( 746 ) 



_L = () the course of the o-lines has also been simplified, and at 



das* 



least with a volume which is somewhat above the limiting volume, 



they run chiefly in the direction of* the v-axis. 



Many of the results obtained about the course of' the spinodal 

 curve, and about the place of the plai (points, at which we have 

 arrived in the foregoing discussion by examining the way in which 

 the p- and the j-lines may be brought into mutual contact, may 

 be tested by the differential equation of the spinodal line. This 

 will, of course, also be serviceable when we choose another region 

 than that discussed as yet. 



From : 



d*ty d s tp f<Pip\__ 



</r" dx* \ dxdv 



we derive : 



[d*\L< d*xb d*y d*ty n d*ip d*1\> | , 



__L — l -| 1 -L — 2 — - — — dv -f- 



[ das* dv* dv* dx*dv dasdv dxdv* ) 



Id'tb d'tp d*ty d*tp d*ip d 3 y ) 



-|- ! 1 — 2 } da; -f- 



\dx 3 dv* das* dxdv* dx* dx*dv) 



l _ d'ri éhp d\ d'y 2 d* n £±) dT==Qt 

 j dx* dv* dv* da:* dxdv dxdv) 



We arrive at the shape of the factor of dT by considering that from: 



ds = T di] — p dv -j- q dx 

 follows : 



dtp -=z — i] d T — p dv -j- <J dx 



SO 



/dxp\ i d*y U*rf\ 



tbat IsrJ = " " and 8 ° 3w = " WJ J tc ' 



This very complicated differential equation may be reduced to a 



simple shape. 



Let us for this purpose first consider the factor of dv. By substi- 



fd*qy d*ip 



. . , . \dx~dv) e d*x\: fdv\ 



tutmg in it the quantity — — — for — -, and I — J tor 



Cl IIS dX \J1X y p 



d*\\: j fdv~\ e _ dxdv 



d*xp 



~<M dv* 



this factor becomes : 

 d* 

 dv* j dv* \dasJn ' dxdv* \dx J D ' dx*dv ] 



l*xp id z \p fdv\* d*ip f dv \, d *ty 



iv* I dv 3 \dxjp dxdv*\dxjp dx*di 



_ dip 



From p = — we derive : 



dv 



