Physics. — "On the Occurrence of Solid Substance in Bijiary 

 Mixtures ivith Unmixing" I. Bj Prof. F. E. C. Scheffer. 

 (Coininiinicated by Prof. J, Böeseken). 



(Communicated in the meeting of November 30 1918). 



1. Introduction. When two phases coexist in a binary system, the 

 condition that the temperature and the three quantities ( — | , 



— , and If) — V — — '^' ~r shall be equal for the two pha- 



\dxj„2' \dv JxT \dxJ^,T 



ses, must be satisfied. On the surface tit =f\v,x), constructed fora 



detinite temperature, the coexisting phases are obtained by rolling 



a bi-tangent plane over this surface. Another method to find the 



coexisting phases consists in this that the system of curves (-^j = 



\dv Jx T 



= constant (w-lines), ( — ) = constant (o-lines) and u? — vf -= ) 



\dxJ„T ^ ydvj. 



4~) = 



\dxJvT 



'xT 



constant (potential lines) are thought to be traced 



projected on the v—x plane; then two points on the ip-surface indi- 

 cate coexisting phases when through the projections of these points 

 run a same /)-line, a same ^--line, and a same potential line. 



The points indicating coexisting phases, furnish in the v — .r-pro- 

 jection a locus the inclination of which is determined by : 



d'tf) d*\\} 



(v, — v.) 1- (o!, — ;r,) 



aVj dv^da^ 



in which the indices 1 and 2 refer to the two coexisting phases '). 

 The indicatrix in a point of the tp-plane is given in first approx- 

 imation by the equation : 



d*tl) d*tb d*\b 



«« --^ + 2vx-—}- -^a:'~^-\-av-\-tia; i-Y = . . (2) 

 dr, dv^dx^ dXy 



1) Van der Waals— Kohnstamm. Thermodynamik. II. S. 196, equation I. 



