left side of 12 and on the right side of 1. Also in this case this expression 
is positive and even within broader limits. 
In the case that a value of 2 for which the left hand member of 
equation (2) vanishes, is higher than the value discussed for these 
three expressions, a minimum value of 2 will exist, which represents 
a really occurring minimum critical temperature. Let us write equation 
(2) in the following form: 
{(4,—4,) (a, Ab) — (an Ab) (a, —20,) (aA) — (a,,—26,,)3} — 
—{(a,,—A b,,) (a,;—4 b,,) — (a,—2 b,) (a,, —4 Oasis 
The first member is negative if we choose for the value of 2 either 
the minimum value of 4 for the pair 1 and 2, or for the pair 1 and 
3. We will denote these minimum values by (Ax), and (2,), 5- 
On the other hand the first member is positive if we choose for 2a 
value for which the expression, the square of which must be taken, 
vanishes, — this holds however only in the case that the value or 
this last root is lower than that of the quantities (4), and (amn),,. In 
this case the equation (2) has a root which satisfies all the requirements 
for a minimum value of 4 at positive values of 1—w—y, wv and y. 
As an instance we choose the following numeric values: 
ON Lea gS A GA Puna? eme PAN OS 
Ee tk 
b, b, bs Dis 4 beg 03 
a=48, 0,=448, a,=3.872, a,,=4.2, ABT , a,,—3.4924 
From this we find: 
(Ain), = 2.933 
(Gy = 9.969 2. 
Gai =o bores 
A value for 2< 2.933.... makes therefore the three following 
expressions positive : 
(a,—A b,) (a,—a b,) — (a,,—4 b,.)° 
(a,—2 b,) (a,—A b,) — (4,,—4 Db) 
and (a,—A b,) (a,—A b,) — (a,,—2 ba) 
For the value of à for which the quantity: 
(a,,—2 b,.) (a,,—4 6,,) — (a,—A b,) (4,,;—A bs) 
is positive we find: A >> 2.884.... 
For the value for which the expression 
(a,,—Ab,,) (a,,—46,,) — (a,—A46,) (a,,—A4,,) 
is positive we find: 2 >> 2.855 and the last of the given expressions 
. wie 4 5 7 - d,. al 
is positive within the limits “~<“a<—. 
bs b, 
