158 COEFFICIENTS OF INDUCTION. 



and lastly, by equation (40) of (741), which holds for a great distance, 



__*!!{, _I*.H ft_ 



X* { 2X i 2.4** 



} 



The action is at first proportional to the distance x of the two 

 circles ; it then becomes inversely as the fourth power, which might 

 be seen d priori from the resemblance of currents and magnetic 

 shells. 



If the circuit A is a coil of rectangular channels of dimension 

 2^, 2<r, and mean section a, the mean action on the circle A', and 

 the reciprocal action on the two systems, can in like manner be 

 deduced from expressions (39), (41), and (43) of the last chapter; 

 but in some cases it might be useful to push further the expansion in 

 respect of increasing powers of x. 



788. These expressions are no longer sufficiently convergent in 

 the case of two very near circular currents and of the same order of 

 magnitude ; we may use then Maxwell's formula. With the values 

 (54) we get from it 



(65) 



When the circles are equal 



