( 479 ) 
“aay U 
» 
a: — (Le) <0 
Ka 
Ie 15; 
EEE 
——, we obtain 
And taking into account that «2, = Vase 
as condition : 
Est 
nl> VIe He, 
I have given it in this form in the “Erratum” accompanying the 
preceding Contribution. 
Before discufssing the signification of this condition I will remark that 
we might, indeed, have obtained this result in a less intricate way. 
Let us directly put the value »v = b, in the equation for the closed 
curve, and let us examine what value of « then satisfies the equation. 
If v= b,, then v—b = (6,—4,) (1— 2), and v? = 6,?. Equation (a) of 
Contribution X p. 318 becomes then: 
wal dens cx (l—e) 
n a 
or 
(a) OREN EE 1 
Lo ee) 
c c 
or 
1 1 
We ole ila Ee) oz (len) 
then we find as condition for the ay eee ae of z for which v= bb: 
1+-e, if 
ae a Ge 
—x(l—z)=0 
or 
OLS aes alice Ea RENT 
ae (x—1)? 
As 1+ «, must certainly be positive, because a negative value of 
a, is inconceivable, we see that if the above equation has real roots, 
it must have two for positive values of z in all possible cases, also 
if «, and «, should be negative. The condition for the roots being 
real is: 
32* 
