452 



Prof. A. Gray on the Dynamical 



Hence for the energy spent otherwise than in increasing 

 the electrokinetic energy in the medium, we have 



+ 00 



yd^-dT=^-Y\ \\{KdB-i{KdB + BdH.)}dxdi/dz. . (22) 



— 00 



If the magnetization be carried through a closed cycle, so 

 that the medium is brought back to the same state as at first, 

 the electrokinetic energy returns to the same value, and the 

 integral of the quantity within the inner brackets, which is 

 d(BH), is zero. Thus the energy furnished to the medium in 

 the closed cycle is 



-& r ${{ RdB } dxd y d2 > 



the inner integral being taken with respect to B round the 

 cycle. 



If we take the changes per unit of volume at a place where 

 the induction is B and the magnetic force H, we have for the 

 energy given to the medium the value HdB/^ir, and for the 

 increase of electrokinetic energy d(BH)/87r. Therefore, for 

 the energy spent otherwise than in increasing the electro- 

 kinetic energy, we get the expression 



i- B.dB - ~ (KdB + BdR) . 



Hence if P, Q (fig. 1) be two points on a curve of mag- 

 netization of which the ordinates are values of B, and the 



Fig. 1. 





Y 











s 





H 2 





(« 







Hi 



V 



















Bij 



B 2 





M 



IsT 



abscissae values of H, we have for the whole energy spent 

 otherwise than in increasing T, in this part of the curve, the 

 value 



