COUPLE OF ROTATION OF TWO CIRCULAR CURRENTS. 163 



When the circumferences are replaced by coils with rectangular 

 channels of small dimensions, these different conditions relative to 

 the mean radii give still a force which is sensibly constant. 



793. COUPLE OF ROTATION OF Two CIRCULAR CURRENTS. 

 If the axes of two circular currents cut each other at an angle 

 (Fig. 146), the moment of the couple due to the mutual actions, 

 which tend to vary the angle 6 that is to say, to make one of the 

 currents turn about a right line passing through the point C and the 

 perpendicular to the plane of the axes is 



6 = -^ = - 4 7rV sin 2 a sin 2 a' sin - Xi(a')Xi(a)Xi(0) + . . . 

 (7o) / 



If the origin C is at the centre O' of the circle of radius a', we 

 have //.' = a', /*' = cos a' = ; we get then 



F* ()*<*) + 



(7i) 



When the planes of the circles are almost rectangular, we may 

 put 6 8, the angle 5 being very small, and we have 



(72) 0= 



The value of P is 



n+i u 2.4... 2* 



and the first terms of Q 



M 2 



