236 



Dr. J. Larmor. On the Elcctrodynamic and [Jan. 2, 



part of the path is negligible compound with that along the isothermal 

 part. Thus 



E = -i(EW-By)»S- 



Now the experiments of Curie on the relation of k to 6 in weakly 

 paramagnetic materials make k vary inversely as 9 ; and this result has 

 more recently been verified down to very low temperatures by Dewar 

 and Fleming. This gives 



E = |k(H 2 2-H^). 



Thus the movement of the magnetisable material at uniform tempera- 

 ture is accompanied by a supply to it of heat, equal to the mechanical 

 work done by it owing to the attraction of the field • and this heat 

 is just what is wanted to be transformed into the additional energy of 

 intrinsic magnetisation (ii) of § 2. It is to be observed that in the 

 actual experiments k was small, and the other part (iii) of this energy 

 therefore negligible : so that no conclusion as to the extent to which 

 its source is thermal can be derived from Curie's law. 



6. The uncertainties of § 4 do not of course affect the estimation 

 of the loss of motive power arising from cyclic magnetic hysteresis, 

 for we have here to do with the mutual energy of the applied field 

 and the magnet, not the intrinsic local energy of the latter by itself. 

 If the applied field is (a, /S, y), the total energy employed in polarising 

 the magnetic molecules in volume 8t is 



(Aa + B/? + Cy) Sr. 



So long as the polarisation is slowly effected against the resilience 

 of reversible internal elastic forces this is stored as potential energy ; 

 but any want of reversibility involves degradation of some of it into 

 heat, while if the field were instantaneously annihilated the molecules 

 would swing back and vibrate, so that ultimately all would go into heat. 



Let us pass the magnetic body through a cycle by moving it around 

 a path in a permanent magnetic field (a, /3, y). An infinitesimal 

 displacement of the volume 8r from a place where the field is (cc, /3, y) 

 to one where it is (cc + 8cc, f3-\- 8/3, y + Sy) does mechanical work, arising 

 from the magnetic attraction, of amount 



(A8x + B8fi + C8y) St. 



The integral of this throughout the whole connected system gives 

 the virtual work for that displacement, from which the forces assisting 

 it are derived as usual. Confining attention to the element 8r the 

 work supplied by it from the field, to outside s}~stems which it drives, 

 in traversing any path is thus 



8t \ (A/a + B^ + G/y), 



