Mohotrovic Potential. 445 



1 f 



If we apply these to the evaluation of S 7 = .777 (/t^> x F 



where i =co. : z — a-'/. . . we have to deal with "* •/ 



or j 



The result when principal axes are used is 



S / =^[2© 3 2 (L a 4 + Mo^)--22a> lG , 2 N W 2 ]. (117) 



In this form it is not obvious, but it will appear later that 

 S is essentially positive. For a sphere without special choice 

 of axes, if 



8 V 2 1 ' X 1— « 2 i 1 + K 



tc- = 2.jj- and f = —loo- , 



then 2 ,7/ „ „ r j T - 



so that •:_ .4 r 1 ,7/ -1 



If the axis of translation is also that of rotation, viz. that of z, 



b_ 35V 2 Lr 2 i,- 3 l0g l-J' 

 and then 



D rfS' 1 dS' p 2 To/6> 3 a\ 2 a 2 r3-r 2 1+r 3 1 

 R= dw~Y <(r = ^D \y) V L 2? log l-,"^J' 



which may be compared with the value of B, for the 

 translation of charge, viz. 



p! T ^!rl±^' 2 ioo- 1 ±''_ 1 i 



:>V L W ° g l-r rj" 



The ratio is -,_■( .\\ when r is small, and approaches 

 _ ( . . 1 as r approaches 1. 



The notation 8' is used on the ground that magnetic force 

 not induction is the quantity determined, i. e. a magnitude 

 with the dynamical character of a velocity; and accordingly 



we write R=-, cf. §§12 and L9. In this connexion the 



absence of a factor L — 2p* in the numerator of the vecto- 



