2()2 Mr. J. Parker on the Theory of Magnetism and 



fixed in the element. If, therefore, the element be homo- 

 geneous, and we suppose, for simplicity, that its state depends 

 only on the intensity of magnetization I and the absolute 

 temperature 0, the energy of the element may be written 

 F(I, 0)dr. Calling the value of F(I, 0) when 1 = 0, which 

 is clearly finite, we may put F(I, 0)dv in the form Odv + 

 \F(l,0\-C\dv, or Cdv+f(l, 0)dv, where f(I,6) = when 

 1 = 0. We have then 



U'-Y-W=JC^+j/(I, 0)dv, 

 or 



U'=Y + W+JCVto+J/(l, 0)dv. 



Now if U ' be the value of U' when the system (in its original 

 state) is deprived of its magnetization, but otherwise un- 

 changed, we shall have, since both Y and f/(I, 0)dv vanish 

 when 1 = and W does not alter, 



Uo'=W+JC^. 

 Hence 



U'=U„'+Y+j/(I, 8)dv. 



If, therefore, we assume that U 7 — IV is the same as if the 

 system was not broken up, or equal to U — U , we obtain 



U=U + Y+j/(I, 6)dv (1) 



Similarly we may obtain 



<f>'=§Ddv+$li(l, 0)dv, 



k>'=$Ddv, 



and therefore 



f =<fo'+j7 t (I, 0)dv, 



from which we may infer 



<f>=cj> o +§h(I,0)dv (2) 



The very simple expressions (1) and (2) are due, I believe, 

 to Duhem, by whom they were given in 1888. Before 

 making use of them, I will show how the energy of a 

 magnetized system is discussed in the ordinary text-books. 



The principle of the conservation of magnetism being taken 

 for granted, it is first assumed that magnetization may be 

 separated from material bodies ; in other words, that the pro- 

 perty of matter of exerting actions at a distance may exist 



