322 B. Rosing on the Participation of Matter 



Here the terms {pp) a p a , (PP)pPp • ■ ■ represent forces of 

 inertia for the coordinates p a , p~, . . . and the function F 

 represents the free energy of deformations according to 

 Helmholtz's theory. It must be observed, however, that we 

 simplified the formulae by taking the coordinates p a , p^ . . . 

 to be independent of each other, and the functions p a , p^, . . . to 

 depend only on the coordinates ® and p a , p^, . . . respectively. 

 On the supposition of indefinitely slow changes in the coordi- 

 nates p a , pp ... we can neglect the forces of inertia ;. 

 further, by giving to the equations the form 



dp a dJ dF 



dS J2+Pa dt' = ~Wa 



dp,o dJ dF 



d® +p ?dt dfy 



, „ dJ dJ tl 



we can neglect the forces P a ' a T t > Pp a T t' • • • on tne same 



grounds. Lastly, putting 



*«=-„ d ll = -a a , .... (21) 



we get the equations in the case of indefinitely slow changes 

 to be : — 



BF 



a J 1 = ~ — 5 



> (22) 



T2 ^F 



P ^PfB J 



which show the equilibrium between the components of pressure 

 proportional to J 2 and the corresponding forces of elasticity. 



Let us now consider equation (18). After integrating 

 from the initial moment, when I = J = H = 0, this equation 

 gives : 



*+**v.'-«W+ • • • -f|£ft J *-f l5ft»- • ■ • = 



Once more assuming the indefinite slowness of change, we 

 shall have for static magnetization : 



