551 



We i)ut /i the length of the conjiigationline MM^ which joins the 

 liquid M with its correspoiidiiig vapour ,1/,. The liqiiidline of the 

 temperature T -{- dT will now inter.seet this conjugatioiiliue in a 

 point M' in the vicinity of M. We represent MM' by dl^ ; we take 

 r//i positive in the direction from M towards M^. We then find from (2) 



D 



dT (6) 



l^ ifiTj cos^ (f^ 



wherein : 



K, = r -f 2 ^^^ . + ( ■'^^— ^ I t and {,>'—.if = l^' cos' (/,. 



(f^ therefore is the angle which forms the conjugationline MM^ 

 with the A'-axis. 



We now suppose 1"' that the saturationcnrve of F and the 

 liquidcurve of the region L — G go through a same point M\ 



2'^ that the two curves touch each other in that point. 



From l^Ut follows that r, ,s and t have the same value in /v and /v^ 

 and that B and D apply to the same liquid. 



From 2"^^ it follows, as is easily deduced, from the equations of 

 the two curves, {P and T constant) that: 



and therefore also r/ =:r/j. The meaning of this is that the lines 

 FM and MM^ coin:*ide. This follows as we saw already before, 

 also immediately from the indicati-ix theorem. From this now it 

 follows that we may substitute /, l and <( in (6^ for /j, k^ and (f^. 

 We then obtain : 



dh=-j^^dT (7) 



IK- cos' (f 



Now D is positive ; if we assume further that heat is to be 

 supplied for dissolving solid F, then B is also positive. From this 

 it follows that d/ and c//, always have an opposite sign. In order that 

 the liquidcurve of the region L — G and the saturationcnrve of F 

 may move in the same direction, when 7' is changed, the point M 

 must therefore be situated between the points F and M^. This is 

 then also in agreement with fig. 4. 



From (5^ and (7) it follows, that the two curves will move with 

 the same rapidity as 



B D 



- = - (8) 



