276 Mr. J. Parker on the Theory of Magnetism. 



We have, therefore, if no appreciable change takes place in 

 the form or size of B, 



SQ^e&^ldv, 



where the integral refers only to the soft body B, since no 

 change can take place in M. 



If the operation consist in moving B nearer to M, I will 



increase or SI be positive. Hence, if -^ be positive for all 



values of I, the operation will cause an absorption of heat, or 

 would cool the body B, if heat was not supplied from without: 



if -t| be always negative, there will be an evolution of heat, 



or the operation would heat the body B. 



III. We will, last of all, examine, with Duhem, the method 

 proposed by Jamin for the determination of the distribution 

 of magnetism on a permanent magnet. 



A small piece of soft iron, B, being placed in contact with 

 the permanent magnet at any point P, the smallest force 

 required to detach it is measured, and it is supposed by Jamin 



{dV\ 2 

 that this force is proportional toy -j-\ , where V is the poten- 

 tial of the permanent magnet at P and dn an element of the 

 outward drawn normal. 



We observe, in the first place, that the small piece of soft 

 iron B is magnetically equivalent to a layer on its surface. 

 Consequently, the magnetic force at any point is the resultant 

 of that due to the surface-layer of B and of that due to the 

 permanent magnet. Within the body B, the force due to the 

 surface-layer of B is the greater of the two. This will com- 

 plicate the problem, and so, for the sake of argument, we will 

 agree to ignore the surface-layer of B. With this assumption, 

 it follows that the equipotential surfaces and lines of force 

 will be due entirely to the permanent magnet, and that the 

 total magnetic force exerted on B by the permanent magnet 



acts along the line of force at P, and is equal to I -7- dv, 



where dv is the volume of B, and ds an element of the line of 

 force in the positive direction of F. If, for simplicity, we put 



dW 



ds 



I = £F, this result becomes \k -j- dv. Now if the line of 



d¥ 2 

 force at P be directed outwards, —7- will be negative, and if 



dF 2 



it be directed inwards, -v- will be positive. Thus in both 



