as are terminated by Planes , &c. 
3 °5 
expressed by 
<P (r , x ,u ) — <p ( r , o ,u ) 
4- <P ( r 7 , x' ,u' ) — $ ( r' , X 7 , u r ) 
+ <p (r" , x 77 , w 77 ) — <p (r 77 , X 77 , u" ) 
+ (p (r 777 ,— x /7/ ,zi /,/ ) — <p (r 777 , — X' 77 , w 777 ) 
4” &c, &c. 
And in the same manner is found the attraction of the lower 
portion. If any part of the polygon, as p/, is parallel to pq, 
the attraction of that portion of the solid may be found by 
Prop. A. 
Scholium to Prop. 25, page 273. 
The following expression includes the attraction (on a point 
at the pole or vertex) of all this class of solids, where the 
generating plane is a regular polygon, and guiding curve a 
conic section : or where y* = (/ 3 a 1 4- y^ 2 ). 
A = 2/2 (x -f - 
n@ 
0a 
+ 7 * 
^ 7 T 4” 
arc (tang. — ~ s/^x 4- yT) — { (» — 2 ) 
j; Jo. — 
X ■ 1 + ya 2, 
in which p, = (1 4- r 2 ), 1/ = 1 4- yet* ( 1 + r 2 ), and 
znr0a, z 
v ( I + yal 1 ) 
V v 
( A 
M^ + v/f + n, or = 
2 nr 0a 
arc 
^ ' 11 ( i + 
(sine = -^7=) 5 accordingly as ? is positive or negative. 
Ex. 1. Let y = 0, « == 1, y = / 3 a: ; in which case the solid is 
the polygonal parabolic conoid treated of in the proposition ; 
and we have pc = /3 ( 1 4- r 2 ), v = 1, whence 
