( 228) 
a a 
Sorat 12 . ‘ . 12 
value of à we have an > and for a maximum value dn 
) 
12 12 
If 2 has the value of 2, also the following two equations hold: 
0 A,,—And,, 
lt a,—Anb, 
and 
ae se Qig—Am) 
Ld a, Amb, 
v xe 
As must be positive because » must lie between O and 1, 
eu 
the sign of @,,—4,b,, is opposite to that of a,—Anb, and a,—Anb,. This 
agrees with what we have deduced concerning the relative value of 
1a 
bi 
We should have obtained the same results, if we had written the 
Am and 
relation @, = 2), in the following form: 
—Ab,.}? 
ne RAe AD a) ME 
| (a,—Ab,) 
a,—Ab, 
In the ease that a,—db, is positive namely this equation cannot 
be satisfied if the coefficient of «7 is positive; so if 
(a,—Ab,) (a,—4b,) — (a,,—46,,)? > 9. 
If the coefficient of 2? is zero, then this equation can only be 
satisfied if we put: 
(a,—4b,) (1—z) at (Oe) oa 0; 
„On the other hand in the ease that ¢,—2, is negative this equation 
cannot be satisfied if the coefficient of 2? is negative. This however 
also yields: 
(a, —Ab,) (a,—4b,) — (a,,—4b,,)° > 0. 
If therefore we have the equation: 
(a,—Ab,) (a, —ab,) — (a,,—Ab,,)* > 9 
then the value of 2 must be either less than the minimum value of 
Ay 
At . 
—~ or more than the maximum value. 
dor 
We must however distinguish between a minimum’ value of 4 
EH 
which occurs at positive value of iL and a minimum value of 2 
tI bi 
v& 
. The former, which really 
corresponding to a negative value of 
ih 
: : Qi, . a a 
exists, requires that — is both smaller than — and than ~. The 
ie 4 b, 
