( ^21 ) 



in fig. 12 can of course appear, so that the biiiodal litiB vanishes 

 because it falls inside the sector POr' . 



Remarkable in both cases is that the stable part of the line of 

 saturation of F, although it represents an unbroken series of solutions, 

 yet shows a discontinuity. This makes its appearance in the critical 

 solution saturated with solid P. 



III. Point is a point of osculation. 



As in a point of osculation we have c^^O, c^^O and c^^rO, 

 we get from (2) for the equation of the curve of contact: 



{M,p \~,i,q^ ,v' + {2d,p^2d,q) xy + {d,p^,-M,q) t/^ + . . . = 

 or if we make the A'-axis to coincide with OP: 



?,J,.f + -Id^.r,! + d,y' + ...=: (26) 



So the curve of contact consists either of an isolated point or it 

 shows in 6> a node. From (26) it is evident that the directions of the 

 two tangents are independent of the distance from point P to point 

 0; they depend only on the direction of the line OP. 



The above-mentioned pro|)erty that the curve of contact and the 

 binodal line are curved in the same direction in the vicinity of the 

 plaitpoint (//jy) caused us to surmise that this also would be the 

 case with a sx-ond branch of the binodal line, should such a one 

 pass through the plaitpoint ^). 



This surmise can be aftirmed in the following way and it can also 

 be shown that the curvation of such a branch corresponds entirely 

 to that of the curves of contact passing through the plaitpoint. 



To that end we assume again as ]^-axis the 

 tangent to the spinodal and the binodal line 

 of the plaitpoint 0^ (fig. 13); for the A'-axis 

 we choose the line of conjugation 0^0.^ and 

 we put 0, 0^ = p. 



The tangential plane in a point ,i\ , //j , z^ 

 in the vicinity of 0^ is : 



the one in a point .''.^ , .//j , c, in the vicinity of ( K, is: 

 Z - z, = (A-.r,) -^ + {Y-y,) ^ 



1) Coinp. the paper of Mr. Kuenen (Proceedings of Oct. 1911, p. 420). 



Fig. 13. 



Z 



