§74 JMr. Knight on the Attraction of such Solids 
tion becomes A = n (x -{- a) 2A — 7r ) + 2 xk -f znarL ( s / x 
4- \/ x ( 1 4- r ) 2 ) + corr. 
When 1 = o, A — y ; so that, if the fluent is to begin at 
that term, we have corr. — — %nocr L V ( 1 4- r*) a. 
If we would find, from this expression, the attraction of the 
limit of these solids (which is the parabolic conoid) we must 
observe, that the arc A may be put under the form 
— arc (sine == r -- x whence, because r is infi- 
2 v Vi y/ x + J 
nitely small, 2A — tt = — 2 r . = — 2 — . — —l . qu. 
J V'x + ct n V'x+a. 1 
prox. ; substituting this value, and n for nr, and neglecting r% 
we get 
A — 27T I X — s/ X* -j- aX 4“ «L ( V X V X + *) } + corr. 
for the action of a parabolic conoid on a point at its vertex. 
Prop. 2 6. 
Let the curve pr be a parabola convex to the axis pm, in 
2. 
which casey = ~ ; and we have, by proceeding as before, 
A = 2 nfx arc (tang. = y \/ 1 4 ~ — } ) — (»— 2) ttjt; or 
A== 2«.r arc (tang.= y 1 4* .x % ) 2 nfx arc (tang. — ~ 
\Z 1 4 — x 2 ) — (n — q) ttx ; if we put a* = — — 2 , the 
term, under the integral sign, becomes 
— 2;7/r arc (tang. = — V a? 4" x% ) 
x ( i -J- r z ) a r x 
y/a z -\-x z | (j -J-r 2 )a 2 -f x z 1 
