2 88 



MEASUREMENT OF CURRENTS. 



we may simply write 



C m = I sin (0 - a) - A sin 2/3 \ HM . 



- 





To account for the effect produced, we may construct the two 

 curves B and B' (Fig. 172) of equations 



v = sin/3, 

 y =A sin 2/3, 



and superpose them with a difference of phase equal to a. The 



Fig. 172. 



Fig. 173- 

 abscissae of the intersections correspond to the positions of rest of 



the needle. 



Suppose first that a = 0, that is to say, 

 the needle in the plane of symmetry. This 

 There are five positions of equilibrium, O, 

 the needle may occupy three, O, P, and 

 corresponds to zero, is unstable ; the two 

 correspond to deflections near 90. When 

 have the arrangement of Fig. 173, or that 



the initial position of 

 is the case of Fig. 172. 

 P, P', Q, and Q' ; and 



P'. The first, which 

 others are stable, and 

 the factor A is < I, we 

 of Fig. 174, according 



