550 



Q. The ('Oiwespoiiding vajiOiu-L'iii-vc in^M^Q^ is dotted. Tn fig. 5 

 tiie part M^Q^M^ is drawn circumphased. Of course it may be 

 also exphased. 



If we determine the boilingpoin<^curve of F under a pressure somewhat 

 different from that, to which fig. 5 applies, the boilingpointcurve 

 will suffer also a small change of form. The double point M dis- 

 appears and either two branches separated from each other occur, 

 of which the one surrounds the other, or one single curve is formed which 

 is very concave and which has two parts which are curved sharply 

 towards each other. The same applies to the corresponding vapour- 

 curve. When in a system boilingpointcurves as deduced above 

 occur, some of our previous deductions must be changed to a certain 

 extent and they must be completed; this however is left to the reader. 



Now we may still determine under what conditions the 

 liquidcurve of the region L — G and the saturationcurve of F will 

 move with the same rapidity in the point M of fig. 4. 



To the saturationcurve of F applies : 



\{a-x) r + {^-y) .] dx -f- [(«-.!•) s -f {,i-y) q dy = BdT . (1) 

 To the liquidcurve of the region L — G : 

 [{.v,-.v) r + {y, -y) s] dx + [(.i-,-.^-) s + {y,-y) t\ dy = - Ddt (2) 



(For the significance of B and D see communication (II) ). 



We now take any point M of the saturationcurve of h . We call 

 / the length of the line FM. The saturationcurve of the temperature 

 T -\- cVr will intersect the line FM in a pohit M' in the vicinity 

 of M. We put MM' = (// and we take dl positive in the direction 

 from M towards F. We then have : 



dx dy dl 



(3) 



a— X ^ — y I 



If we substitute these values of ch and dy in (1), it follows that: 



BldT 

 dl — ... (4) 



or: 



dl=-rf^^dt (5) 



IK cos (f 



wherein : 



iT .— r + 2 *-^ s + I ^— ^ ) t and (« - xf = l' cos' (f. 

 a — X \a — xj 



Therefore (f is the angle which the line jF 37 forms with the X-axis. 

 We now take any point M of the liquidcurve of the region L — G. 



