344
ON THE CENTRO-SURFACE OF AN ELLIPSOID.
49. We have then
2 o 7
a¥ =
/3
1 + r. 1 + Í,
7 s A + r + 3q + 3g(r + g)\
/3 V 7 7 2 / ’
= -t( i+!A3î_6 ÿ
/3 V 7‘ 7
“ £ 1 1 + q*
r r
4 (7 — a) 6a
_ _ 7_
/3
1 + q 2
7“a 7-a
2 (/3-7)1.
7 2 a
• > a? / v\ [ v\^
and in the same way from cV = — ^ ^1 — -J ^1 — -J , we have
moreover we have at once
/3
6y =
7 oc
gV _ 3ç 4
7a 7a
Hence, writing x + Bx, 0 + By, z + 82 for x, y, z, we find
._!* 2 (^-7)
2 ' 7 2 a
-2 (a-13) 9
OZ —iz . . 0-,
2 7a 2 1
or, what is the same thing,
a, : & = : ± * JI : ,
7 2 a 6 V 7a 7a-
where ¿r, 0 denote the values at the umbilicar centre.
a J x-‘ =
Nodal curve in vicinity of real outcrop, viz.
z — 0. Art. Nos. 50 to 52.
/33 (7 - a y _ «3 ( a _ 7 )3
7 (a — /3) 3 ’ ^ 7(«-/S) 3 ’
2 4- *7
ga/3X2
. a
50. Write