( 58) 



course of the //-lines being modified by lite temperature, the value 



of T will also influence this shape. 



Let us first put a left region at a value of T below T^ and also 



below Ti-.,. Then tangents may he drawn to all //-lines from the 



origin. The points of contact on the side of the small volumes then 



form a continuous series of points which begins in the point in which 



dp 

 the liquid branch of the curve — = intersects the 1 st axis, and 



moves further and further away from this curve as it approaches 



the 2 nd axis, remaining all the time at smaller volumes than those 



of the curve mentioned. The points of contact on the side of the 



large volumes also form a continuous series of point, which starts in 



dp 

 the point in which the vapour branch of the curve — =0 intersects 



<lr 



the 1 st axis, and also moves further and further away from this 



curve as it draws near the 2 m ' axis. This series of points has always 



dp 

 larger volume than the curve — = 0. So when a potential line 



dv 



passes through such a series of' points it is directed parallel to the 



I "-axis. The locus of the points' in which a potential line runs parallel 



to the A'-axis, and which is found by drawing tangents from the 



origin to the ^yhues, is a curve consisting of one single branch, 



which at small volumes crosses (he tield from a certain point of the 



first axis to the point v = b and ,v = l. Hut the shape of this curve 



is very different, dependent on the more or less complicated shape 



of the y-lines. Without entering into further details we shall only 



observe, that when g-lines run as is the case in the absence of 



d'ty 



— = 0, this curve will have no point in common with the preceding 



d,v* 



d*i!> </> 



one; but if = exists, and intersects — = Ü, the curve on 



da* dv" 



/dv\ , dhp , ■ • , ,■ 



which — = 0, passes round = Ü, and twice intersects the line, 



\d!cjp 0t ' d.rS 



on which I — ]=cc. These two points of intersection are again of 

 \dxJpot 



importance for the shape of the potential lines. Then again a loop- 

 potential line passes through one of these two points. In this case the 

 double point is the point of intersection on the right, and the point 

 of intersection lying on the left serves then again as isolated point, 

 round which a series of potential lines run in closed figures. That 

 in this case the point lying on the right is the double point, is in 



