85 
For the surfaces which have no centre, a=0; a’=1, a”“=m, c’ = — 
ro|'S 
Avge 
e= => =m 
A 
© ale toHAD 0 p? m—1 
ues AeA. bn A, af® 0 
we shall consider 2a the greatest axis and 2c the least, in surfaces 
which have acentre. Also m will be considered greater than unity 
and p positive. These suppositions, while they simplify the investi- 
gation, do not impair its generality. 
Prop. 
To determine the lines of Curvature of the Ellipsoid. 
The equation of the ellipsoid is 
a°b?2z? + a®c?y” + b’c?x°=a*b*c* 
The quantities e and f are therefore 
_B@ =e) 
a?(b? —c*) 
Ba? oh 
pa B@ad, 
Since a > band b > c the quantities e and f are essentially positive. 
‘To determine the lines of curvature it will be necessary to in- 
vestigate the loci of the equations 
P2 
