520] 
IL £ = -a 2 , 
£1 = - ar 
ON THE CENTRO-SURFACE OF AN ELLIPSOID. 
9/3y£l 
r) = — a 2 + 
(/3-7) 3 ’ 
/ 7 „ (a — fi) 3 „ /3 (7 — a) : 
(° r n + lr ~- y (W lr 'iY’ v + <r ~ (B-rvy 
/3-7’ 
% = - ft“- 
N 
11 
© 
0 
II 
11 
1 
« 
1 S i 
XT'2 _ 7,2 7 “ ^ 
1 a /3-7’ 
Z cS ^(7-«) s 
«(/3-7) 3 ’ 
72 _ „a/ 3 ? -« 
"1 — 0 „ 0 > 
a /3-7 ] 
Ellipse, concomitant. 
Ellipse, sequential. 
a? = 0, 
Jv _ yo-w 
7 «03-7)*’ 
« (/3 - 7) 
- (Outcrop). 
337 
(Observe that at point F x , ^ of ellipse -p-+—=1, the coordinates of the centre 
of curvature are y = ~jjr> z= —, and it thence appears that this is the point in 
regard to which the ellipse is sequential.) 
III. 
f = cab 2 + o)~g 2 , rj = — a 2 ; 
li = orò 2 + eoe 2 , Vi = — a 2 . 
X =0, 
F 2 = - ÒW, 
Z 2 = — c 2 eo, 
^ = 0, 
F x 2 = — 6 2 CO, 
F x 2 = - c 2 eo 2 , 
« = 0, ' 
by = - a 2 , , 
c 2 * 2 = — a 2 , J 
(Node of evolute). 
39. Observe that these are the only ways in which it is possible to satisfy the 
equations 
0 = (a 2 + |) 3 (a 2 + v) = (a 2 + |i) 3 (a 2 + Vi), 
viz. starting from this equation we have 
I. 
C. VIII. 
n 2 + £ — 0, ci 2 + tjx — 0, 
43