ring 

 on rin 



Atoms and Molecules. 903 



becomes 



I: = ^T" 2 {-'- 2 +^«i 2 +^)''- 4 -[^ 5 ( a ' 2 +^ 2 ) 2+ T aiV ]'' 



+ [ff («, 2 + « 2 2 ) 3 + ^ („,» + 0,1)0, V]»- 8 



-[S (ai2+a22)4+ S 5 ( ai2+a ^ Va22+ ^ 5aiV ]'" 10 '- 



.... (18) 



By making the radii both equal to a and the charges both 

 equal to E 2 we have the force between two rings of the same 

 radius and charge : 



^ E 2 2 r „ , „ 2 4 45 4 6 175 , 8 11025 8 _ 10 1 



on ring. ^ ^ /-j^\ 



To check this result, the force (14) may be directly 

 derived from the expression for the force between two 

 elements of the two rings, namely 



k [r 2 + 2a\l-cosy)]^' ' ' ^ 0) 



By expanding the denominator in series and integrating 

 each term separately for the phase angle y between the 

 limits and 2-77, it has been shown that equation (14) 

 results. The general equation used above, however, will be 

 of much use in other cases. 



By making a ± = and a 2 = a we obtain from (13) the 

 force of a ring of charge, E 2 , upon a point of charge E 1? 

 namely 



v EiE 2 f -2 , 3 . _ 4 15 4 6 , 35 t 8 315 . 10 1 n( . 



ring K L 2 O 10 12o J 



on point. 



To find from these the whole electrostatic force of one 

 non-spherical electron upon the other, as in fig. 5, add 

 to (14) twice (16) and include the force of Ej in one electron 

 on E x in the other as point charges, giving 



F r = \\ -eV-s + SE^ + EOaV-* 



electron "» t 



on electron. - ^ „ ^ 



- ^E 2 (3E 2 + E0« 4 )- 6 + y E 2 (10E 2 + E,)oV- 8 

 - 3 ^E 2 (35E 3 +E,)a^-w... }. . . . (17) 



