s6o 
Mr. Knight on the Attraction of such Solids 
Prop. 10. 
Let fig 6 4 represent, in every respect, the same as it did in 
Prop. 4; join pr, pv, pr' ; it is required to find the attraction 
of the square pyramid pmrvr', on the point p at its vertex. 
If we proceed as in Prop. 7, but make use of the expressions, 
for the action of the rectangle mrvr', found in Prop. 4, and 
put x for a , mx for b, m'x for b 1 , (where m = tang, rpm, mf 
= tang, r'pm ) there will result 
A == x<p (1, m, r) -f- x<p (1, m', f) — ^ ; 
B = x x (1, m, r) + xty (1 ,(< r') ; C = x$ (1, m, r) -f x x 
(1 i m , ,r'). 
But it will be better to make use of the more simple expres- 
sions, that were given in Prop. 4, by which means, we get 
A — arc (tang. = — — ] x 
v ° V i-ynp+m! 1 ! 
. r, (t / / I “ , > T ^ + m ) 
C — |L. (\/i -m + m) — L. -7== ]*• 
Prop. 11. 
Let the base of the pyramid be a regular polygon ; the 
vertex situated perpendicularly over the centre of the base; 
the attracted point at the vertex. 
By making use of the expression in Proposition 5, putting 
x for a , and mx for b [m being the tangent of the angle, at 
the vertex, formed by the axis of the pyramid and a line 
drawn from the vertex to the middle of one of the sides of the 
base, we get 
