the Absurdity of Diamagnetic Polarity. 261 



tively parallel to the axes and equal to A, B, 0, be placed 

 successively in the same position as the given body, the sum 

 of their actions will be equal to that of the given body. 

 Hence, since the body whose magnetization is parallel to 0«# 



dA 

 is equivalent to a volume distribution — - and a surface- 

 layer whose density at a point P where the outward drawn 

 normal makes angles (\, /jl, v) with the axes, is A cos X, we 

 obtain 



_/dA dB dC\ 

 p ~ \da: + dy + dz /' 

 and 



<r = A cos \ + B cos fj, + C cos v, 



or, if the direction of magnetization make angles (« ; /3, 7) 

 with the axes, 



cr = I(cos a cos k+ cos j3 COS LL+ cos 7 cos v) 



= I cos 0, 

 as before. 



We may now find the energy U and the entropy cf> of any 

 magnetized system at rest, with its magnetization in equili- 

 brium, stable or unstable. For this purpose we shall first 

 obtain the energy U / and the entropy (// of a magnetized 

 system identical with the given system except that it is broken 

 up into an infinite number of small pieces. 



Without altering the internal conditions or the magnetic 

 distribution of any part of the system (U 7 , </>'), let all its 

 elementary portions be removed to infinite distances from 

 one another, and left without velocity. Suppose that in thus 

 preventing the forces acting between the various elements 

 from producing velocities, the work obtained from the system 

 is Y + W, where the part Y is due to the magnetization of 

 the system and W to gravitation. Then, since the operation 

 is clearly reversible and unattended by any thermal pheno- 

 menon, the energy will now be U'— Y — W, and the entropy 

 (f>'. Also, since the values of the energy before and after the 

 operation (U', U' — Y — W") depend only on the two states, it 

 is clear that Y + W, and therefore Y alone, is independent of 

 the manner in which the change of state is effected. 



Let us now consider one of the elements after it has been 

 removed to an infinite distance from all the other elements. 

 Its energy will be proportional to its volume dv, if that 

 volume is small enough ; and, if the substance be homo- 

 geneous (that is non-crystalline), will be independent of the 

 angle the direction of magnetization makes with any line 



