520]
ON THE CENTRO-SURFACE OF AN ELLIPSOID.
349
we have
y _(K-3) (a- 1)
So- +1 - K ’
t 0 _ 3Kcr (cr — 2) + 12a-
r + 3= 3cr + 1 — K ’
(o- - 1) (3a - 2) K
A + V ~ Sa+l-K
or substituting for K its value we have
y, 1 K(a-2) + 4i
A + 1 3<r + l—iT ’
Y_ 3 (o- - 1 )jA r (a - 1) + I}.
3 cr + 1 — K
_ _ 3 (<r — 1) \K(a- 2)+ 4}.
Sa+l-K
K (<r - 2) + 4 = - -) 3 io- 2 - 2(7 - 7 -^
ya
(7 ~ a ) 3
yet
(7 - a ) :
(7 +
2
,7
y — ctJ \ y — a
3cr + 1 — K = {(3cr + 1) 7a + (7 — a) 2 <7}, = (Ho- + 7a),
if as before O = /3 2 — yet; and the result is
f = -& 2 -|(7-a)c7 jl -
3 (cr
+
2a
2 7
7 — a/ v 7 — a
(7 (3(7 — 2)
' s\r / il(T + ya l v
2a \/ 27
7 — a/ V y— cl
3 <7 +
(7 (3(7 — 2)
and changing the sign of the radical we have the values of tj 1 .
06. Write for a moment
A - \ (7 - «) o' -1 “
3 (7 + —
2a
7 — a
2 7 \
/ — a/)
(7 (3(7 — 2)
= (A — a + a V S) 3 = ^4 + i? V>S,
3 (7 +
2a
2y
(7 (3(7 — 2)
= 4'+.BV£;
then in the product of these two expressions the rational part is = A A + BB'S; but
from the manner in which they were arrived at we have 0 = AB +AB, and the
rational part is thus
=-