6^-2 



We may (ind this condition also in the following way. The 

 boilingpointcurve of F is fixed by : 



[(«_,,) r + (/?-//>] dx f [(« -.'>•) 6' + (/?-//) t] dy = B.dT . (9) 

 [(..— .t-)r f (^,-,v).].?.r + \{.r,-.v)s + 0/—. v) ^] ^// = - D.dT (10) 

 From this follows 



{Fr + Q.) rf.,; + {Ps -\-Qt)dy=Q ( . 1) 



wherein 



P= («— .t) D + (a-,— .1-) 5 and Q ^ {S-y)D -f- {y,-y) B. 



Ill order that the point of the curve under consideration may be 

 an isolated or a double point, the coefficient of dr and (hf must be 

 = 0. Therefore P=0 and Q = () or 



[a-.i^D -^ {x^-,v)B=0 and {B—y)D^{y,—y)B—0. (12) 



If B and D are not =7^ 0, then 



follows, which we have also found for this. This means, that the 

 considered point, its corresponding vapour and the point 7^^ are 

 situated on a straight line. Fiirthei- it follows that the liquidcurve 

 of the region L — G and the saturationcurve of F touch each other 

 in the contemplated point. If we substitute for B and D their values 

 in (12), then we tind : 



(,i-..)/A + (.;-.^>i + (.t-,-«)//=0 . . . . (18) 

 or 



{^~y)ll,-\-{y-^yM-V{:]j--m-^^ ' • • • ('4) 

 The ürst part of (13) and (14) represents the change of entropy 

 when a reaction takes place between the three phases F, L, and G. 

 From this it follows therefore, that the contemplated point of the 

 boilingpointcurve will be an isolated or a double point, when an 

 isentropic reaction takes place between the three phases F, L and 

 G; in other words, when no heat must be supplied or removed. 

 In (8) the same is expressed in quite an other form as in (13) and 

 (14). In order to examine whether the contemplated point is an 

 isolated or a double point, we must calculate terms of higher order, 

 namely Adx" -\- Bdxdy -\- Cdy^. 



Because the fixing of A, B, and C gives cause for extensive 

 calculations, we will leave that aside. 



To be continued. 



