743 



In the points H and H, of figs. 4—6 (XI), tlie pressure is equal 

 to Ph, ci' = () and .r, ==0; further we put y = {i/)o and i/, = {,/^)^. 

 For a point in the vicinity of 7i 6' on this saturationcurve under i(s own 

 vapour-pressure, the pressure is Pii-\-(lP, a;=è, a;^ = ^„ y = (y)^-\-v, 

 and y^ = {y,)^ + i^^. 



In the points ifand H^ themselves the binary equilibrium F~\- L-\-G 

 exists ; to this applies : 



(y~l^)^ U+^ = ^ = ^ ... (8) 



wherein the pressure is equal to Ph, y = (y)„, y, = (y,), and U 

 and f/j are independent of .v and v^. 



We now take the condition (6), from this it follow^s : 



X, dU dU, 



X 



d.v d.v 



Therefore, we obtain for very small values of .r and .v^ : 

 , §, 1 . fdU Of/A 



or 



ê^=Kê (11) 



wherein K is determined in (10). 



We now take the condition (7) ; in this we put the pressure 

 P equal to Pn+dP, .x' = 5, a\ = l^, y — {^i/)^-{-ii and y, = {y,)„-\-^^^. 



If we expand both terms of (7) inio a series and consider that 

 in the point H (8) is satisfied, then we find: 



dV ds dt d'V ds 



oy o.v oy oyoP a.vdy 





(12) 



d' U d' U Ö' U 



Herein r = -c — s=:~— - ^ = ,— - ; these values must be kept, as 

 O.v^ oxoy oy^ ^ 



they are in the point H. The second member of (12) is indicated by 



[]j; this means that we deduce the second membei- from tiie first by 



substituting $i, ij^, s^, t^ etc. for |, i], s, t etc. Now we expand (4) 



into a series; if we keep in mind, that in the point H (8) is again 



satisfied, and that x and o\ must be put equal to zero, then we 



find a series, which we write in the following form : 



/2T ^ + 1 tif - {V-v) dP - i {^^- ^ dP^ + R f (;/-/?) L = () (13) 



In A^ only terms occur, which are infinitely small with respect 



48 

 Proceedings Royal Acad. Amsterdam. Vol. XVI. 



