8 © 
in general,/ 
Mr. Ivory on the Attractions of an 
x z . dx x 3 
i + ^x 2 -) . ( i -f a' \i z ) '/(H- ? z x z ) . ( 1 4- a'^x 2 ) 
— ~ -j- ~r * 
i'^F 
! dx 
dF 
' * 1 dX 1 * 
2ff . OX 
therefore, making .r = l, the first term will become, 
2? r . fl* f I I /dF\ , I fP\\ 
V7T ’ t A/(i+A"j 7(7+7*) 1 * Um ‘ U*'l ) 
With regard to the term containing b 2 , it may be changed 
into an equivalent expression similar to the first term we have 
just been considering: for if, at entering on this investigation, 
we had substituted in the equation of the solid, x = R . V i — p/* 
■. cos. V ; y — R' . p/ ; % = R . v / 1 — p/ 2 . sin. 2 «s ' ; which sub- 
stitutions are entirely arbitrary ; we should have found s = 
e\i! 2 -j- (i — (A 2 ) cos. V-f j-f x ( l — p/ 2 ) sin. V; and the term 
we are seeking, multiplied by b *, would have been changed 
into 
r.ffiog.s.dx.Jx'.ax-i)-- 
and hence by proceeding as before, we derive this value of 
that term 
r , ff tXidx±L _ r yyy. . ^ ^ , 
and if we put = — i).p/ s ; q —f -j- ( e — /) . p /2 ; 
: then, s ~p . cos. ‘s' 4- q . sin. V ; 
COS. U 1 1 1 2 ’ 
du ; consequently, by substitution, and integrating with 
also v7E| . 
p ; COS. U 
du 
S "Y pq 
regard to «, and confining the integration with regard to p/ be- 
tween the limits p/= o and p'= i ; we shall get, 
e . fT z . d/X 27 jr . 
27T . b~ . 
^ | I+(«— O.f*'* j • •#*'*]■ 
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