( 483 ) 
€, Ph met it &, (, - A 
(n—1)? 4 (n—1)? An? 
it appears that the locus of the points ¢, ande, for which the closed 
curve has the same width, is again the same parabola OPQ, but 
shifted in opposite direction of the axis by an amount of such 
a value that the projection on the e-axis is equal to (n—1)’ 
i cad . For the points of OPQ itself the width is, therefore, equal 
be 
= ny 
to 0, and for the origin, in which ¢, and e, is equal to 0, 2,—7,=1, 
and the curve occupies the whole width. The decrease of the values 
of «, and «, obtained by shifting in the opposite direction of the 
2 
te 
Lv 
axis of the parabola, promotes therefore the intersection of 
2 
and ce = 0, and so furthers the non-miscibility. In the same way 
ve 
E oe, 
we find, representing the value of Sn Lm: 
&,—n’é 
1 a Dare = = ee . 
(n—1)? 
So if we trace a line parallel to the axis of the parabola through 
if 
the origin, this line is the boundary for the points for which z,, re 
1 
For the points for which ¢, >n*e,, tm > ca and the other way 
about. 
And finally this property. We may also write the equation (@’) of 
p. 319 Contribution X indicating the limiting value of & which cor- 
responds to given value of e‚ and «, as follows: 
Eerd nen 
TES ae 
Let «=z, for one of these limiting values, then this equation 
becomes : 
nete A at ee ee 
(ale, (elle, 
And for constant value of z,, this Jast formula represents a straight 
line for the points (,, &,). On this straight line also the point must 
lie for which not only the one limiting value of z==,, but also 
the second, and for which the two values of x therefore coincide. 
as 
V 
In this case 7, = and 1 —z, = 
n—l n— 
ne, 
. Hence we get back again 
