242 HAROLD L. ALLING 
in conjunction with the diagram, it will be observed that it experi- 
ences a sharp change in direction at the point indicating diopside. 
Now in the hyalophane series, we possess sufficient data to 
show that the specific-gravity curve is straight and therefore that 
there is no “molecular compound”’ between orthoclase and celsian. 
Consequently we must reject the theory stated by Miers, Moses, 
and Parsons as untenable. 
THREE-COMPONENT SYSTEMS 
TERNARY DIAGRAMS 
In dealing with two-component systems we have to consider 
two variables—the temperature and the composition. This 
necessitates the employment of two-dimensional diagrams. But 
with three components we must employ three dimensions, in other 
words, solid figures. ‘These are bulky affairs which are difficult to 
represent upon paper. ‘There are two methods by means of which 
this may be accomplished: first, by perspective drawings (special 
form of ‘“‘block diagram’’); or second, by plan drawings, ignoring 
the vertical co-ordinate (temperature), and projecting the liquidus 
surface to the base. The base is an equilateral triangle. The 
lines forming its side are the plan views of the binary systems. 
The corners, then, represent the pure components. This method, 
developed by Roozeboom, divides the sides of the equilateral 
triangle into 100 parts. The percentage composition of each of 
the three components, forming the ternary system, is obtained 
from its position and the distance of the point P (see Fig. g) 
from the three sides of the triangle in directions parallel to the 
sides. 
The procedure of representing a three-component mixture or 
solution by a point within the triangle can best be shown by an 
illustration. Let us suppose we wish to represent a mixture com- 
posed of 50 per cent of L, 30 per cent of M, and 20 per cent of N. 
First 50 units are measured off on the side of the triangle LM 
(Fig. 9) from the corner M. Let this be point A. Next the 
constructional line AB is drawn parallel with the line MN, as 
shown. From L, 30 units are measured off on the side WL. 
This is point C. From C the line CD is drawn parallel to LN. 
