282 Mr. Knight on the Attraction of such Solids 
variety that occurred to me, are sufficient to shew the use that 
may be made of the expressions given in the first section. 
The attractions of certain infinitely long cylinders, which 
were derived, as corollaries, from some of the preceding pro- 
positions, present us with several curious relations ; with these 
I shall terminate the present division of my subject. 
Let pout, fig. 18, represent the base, or section, of a circular 
cylinder, infinitely extended both above and below the plane 
of the figure. Let p be an attracted point in the circumference 
of the section. Draw the diameter pu, and, at right angles to 
it, the diameter ot. 
By Cor. 1, Prop. 27, the action of the whole cylinder on the 
point p is 2&7r [k being the radius of the circular section); the 
action of that half of the cylinder, whose base is the semi- 
circle opto, is 2k (7r — 1 ); the action of the other half of the 
cylinder, which is furthest from p, is 2&: therefore, 
1. The attraction of a sphere is to that of an infinite circular 
cylinder of the same diameter ( on a point at the surface of 
each) as | to 1, which is the ratio of the solidity of a sphere 
to that of its circumscribing cylinder. 
2. The attraction of the whole infinite cylinder, on p, is to 
the attraciion of that half which is furthest from that point, as 
the circumference of a circle is to its diameter. 
3. Consequently, the attraction of the nearest half, is to that 
of the furthest half, as the difference between the circumfe- 
rence and diameter of a circle is to the diameter ; or nearly as 
3 to 1. 
4. In the circle optu, fig. 18, inscribe the parabola ow'pvt, 
whose equation is kx = y*, so that its vertex may be at p, and 
its axis coincide with pu: this parabola will plainly cut the 
