Model of Ferromagnetic Induction. 



49' 



It follows that as H is increased, the limit of stable 

 deflexion is reached when 



=.o. 



dx ' c 3 sin (« — 6) 



We are concerned only with a very narrow range of stability, 

 and it will simplify the expression if we confine it to cases 

 in which sin (a — 6) may be treated as sensibly equal to sin a, 

 cases namely in which 6 is very small and a. is not small. 

 Under these conditions the criterion for rupture becomes 



a. — v 



since o 2 =x 2 -\-(a--r) 2 . in other 



which gives x = "re- 

 words the deflexion ceases to be stable when the angle OP'P 

 1 



becomes tan 1 — ^= or 35° 16'. 



The criterion is a geo- 

 metrical one : it is independent of the strength of the control, 



Fkr. 3. 



which depends on m' — m". A narrow range of stable 

 deflexion is retained by keeping the poles near together, 

 though the strength of the control may be made vanishing!}' 

 small. 



A model illustrating these points is conveniently made as 

 in fig. 3, using straight pieces of steel wire with ball ends 

 for the magnets. The central magnet is pivoted on a needle 

 and carries a vertical piece of brass tube to give it gravi- 

 tational stability. The fixed mngnets are held in supports 



Phil. Mag. S. 6. Vol. 43. No. 255. March 1922. 2 K 



