463 



h. Influence of the magnetic field on the rotational energy. As 

 according to the quaiituiii-theory the lotatioiial energy of the mole- 

 cuhxr magnets depends npon the tVc(|nencics whicli occur in the body 

 consi<lered, and as tliese frequencies may be changed nnder the 

 influence of tlie magnetic field, the rotational energy may depend 

 upon the field. The way of dependence can be deduced thermo- 

 dynamically, if the energy in tlie absence of a field is known as a 

 function of temperature (cf. § 2). 



The heat which at an infinitely small reversible change has to 

 be supplied to a ferromagnetic body, of which the state may be 

 determined by 7' and J/,n , is given per unit of mass l^y ^) 



dQ = dU, — HdM,„ (18) 



in which U^- also refers to the unit of mass, and H, as in this 

 section under a, represents the total field acting on each magnetic 

 molecule, the molecular field being included. The second law of 

 thermodynamics then gives 



Following the supposition mentioned in the beginning of this 

 section under a we may write 



Il=znu,n,f{Mn.) (20) 



where f{M,,,) is determined by (7) and (8). The index ^ in u,m 

 indicates that the rotation energy has been changed by the field, u,, 

 as in § 2, will indicate the rotational energy in the absence of the field. 

 With (/i- = ???«,. m (19) becomes 



/(i)(a^)r="™-''(^)./,;, ■ • • • *''* 



The general solution of this partial differential equation is 



Unn_ ( —\f{Mr^)dM, 



rj.^<l\Te y- "•' ) (22) 



1) This equation was deduced by me from a consideratiou of the energy which 

 has to be supplied to one of the molecular magnets, of which the moment is 

 supposed to be constant, when its rotation energy and its orientation with regard 

 to tlie field H are changed. In this, following Weiss, I supposed the total inter- 

 action of the molecules to be included in the form of the molecular field in H. 

 One obtains for the energy to be supplied du^. —Hd-jfj, if do^j is the change 

 of the component in the direction of H of the magnetic moment. Summation over 

 the unit of mass gives (18;. Gf. the appendix to this communication It for a more 

 detailed proof, which Prof. Lorentz kindly communicated to me. 



