TO THE THEORY OF MAGNETISM. 95 



If the magnetic particles composing the body were not 

 perfect conductors, but indued with a coercive force, it is clear 

 there might always be equilibrium, provided 'the magnetic state 

 of the element dv was such as would be induced by the forces 

 ~ ~ 



d dV ., d dV ,,, , ~d^' dV n , . , c 

 -j-r + -r-r + A ', -f-r + -7-7 4- B and -^ + -j-r + C , instead of 

 ax ax ay dy dz dz 



~d^' dV d& dV , d& dV 



--TT + -J-T i ~-T7 + -j~r and -~ + -yr ; supposing the resultant 



dx dx dy dy dz dz ' 



of the forces A', B 1 , C' no where exceeds a quantity /3, serving 

 to measure the coercive force. This is expressed by the con- 

 dition 



the equation (c) would then be replaced by 



A, B, C being any functions of x, y, z, as A ', B', C' are of 

 x, y ', a' subject only to the condition just given. 



It would be extremely easy so to modify the preceding 

 theory, as to adapt it to a body whose magnetic particles are 

 regularly arranged,by using the equation (a) in the place of the 

 equation (5) of the preceding article ; but, as observation has not 

 yet offered any thing which would indicate a regular arrangement 

 of magnetic particles, in any body hitherto examined, it seems 

 superfluous to introduce this degree of generality, more par- 

 ticularly as the omission may be so easily supplied. 



(16.) As an application of the general theory contained in 

 the preceding article, suppose the body A to be a hollow spherical 

 shell of uniform thickness, the radius of whose inner surface is a, 

 and that of its outer one a/, and let the forces inducing a mag- 

 netic state in A, arise from any bodies whatever, situate at will, 

 within or without the shell. Then since in the interior of A's 

 mass = 80, and = 8 F, we shall have (Mec. CeL Liv. 3) 



d> = 2<& ( V + 2<fr. c V- i - 1 and F = 



