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