2. If we now consider a material element which can be arbi- 

 trarily deforined, we can snbject its state to an infinitely small 

 variation. With respect to the deformafioJi this variation will be 

 determined by six mntually independent qnantities, three dilatations, 

 which determine the chanpje of volume, and three, which determine 

 the change of form. Hence speaking thermodynamically, the variation 

 of state of this element (which need not necessarily be infinitely 

 small, provided it is to be considered as homogeneously deformed) 

 is determined besides by the temperature, by six mutually independ- 

 ent cpiantities. It now follows from (3) and (12) that for a virtual 

 isothermal variation of state the following equation will hold for 

 the unity of mass 



^^= (X.,.t.^, f Yyy,,yA,z,i- ny, + Z,:,^^.+ A>_y) . . (14) 



Q 

 If we now start from the uuity of volume, and call the free 

 energy of it if'', the following form holds for it 



(kp' = — (A>xr F,.!/,^ i-Z,z,-\- r:>/, + Z:,z^^Xy.v,) . . (15) 



(In this it should be borne in mind that after the variation the 

 volume will in general be no longer equal to unity). 

 Now 



dtp 



§? = -" ('«) 



holds generally for the free energy on change of temperature, when 



in the expression for the external work with an intinitely small 



variation no term with éT occurs as factor. 

 Hence: 



(^ip= {X,x^-+Yyy,^^Z,z,^r,ij, + Z,ty^rXyf>^y) — n^T. (17) 



Q 



holds for virtual variations of state, in which also the temperature 



can undergo a change. 



When we start from unity of volume, we have 



dtp' = - (A>:,+ Yyyy^Z.z, f r,y,-^Z^z^-^Xyj^y) - riöT . (18) 



where r/ represents the entropy of the nnity of volume. 



3. Let us now consider a system consisting of two phases, a 

 liquid and a solid state. We assume the system to be at rest. Let it 

 further as a whole be subjected to the hydrostatic pressure p, while 

 arbitrary deforinative forces can be active on the surface of the 

 solid phase, with the exception of that part that is in contact with 

 the liquid phase; we exclude volume forces. Consequently the same 



' 4y 



Proceedings Royal Acad. Amsterdam, Vol. XVII. 



