531 

 Chemistry. — "ƒ??.-, mono- anti divariint equilibria" II. By 



Prof. F. A. H. SCHREINEMAKERS. 



5. Ternary systevis. ') 



In an invariant point of a ternary system five phases occur, 

 which we will call 1, 2, 3, 4 and 5; consequently this point is a 

 quintuplepoint. Five curves, therefore, start from this point, which 

 we shall call (1), (2), (3), (4) and (5) according to our former 

 notation. Further we find ^ i,» + 2) (h -f 1) =r 10 regions, viz. J 23, 

 124, 134, 234, 125, 135, 235, 145, 245 and 345. 



We call the tiiree components of which the ternary sy.stein is 

 composed: A, B and 6'; the five phases then can be represented 

 by five points of the plane ABC. These five points may be situated 

 with respect to one another in three ways, as has been indicated in 

 figs. 1, 3 and 5. In fig. 1 they form the anglepoints of a quint- 

 angle ; in fig. 3 they form the quadrangle 12 5 3, witiiin which 

 the point 4 is situated ; in fig. 5 they form the triangle 1 2 5, within 

 which the points 3 and 4 are situated. 



We can however consider figs. 3 and 5 also as quintangles; in 

 each of them the sides iiave been drawn and the diagonals have 

 been dotted. We call fig. 3 a monoconcave and fig. 5 a biconcave 

 quintangle. 



We are able to make of fig. 3 a monoconcave quintangle in difierent 

 ways ; we do this, however, in the following way. We draw in the 

 quadrangle, within which the point 4 is situated, the diagonals 15 

 and 23. These divide the quadrangle into four triangles; the point 4 

 is situated within one of these triangles. Now we unite the angle- 

 points 1 and 2 of this triangle with the point 4 and we consider 

 the lines 14 and 24 as sides of the quintangle, so that a mono- 

 concave quintangle is formed. 



In order to change fig. 5 into a quintangle we draw a straight 

 line through the points 3 and 4 ; this intersects two sides of the 

 triangle, in our case the sides 12 and 15. We now replace the side 

 12 by the two lines 14 and 24, the side 15 by the lines 13 and 

 35, so that a biconcave quintangle arises. 



In the figs. 1, 3 and 5 the anglepoints are numbered in the follow- 

 ing way. We take any anglepoint and we call this the point 1 ; 

 two diagonals start from this point. Now we go along one of 



•) For another treatment confer F. A. H. Schreinemakees. Die heterogenen 

 Gleichgewichte von H. \V. Bakhuis Roozeboom IIP. 218. 



