( 190 ) 



pears, as may be derived from the figs. 1, 2, 3, 1. c. Between 

 certain values of p and at suitable values of T there are isopiests, 



on which - — is four times equal to 0. On such isopiests — is 

 ^•v pT dx^pT 



d'^ 



three times and -— twice equal to 0. We now can choose 

 d'V\,r 



the value of p and T sucli, that these two points in which 



d"^ . d'^ 



— is 0, coincide. As then two values of .v in which — =: 



d.v'^pT dx''p2' 



also coincide, such a point is a plaitpoint. For such points 



/'dK\ , APCA fd'Z\ 



I — and -— and — ^ is equal to 0. These three equations 



\dxy,,T \d.vy,,T yd'V'Jj.j 



determine then the value of .v, p and T, at which such a double 



j)laitpoint appears or disappears. 



rd'^\ 

 It in (3) and (4) we put the quantitv -— I = 0, then both 



\d-l' JpT 



I — I and I — - I will also be equal to 0, from which follows that 

 \dxJi,i \d'Vjj,i 



not only the plaitpoint temperature, but also the plaitpoint pressure 



will present a maximum and a minimum. As we only assume the 



case that — r, is positive, there will be found at the same time a 



maximum value or a minimum value for the two curves. In the 

 points E and .1 there is therefore no maximum or minimum for 

 the plaitpoint curves, and this is also to be expected for the curve 

 of the three phase temperature, though this pei'haps might call for 

 further examination. For the properties which are to be derived by 

 us this is, however, not of great importance. 



Let us now proceed to describe the properties of the sections of 

 the ([), T, .t')-surface normal to the .I'-axis or in other words the 

 course of the (/;, jf').rcnrves. 



We remark then in the tirst place that for values of x below 

 XD and above xc the (/>, 7').rCurves will present their usual shape 

 without any complication. For values of x between xd and xe and 

 also for values of x between xa and xc there is a complication in 

 these {p, jr).i-lines. For values of x between xj) and xe the three 

 phase temperature lies higher than the plaitpoint temperature; the 

 reverse is the case for x between xa and xc- On such {p, J')^:- 

 curves the usual plaitpoint occurs, but at a plaitpoint such curves, 

 considered in themselves, do not present any particularity. But a 

 point also occurs on them at which the three phase pressure is reached, 



