( 192 ) 

 after division of numerator and denominator by a\ — x s 



dp __ ydxJpT 



l, i — v s — («i — *») -1— 



\dxJ,A 



dT v lt ' 



dp 

 It appears from the form for — , that this value is equal to 



dT 



if a section is made through the surface of saturation for 



dp\ 



dT), 

 x = x s . 



In other words : The three phase triangle in its extreme position 

 touches the section mentioned — and to this we might also at 

 once have concluded. It will also be immediately seen, that the 

 coinciding of the points ,r, and ,r 8 of the three phase triangle takes 

 place in a plaitpoint, and that therefore the final point of the line 

 p=f(T) lies on the plaitpoint line. Then we have a plaitpoint in 

 the point where ,i\ and x 3 coincide, and the p, 7-projection of the 

 plaitpoint line being the envelope of the p, T-projection of the sections 

 of the surface of saturation for constant values of .1*, the plaitpoint 

 line and the p, ^'-projection of the sections touch, and so also the 

 final point of the p, T-projection of the three phase pressure, as in 

 that final point the last element of this pressure coincides with the 

 section mentioned. This contact has not yet been taken into con- 

 sideration in former diagrams. If there are two final points of the 

 three phase pressure, then there are two separate portions of the 

 realisable portion of the plaitpoint line, which are joined by the 

 three phase pressure, the meeting-points being again cusps, just as 

 is the case with the hidden portion of the plaitpoint line. Now, 

 however, rises the following question. We know from the shape of 

 the section of the surface of saturation at given value of x, that in 

 the simplest case it consists of two branches, and that on the upper 



dp dp 



branch the value of — may also be negative. Can now also — 



dT dT 



be negative for the three phase pressure ? As far as I know this 

 has never been observed; but the observations on the rise of the 

 three phase pressure with the temperature, and the other circum- 

 stances, viz. the values of x and v, have been only little examined 



