in the Motion of the Magnetic Field. 325 



into differential form. Let us suppose that the process of 

 magnetization takes place at constant temperature. In this 

 case the free energy F is a function only of the coordinates 

 Pay Pp, .... But these coordinates can be expressed by the 

 system of equations (27) as a function of J 2 . Therefore the 

 energy F may also be considered as a function of the same 

 quantity J 2 . In this way we have 



SF=|JrfP (28) 



If we now differentiate the equation (26), considering H as 

 an independent variable and using the formula (28), we have 



dJ . 2/cXdF dJ_ 



dn~ v dJ 2 dH ; 



let us replace yrj by its expression from equation (25) ; 



dti~ \|_3 U + JdR + J ; 

 we have, lastly, 



di + v a j a 



v 3U + Vbj 2 



(29) 



This is the differential equation of static and isothermic 



magnetization. Here, as has been said above, ^-^ must be 



considered as a function of J 2 , where J, in its turn, is ex- 

 pressed in terms of I and H by help of equation (25), 



*Y? + l)l + xJ+H=0. 



3 ^ 



The form of this function of F is defined by the way 

 in which F depends onp a ,pp. ... as shown in equations (27). 

 Actually, by differentiating the equations (27) at a constant 

 temperature, 



d 2 F d 2 F 



and by introducing the quantities dp a , dp$, , . . from here in 

 the expression (24) for SF, we shall have 



