as are terminated by Planes , &c. 263 
Prop. 9, or into portions of pyramids, like that treated of in 
Prop. 15; and consequently the solution of the problem may 
be obtained by means of these propositions. 
§• III. 
Of the Attraction of Prisms . 
Prop. 17. 
To find the attraction of a right prism, whose base is a re- 
gular polygon, on a point in the produced axis. 
We saw, in Prop. 5, that the action of a regular polygon* 
on a point situated perpendicularly over its centre is 
A = 2 n arc (tang. — ■ y \/ 1 ~r- 6 s ) — (« — s) ?r. 
To find the attraction of the prism, change a into x , mul- 
tiply by x 9 and take the fluent. 
Now ^ x arc (tang. = ~ s/ x*-j- ( 1 4- r) & ) = \J* X x q> ( x, b , r) 
= x arc (tang. = — \/x 2 + ( 1+r 2 ) b) —JT X arc (tang. = ~ 
s/ x* (1 + r') b') = x arc (tang. = — V x* -f- ( 1 -J- r z ) 6 2 ) 
rb z xx 
(b z -{-x z ) (1 -f r z ) 
■, because arc = 
tang. 
1 + tang. 
+/i 
taking the fluent,* it becomes = x arc (tang. = ~ 
Vx-+ (i+r‘) b‘) — b L . liiXg+232. 
; and, by 
f 
* Put jt 1 + (1 -{■ r z ) b z — z z , b 2 -f x 2 — z z — r z b z , xx — zz ’ 3 then 
rb z xx 4^ rb 2 z 
(b 2 - j-x 2 ) b z -i-x z 
(z-{-rb) z 
r 2 b 2 
— L . - g (Simpson’s Fluxions, 
2 s — 
, b _ 
^/(i-[-r a ) -f rb 
