( 2.s:i ) 



(liat (lio \aliio of' .r, ill \]\o solid slalc will a foi-lioi-i be smaller than 

 llial ot' I lie |»liase coexistiiiLi willi il, wliellier liie laller is a gas or 

 a li(iiii(l |)iiase. W(^ do nol wish lo slale |>osili\'ely thai there are 

 no exceptions to Ihis nile. Ihil lor the case ether and aiillira(|iiinojie 

 we may safely assnnic that ./,, — .!■/■ is negative. 



Now it remains on\\ to know the sign of v-,/-, to he able to derive 



dp 

 the sioji ot — . 



fd Vf\ 

 The expression /%/• stands in the | dace of (?•,,. — Vf) — ii\ — .vy) I — ^J 



and represents the decrease of ^■()llllne per nioleciiiar (pianlity when 

 an inlinitel}' small (piaiitily of the solid phase passes into the coexist- 

 ing ])liase at constant pressnre and constant temperature. If this 

 coexisting ])hase should be a va|)our phase, this decrease of volume 

 is undoubtedly negative. But this quantity may also be positive, and 

 if we make the series of pressures include all kinds of values, so 

 if we make the pressure asceiid from xery low values uj) to very 

 high ones, there is undoubtedly at least once reversal of sign, 

 and for the case that the contact-curve under high pressure moves 

 towards ijicreasing values of ,}■ there is e\'en twice reversal of sign. 



To demonstrate this, we inquire tirst into the geometrical meanijig 

 of ?".,/•. Let the jioint /' be the representation of the solid })hase, 

 with Vg and .r.s as coordinates — and the point Q the representation 

 of the coexisting tluid phase with 77 and ,/y as coordinates. Let us 

 draw throngh (^ the isobar and let us determine the ])oint P' , in 

 which the tangent to this isobar of Q cuts the line which has 

 been drawn through /-* |)arallel to the vobune-axis, then — v,,f=PP'. 

 If the point P' lies on the })Ositive side of P, then r.,/- is negative. 

 For the s[»ecial case that the tangent to the isobar of Q passes 

 through P, /".s/ = (K In the same way ?".,/■ would be i)ositi\e, if /^' 

 should lie on the negative side of P. 



In order to know the sign of /'.s/, the course of the ciu'ves of 

 equal })ressnre must therefore be known. In my "Ternary systems" 

 I (Tliese proceedings Febr. 22 "• 1902, p. 453) I have represented 

 for the analogous case of a binary system, for which the second 

 component has the lowest Tj-, the course of the isobars by the line 

 JiKDiy P' l>' in Fig. 2. I have added aiu)ther isobar to the re[)ro- 

 dnctioii of this figure — and I have represented the solid phase 

 by the point Pg. The added isobar passes through the plaitpoint. 

 This isobar has an intlection point somewhat to the right of the 

 plait[>oint. Each of these lines of ecpial pressure having an intlection 

 poijit, then.' is a locus for these points, which I have left out in the 



