( 487 ) 
cx( 1 — x) ca(1—.w) 
eee (sa) aa En 
1 ae 1 
ACE a eee 
ce cl—x (n--l)P? ew = (nm - 1)7(1 — 2) 
or 
call — x) L 
tae Pie ee 1 +| F, 1, we, i! zij 
(n—1)?# = (n—1)?1l—«a (n—1)?w © (n—1)? le , 
Now there is a series of values of ¢, and e, (see p. 483) for which 
En el n'e, 
1 
ei, ——— = Fis d : g 
=i Co is equal to 0. All these values 
are given by a line which touches the parabola in a point for which 
We, 
ates 
mined by the value of n, and lies on the line which passes through 
the value of 
==, so a point which, as the parabola itself, is entirely deter- 
ae deld ieee Era VEN 
the origin in a direction ——=7? (=) This direction approaches to 
Es ei 
Re ies : 
on for very great values of n, and to »° itself for values of # which 
are but little greater than 3. All the values of ¢, and e, occurring 
below the parabola are reached when lines are traced parallel to the 
said tangent. Thus: 
i n's 1 
eps cx ee SE 4 
(n—l?e = (n—1)? l—ez 
represents all the points below this tangent, when « is given the 
negative sign; and then the second member can descend to — 1, in 
which case the origin itself might occur. All the points above the 
said tangent are reached, when « is given the positive sign, and 
I 
then made to ascend till 1 + a@—=-—, in which case the point Q is 
Hi 
1 
reached. For « such that 1 + « = me the point P is reached. 
it 
So we have for points below the tangent: 
er (le) l 
a eal 1 n° 1 
— + —a 
(n—1)?  (n—1)? le 
in which a lies between O and 1, and is =O on the tangent itself. 
For points above the tangent we have: 
