156 COEFFICIENTS OF INDUCTION. 



reciprocal action of the two circuits reckoned positive when it is 

 repulsive, and we have 



In the same way, if one of the circuits turns about an axis 

 through the angle dO, the moment of the reciprocal actions of the 

 two circuits in reference to this axis is expressed by 



786. CIRCUITS WITH THE SAME Axis. When the circuits A 

 and A' are coils of revolution about the same axis, which we shall 

 take as the x axis, the reciprocal action is parallel to the axis from 

 symmetry. This action being null for a suitable position of the two 

 circuits (the concentric position, for instance, for two cylindrical 

 coils), and also null at a very great distance, it passes through a 

 maximum value which corresponds to the condition 



787. ACTION OF Two CIRCULAR CURRENTS. For two circular 

 currents of radii a and a' at the distance x, the value of M may 



in general be expressed by means of elliptic functions (763). 



d dE 



Taking into account the values of - - and (764), we find 



ak UK 



(6o) 



The use of series is often more convenient. The coefficient 

 of induction of the circuit A (circular current or coil) on a circular 

 current of surface S' being equal (761) to mS', the reciprocal 

 action is 



dx 



