3 o6 Mr. Knigi-it on the Attraction of such Solids 
A = 2 n (x-f ( 3 ) arc (tang.= E s/ (3 (i -j- O x + x a ) — j [n— 2) 
x + »/ 3 }» + 2«r(3L (7== + s/ ^75 + 1), 
the same as was found before. 
Ex. 2. Let /3 = a, y = — i,y a = “i («x — x 4 ) : 
here the curve pr, fig. 15, is an ellipsis whose diameters are 
a and b, a being that which coincides with the axis pm. We 
have, in this case, y = ~ (i+r),„ = i— £(1 + r 3 ), and 
the attraction of a polygonal spheroid, on a point at its pole, is 
A = an (x + ~) arc (tang. = 7^7 ( i+f) x+ ( 1 - (1 +GK) 
- {(n-a) x + + 9. 
2 nra z b z 
^ £ III U U 
where <& = — - — --== 
T (!+ r 2 ) 
y/ | a 2 — (i-J-r 2 ) 6 2 | x 
V ( I+ r *)6 2 |x 
v' b z a ( 1 -{- r 2 ) 
+ 
6 2 a (1 + r 2 ) 
2 nra z b z 
+ 1 | , or 
arc (sine 
•y/ 1 (» + r a ) - a 2 | 
6 2 « ( 1 -f r 2 ) ' 4 
(a z -b z ) v(i + r 2 ) 6 2 _a 2 
accordingly as is greater or less than 1 -f- r 2 , or as y is 
greater or less than the secant of half the angle formed at the 
centre of the generating polygon by one of its sides. 
When x — a, the first arc in the above expression becomes 
simply arc (tang. = Ej — i!lzAll } and we have for the action 
of the whole solid , A = ^ — yrrp. n, ^ representing <p after a 
has been put for x. 
In like manner, may the action of the solid be found when 
