as are terminated by Planes , &c. 
273 
Prop. 25. 
Let the directing curve pr be a parabola ; the attracted point 
at the vertex p of the solid. 
We must here make use of the formula in Prop. 5, as we 
did in the last example ; but as the equation of a parabola is 
y* = ax, this latter quantity must be put for b\ Thus we get, 
for the attraction of the solid, 
A — 2 njx arc (tang. = ■— V x z -{- (1 -j- f) ax') — (n — 2) ttx. 
The part, having the sign of integration, may be put under 
the form 2 nx arc. (tang. = ™ 1/ (1 -j- r 2 ) ax ) znfx arc 
(tang. = iv / x 2 -f (1 -J- r 2 ) ax) ; in the last term of which 
put = x, and it will become 
wife' arc (tang. = ~v / % 2 +( 1 + r2 ) i5J ) 
— 2 nar f \ 
(. Vz 7 --)- (1 r 2 -) a (T + a ) ( 
L=1 
f (1-H 2 ) 
inur 
z 
V z*-\ a 
| L ( % ✓ % -j- ( 1 ■=!" r) «) 
)}• 
— arc ( sine == ■■ f. - s 
r v <*/ j _i_ r s 
Collecting all the terras, we have at length 
A = nix arc (tang. = ~ \/ x 2 + (1 -\-r)ax) — 2noc arc (sine = 
~== x -==) + %nar L(«/.r-fv / .r+( 1 -J- r*) a) — 
( n — 2) ttx -f* corr. 
It is observable here, as in the last proposition, that each of 
the arcs in this expression is the complement of the other; 
put A = arc (tang. = — \/ x* -j- (i + r 1 ) ax), and the attrac- 
