( 191 ) 



and at such a point the curve suffers an abrupt change of diiection. 

 As for every value of x the line DEAC is met only once, this 

 sudden change of direction occurs only once in a {p, 7')j,.-curve. 

 This determines the external course of such a section sufficiently. 

 Beyond the point of change of direction the points for which TI^^i 

 and F^i ^^'^ equal to will give rise to a maximum value and to 

 a critical point of contact. But we conline ourselves here to the 

 modifications which are the consequence of the three phase equilibria. 



In the points, at which such an abrupt change of direction 

 occurs, a part of the internal or hidden course of such a {p, T)j.- 

 curve begins and the series of figures {a, h, c, d etc.) indicates 

 this hidden course for the values of .r, foi' which the three phase 

 curve is met. Seen on the {p, T)jc-cnrve such a point presents itself 

 as a node. The part of the curve coming from below continues 

 through the node, also the part coming from above, while there 

 is a third part which joins the points, where this onward course 

 stops. The temperature of the node is, therefore, quite determined 

 by the point at which DEAC is cut by a line parallel to the 7- 

 axis with the given value of x as abscis. But the size of the hidden 

 part is very different. As it has quite disappeared beyond a'n and 

 xc, it is but small for values of ,v onlj' little greater than a-jy or 

 only little smaller than a'r. But chiefly the different hidden parts 

 are distinguished by the occurrence or non-occurrence of a plait- 

 point and when it occurs by the place where it occurs. 



In what precedes it has already been remarked that the plaitpoint 

 does not lie hidden for values of x beyond xe and xa- But for all 

 values of x between xe and xa it lies on the hidden part, so on that 

 which might be called the loop when the (j?, T)^-curve is drawn. 

 This appears at once when the (^;, A')r-figures are consulted I.e. But 

 depending upon the value of x the plaitpoint can have three different 

 places. It may either lie on that part of the loop which may be 

 considered as the continuation of the lower part of the (^?, T)x-curve 

 — or it may lie on the branch of the loop joining the points at 

 which the onward course from below and above stops — or it may 

 lie on the part which may be considered as the continuation of 

 the part coming from above. 



The first case occurs for x between xe and xm> the second when 

 X lies between xm and x,» and the third case when x lies between 

 Xm and XA' So if we have drawn a (;9, 7')x-curve, e.g. one of the 

 figures of the series {a, />, c, d etc.), and when we proceed in the 

 same direction in such a part, also following the loop, we follow 

 the motion which the plaitpoint has when x changes continuously. 



