( 281 ) 
a,—ab, > 0 
a,—Âb, > Q 
a,—Ab, Pee 0 
(a,-—Âb,) (a, —Âb,) — (a,,—Ab,,)? > 0 
(a, —Ab,) (a, —Ab,) — (a,,—Ab,,)? > 0 
(a,—Ab,) (a, —Ab,) — (a,,—Ab,,)? > 0 
(4,,—40,,) (4,;—40,;) war's (a, —4b,) (a,,—40,;) De, 0 
(a,,—4b,,) (4,3 —40,;) — (a, —Ab,) (a,,—40,,) > 0 
(@,,—A40, 5) (4,3 —40,;) — (a, —Ab,) (a,,—Ab,,) > 9, 
and 2, must satisfy equation (2). 
The first set of three inequalities indicates, that this value of 2 
must be lower than that of the components. The second set indicates 
that it must be lower than the minimum value of 4 for each of the 
pairs of components of which the ternary system consists. The third 
set must be fulfilled in order that 2, y and 1—a—y be positive. 
2 ys a 
Sn 
2 1 
a, 
b, 
a, 
Tine 
Let us assume Sand suppose that the values of 
) 
23 . 1 
a, a i Gs, 
— and — are higher than that of — 
b, b, , 03 
without deciding anything 
1 . ann a a 
about the relation between the values of the quantities 7 », and 5 
) 
1 2 3 
According to our assumption the expression 
(a,,—4 bi en A Bis) AT (a, —À b,) (a,,—A be) 
a a et yt Je 
is negative for A= and also for 4=—* and it is positive for 
12 13 
Cos > a, 5 e a > 
IE aa and for 2 = Re: This is perhaps best illustrated by a graphical 
) 
23 1 
a, 3 
and 
, ‚a 
Here the points 12 and 13 represent the values of —* and 
13 13 
the parabolic curve passing through these points the value of 
(aA b,,) (4,3—4 4,,)- 
In the same way the points 23 and 1 represent the value of 
a a d ’ : 
i and of and the parabolie curve passing through these points 
23 1 
the value of 
