(l-V3)-i(l + V3) „„ 
- U2 W*> 
as may be verified by squaring. 
Hence finally, 6 and k denoting the values just obtained, 
— 1 + dscd 
1 + dscd ’ 
3/n &2(1 + d*s 2 ) 
y-W-*)- V 1 \ M 
or, writing as before, X = dscd, we have 
f?r _ ux ^_2*(1 + 0V)\ 
whence 
and then 
that is, 
or say 
(1+X) 2 ’ y (i + xy 
dx 
dx 
2 *dX 
(1 - x 3 f ’ tf ’ (1 + 0V) 2 ’ 
dX = # {1 — 2 (1 + k 2 ) s 2 + 3&V} du, = 6 (1 + d' 2 s 2 ) 2 du ; 
dx 
= 2ty. du ; 
J(l-x 3 )$ 
(1-xrf 
f dx 
(1-0 
the required formula.