919 



The total energy per voliime-uiiitj is thus for the system 



He COS <r A — sin* (t . . . . . . (4) 



The second derivative with respect to </> of this expression is for 



Lh ^^^ 



d* ' ^ d* da' 



The energy is a minimum and the equilibrium stable as long as 



it is positive. 



For the limiting case we have 



d*V 

 H,=-2p — , 



Ox' 



And consequently the coercitive force becomes 



p d'V d'S 



"'=sJ--^"'ö^ = '>'^'- ■ ■ • • • <^> 



the last according to (3j, where abc = 2d*. 



When this formula yields a negative value a positive field stronger 

 than — He is necessary to make the position ff = stable. 



For a weaker field we find the equilibrium-positive from the first 

 derivative of (3) 



d'F . 



H sin (f -\- 2p ^ — sin <p cos rp z=z 

 ox* 



or 



d'F 

 • co8(f = —H/2p — 



p cos (f 1 



The magnetisation is here I = — -— = — H = /?. The 



dai* 

 magnetic field within the sphere is U — j[ I = Ü {1 — ^ ^) and the 

 inductive U -\- I = U {l-\-fi). The constant permeability of the matter 

 is consequently 



d*Hc 



r 1 J 



1 -i/9 d'Hc 



P 



For the divisions into two groups, which we have discussed sub 3 



we can always calculate — — according to the series found in 2 and 

 the relation (2), where in some cases we must turn the j; and ^ axis 



