( 283 ) 



Let us now first consider the initial direction of the sections 

 normal to the 7-a\is. It can now be foniid from : 



log 1 + 



~ MRT ^x 



log\\ — 



MRT dx, 

 '5— ^'i <^P \ 



for the liqnid branch and 



MRT dx. 



— ' :— ^ for the \apour branch. 



MRT dx ' 



For very low temperatures we may put — Tjj^Tf about equal to 



unity, and so : 



i dip) dip 



I ax, \ ox 



and 



log 1 



dip 

 dx„ 



dpc dp dp 



For the case that — - = 0, -—- and -— - is also equal to 0, and it 

 dx dx, dx^ 



may therefore happen, that the two branches of the y>,.i'-line touch 



in the beginning, and that both have an horizontal tangent. 



As condition for this circumstance we have : 



ƒ dTy dlpx 



T dx dx 



which may also be written: 



T-, n da 1 db\ _ /I da 



T \a dx b dxj \^a dx 

 or 



2\ dlTy dlTy dlb 



f 



f 



2 db 

 bd~v 



T d.i 



E.g. for T=\T. 



dx 



dlTy 



"d^ 



dx 



dlb 

 dx 



dlT, 1 dlb 



: J[ =: 0. 



dx 13 dx 



'Di V — V I 



For higher temperatures — 71-zr- is smaller than unity and for the 

 ^ ^ MRT "^ 



critical temperature of the component this quantity' is even equal to 



I'j — V, dp f i\ — V, dp 



0. In this ease we may write — - - fof log (^1 + _- -^ 



and we find 



dp dpc 



dx^ dx 



