ACTION OF TWO RECTANGULAR CIRCUITS. 475 



and keep the apparatus in equilibrium in a position perpendicular to 

 the magnetic meridian. In the apparatus used for this experiment, 

 we take a movable current symmetrical in reference to the axis of 

 rotation. The projection S' is then null, and the couple of rotation, 

 which would impart to the system a uniformly accelerated rotation if 

 there were no friction, ultimately makes it rotate uniformly. 



492. ACTION OF Two RECTANGULAR CIRCUITS. We may cal- 

 culate the action of two rectangular frames AC and A'C', the sides 

 of which are parallel. Suppose, for the sake of simplicity, that 

 the frames are equal (Fig. 119), and their corresponding summits 



Fig. 119. 



A and A' on a perpendicular to their plane. The mutual energy 

 of the two circuits, with currents equal to unity, is expressed on 

 Neumann's formula (352) by 



W= 1 I -dsds'. 



flf 



The value of cos e is equal to unity for two parallel sides, and null 

 for two perpendicular sides such as AB and B'C'. The energy thus 

 becomes 



This expression only contains terms relating to parallel wires. 

 Consider, in the first place, the two sides AB and A'B', of length 

 a, and at the distance //. Let ds and ds' be two elements, placed 

 respectively at M and M' and r their distance ; lastly, suppose that 

 we measure the lengths s and s f from the points A and A'. From 

 the ratio 



