474 PARTICULAR CASES. 



491. For instance, let the system be formed of a current OP of 

 length a (Fig. 118) movable about a vertical axis, one of whose ends 



is on the axis of rotation and the other dips in a mercury cup. 

 The current enters the mercury at A, traverses the two parts ABP 

 and ACP in opposite directions, and regains the axis by the movable 

 part PO. Let I be the total strength of the current, x the strength 

 in the arc B, y in the arc C ; the current will evidently be equal to 



1 in the movable portion PO, 



Fig. i i 8. 



The surface comprised by the horizontal projection S consists 

 of two parts, one ABPO presenting its negative face to the com- 

 ponent Z of the terrestrial action; the other, ACPO, its positive face. 

 The former tends to increase, the second to diminish, and for an 

 angular displacement of the radius PO, the total work is 



-a*(x + y)ZO = - 



2 2 



This work is independent of the position of the conductor OP; 

 the force then is constant. The work corresponding to an entire 

 turn will be 



If the current has a vertical projection S', the motion of rotation will 

 be modified by the directive action corresponding to this projection. 

 It is easy to see that according to the ratio of the two surfaces S and 

 S', the initial velocity, and the value of friction, the moment of the 

 directive action might preponderate over the moment of rotation, 



