a), (b) and (c) may therefore be contracted 

 ii > the equation 



/ 2 = -f # 1/2*7+7 



uere 0- can be given all possible values between -- 1 and -}- 1. 

 If we substitute this expression for / 2 in (i), we obtain 





