264 Mr. Knight on the Attraction of such Solids 
For the sake of brevity, call this quantity F (b, r,x ) and we 
have for the attraction of the prism, 
A = 2?iY [b,r, x) — (n — 2) ttX -f- corr. 
The attraction of any other right prism, in the direction of its 
length , depends on the same function F (6, r, x) ; as in 
Prop. 18. 
To find the attraction of a right prism, whose base is a rect- 
angle, on a point in the produced axis. 
We saw in Prop. 4, that the action of a rectangle, on a point 
situated perpendicularly over its centre is 
A = 4$ {a, b, r) + 4^ ( a , b', d) — 27 r, 
where b and b' are the halves of the sides of the rectangle, and 
r and r' the tangents of the angles, formed respectively by 
those sides and the diagonal. By changing a into x, and mul- 
tiplying by x, we have, for the prism, 
A = 4 fx(p ( x,b,r ) -f- 4 fx(p ( x , b', d) — 2 vx; whence, 
by w'hat was done in the last proposition, 
A = 4F { b, r, x) -j- 4F (6', d, x) — 27 rx + corr. 
Prop. ig< 
Let the base of the prism be a rhombus, the attracted point 
in the produced axis of the prism. 
We found, in Cor. 1, Prop. 2, that the action of a rhombus 
on a point situated perpendicularly over its centre, is (keeping 
the notation there used) 
A = 4<p {a, b, r) + 4 <p ( a , b, r') — 27 r, therefore, pro- 
ceeding as before, we have, for the prism, 
A = 4F (6, r, x) + 4F (6, d 9 x) — 2ttx + corr. 
