the Absurdity of Diamaynetic Polarity. 263 



apart from matter. It is next assumed that there is an in- 

 finite store of positive and negative magnetism at infinity at 

 which we can be supplied gratis with as much as we require. 

 Lastly, it is assumed that the attraction or repulsion between 

 any two small quantities of magnetism m, m', dissevered from 

 matter, is exactly the same as the attraction or repulsion 

 between two small portions of matter at the same distance, 

 magnetized with the same quantities of magnetism m, m! . Then , 

 in order to find the energy U of any magnetized system, we sup- 

 pose its magnetism made up of an infinite number of elements 

 which were originally at an infinite distance from the given 

 material system and from one another, and unassociated with 

 matter. If, therefore, we denote by U the energy that the 

 given system would have if it were deprived of its magneti- 

 zation, but otherwise unchanged, and imagine some agent 

 capable of bringing the magnetic elements from infinity up 

 to the given system, and there placing them in the positions 

 they are to occupy, without exerting more force than is just 

 necessary to overcome the attractions and repulsions between 

 them, we are supposed to get 



U=[J + Y. 



The ordinary text-books make no attempt to find the en- 

 tropy of a magnetized system. In fact, until the appenrance 

 of Duhem's book in 1888, the rigid methods of thermodynamics 

 do not seem to have been thought necessary. 



In order to find the condition of magnetic stability on a 

 homogeneous body of uniform temperature 0, we suppose the 

 body incapable of receiving or losing heat except at the con- 

 stant temperature 0. Then we imagine the magnetization of 

 a single volume element dv to change slightly in direction, 

 and to increase from I to I + 81 ; and we suppose that when 

 the temperature has again become equal to 0, no other change 

 has been made in the system. 



If SQ be the heat absorbed in the process, the principles of 

 thermodynamics require that 



8Q<0ty, 



or, since no work has been done on the system during the 

 operation, 



SU<<9% 

 Hence 



SY+ ( ( §-Ci) dvBL<o > 



or 



8Y + yfr(I,0)dv$I<O,(?ay). ... (3) 



