SYSTEM OF THREE SYMMETRICAL COILS. l6l 



an expression in which we shall replace y 2 by the square of the 

 mean radius a') 2 , or simply by a' 2 . 



If / is the total length of the wire of the coils A and B, and 

 /' that of the coil A', the action of the two coils A and B on the 

 lower end of the coil A' is 



, 

 ah \ 3 a 



In order to calculate the mean action F^ of the coils A and B 

 on the upper end of the coil A', we shall suppose these two coils 

 situate in their mean plane, and make use of the expression (41) 

 of (741), which gives 



27Z7T . 



neglecting very small terms, 



* 



The total action is then 



792. SYSTEM OF THREE SYMMETRICAL COILS. Let us again 

 consider as above two equal coils A and B, the mean planes of 

 which are at the distance 2.x ; and suppose that the currents circu- 

 late in opposite directions in the two coils, and that a third coil with 

 the same axis is symmetrically placed between them. In this case 

 the actions of the coils A and B are in the same direction. 



Let denote the action of one of them on A' at the total 

 distance x, f the total action, when the intermediate coil is dis- 

 placed through 8x, in the plane of symmetry, is 



VOL. II. M 



