496 



Sir J. A. Ewino- on a Ne 



To examine the conditions which determine the range of 

 stable deflexion, let m be the pole-strength at each end 

 of W, and m and m" be the pole- strengths of A and B 

 respectively. Assume the clearance to be the same at both 

 ends of W. Write r for OP (fig. 2) the half length of W, 

 a for OP', x for PQ and c for PP'. 



Let the field H act with a constant inclination a to the 

 line of centres, deflecting W stably through an angle 0. In 

 what follows the angle 6 is assumed to be very small. 



Fig-. 2. 



Then for the pole P the deflecting moment due to the 

 notion of H is ?7iH0M = ?nH? 1 sin(a — 0), and the restoring; 

 moment due to P' is 



mm' -,„_?W ax 



Hence, taking both poles of W into account, but neglecting 



effects of other than the nearest fixed poles, the equation of 



equilibrium is 



tj . , m m{m —m")ax 

 Ziutir sin (a — H)= — v 



2fL 



c 

 x 



or 



a(rn' — m") c z sin (a — 6) 



