192 PROCEEDINGS OF SECTION A. 
Exampre II.—Let u = x (= + a + =) ae 
b? Cc? 
oe sr aes * 
a % a 
whence 4 = 3 S*¥ 4 2 Bos +7 +—)= Cn + 3) 5" 
Ee) a a 
Examp.e III.—To evaluate J [3 (=+ = 7) where Pp, and p, 
are the principal radii of curvature at any rae of the ellipsoid. 
aie aave determining the lengths of the radii of curva- 
4 
ture is - as sas saz =o 
snk yf" 1 1 = 
where L = C. +a) at (= +- at + (+ :) 
entire Letty col 
Py P2 Se 
y 2 Sfi 1 1 
Selet x) ameeas 
1 Ip butt, Ti, 94 Likioalitgeae 
==/fh del Pints a Mas eos “lds 
= oe ux y Naa as. 
whereu == (jo + pas fe 1) and w= — Aas ~) 
1 
H ae. Dafoe a he 
ene &=2 (tart apr) 
“i ee =)=? s (sz) ie oe 
