(ABL) 
a rule for the place of the points (e,‚e,) which satisfy the require- 
ment that the portion cut off by the closed curve from the line 
v= 0,, have a given value. 
From equation (8) of a 479 follows: 
1e — a —nte, le 
Rn et ee ee 1 Oak ed 
Bere ay | 
If we represent the highest value of « by «,, and the smallest 
by z,, then : 
eee] 4 le, 
(n—1)' 
or 
1e, (v,—2,) Br Bee: (a —#,) 
oh (n —1)? 4 | ET DL 
PO ER ret 
ET 1 An? | 
Ie krk) Sa _& (ee) 
ae =e eee jo ee An” | 
So the points for which z,—z, has an equal value, lie again 
on a parabola, and one of the same shape as that of fig. 36; but 
now it has undergone two shiftings. 
The first shifting is that in which all the points of the parabola 
have descended by an amount—=1 in the direction of the ¢,-axis 
which makes it the upper limit of the space now under discussion. 
But the second shifting is one which takes place in the direction of 
the diameter or the axis of the parabola. The amount of the second 
shifting must be such that it can be considered as the resultant of 
a displacement in the direction of the negative ¢, by an amount 
(enal 
equal to " (1 —1)* and a displacement in the direction of the 
(age)? (n—1)? 
4 dek 
ing as ”‚—®, is greater, this second shifting is more considerable — 
but as soon as the shifting would proceed so far that the parabola 
would have no more points inside the original space VPQ we have 
exceeded the possible value of z,—,. The extreme limits of z,—, 
1 n—2 
are then on one side O, and on the other side 1 — a ae 
This greatest value of x, —v,, which is equal to 0 for n= 2 itself 
approaches 1 with increasing value of 7. We may also express the 
Accord- 
negative ¢,-axis by an amount equal to 
