( 616 ) 
Let us take the four substances: AB, AC, BD and CD between 
which may take place the double decomposition : 
AB+ CD= ACH BD 
If we represent the substances AB, AC and BD by the angles 
of a rectangular isoxeles triangle the rectangular side of which has 
the length 1 [fig. 1] substance CD is represented by the point CD 
so situated that the four points representing the four substances form 
the angles of a tetragon. What will now be the composition of a 
Pig. 1; 
phase represented by point p? This may be represented in various 
manners according to the nature of the three substances in which 
it has to be expressed. 
1. We take as components AB, AC and BD. 
The point p then represents z Mol. BD, y Mol. AC and, therefore, 
1—a2—y Mol. AB. 
2. We take as components Ab, AC and CD; p then represents: 
1 —y Mol. AB, « Mol. CD and, therefore y — 2 Mol. AC. 
3. We take as components AC, CD and BD; the point p then 
lies outside the triangle having these substances as angles; it then 
represents 1 — y Mol. BD, 1 — x Mol. AC and, therefore, a + y—1 
Mol. CD; «+ y—1 is negative in this case. 
4. If we take as components AB, BD CD p again lies outside 
the observed triangle; it then represents y Mol. CD, 1—e& Mol. AB 
and, therefore, c—y Mol. BD which latter quantity is negative. 
We may, therefore, assume in four ways that the phase p is 
constructed of three of the four snbstances; it is obvious that each 
