112 PROPERTIES OF CIRCULAR CURRENTS. 



in which A, B, C, are functions of x, we shall have 

 X2iry<fy = iry* A + B^-+C- + ..... . 



If S is the surface Try 2 of the circle, and Fm the mean action 

 of the field on the circle, it follows that 



(51) 



The expression for the mean force is thus the same as that 

 for the component X, with this single difference, that we should 

 divide y 2 by 2, /* by 3, jv 2n by n + i. If we apply this observation 

 to the expressions calculated above, we see that the mean action of 

 a circular current, from equation (33), is 



3-4 



] 



In like manner, we shall obtain the mean action of a coil by 

 equations (34), (39), (41), (43), etc., for various particular cases. 



We shall especially consider equation (39); it gives for the mean 

 action of a coil on a circle at a small distance from the mean 

 plane 



,,, + 3df!-^ 



2.2*a*[_ 2.3^2 2.3 



3*5 /T | 5-6^ 5-7^ 2 + 3* 2 1 

 3 (2. 4 ) 2 ^L I 2. 3 2 2.3 2 J 



3 2 5 2 7 /f ,7-8^ 7.9^3f_ 2 l 



/ TVo ~~ o f) 



4(2. 4 .6) 2 a 6 L 2. 3 fl 2 2.3 a* 



+ , 



