as are terminated by Planes, &c. 28,^ 
which value in the equation of the curve, it is ultimately 
a % ( d* -|» a * ) a: 2 — ( af -J - y a )* ( ^ ^ J r JV 2 ) — 0. 
It is proper to remark, that though, in the enunciation, I spoke 
of the point as being in the surface of the cylinder, yet there 
is nothing in the above method of investigation that supposes 
it to be in contact with the solid : if there is to be a given 
distance between them, the nature of the curve will be the 
same. 
Cor. 1. If we make d infinitely small, there results 
a*x 1 — ( P-j-y*) 3 == 0 for the equation of the curve bounding 
the plane of greatest attraction ; and it is evident, that, by the 
revolution of this curve about its axis, will be generated the 
solid of greatest attraction, when it is sought for without any 
such conditions or restrictions as entered into the preceding 
problem. 
This exactly agrees with the conclusion arrived at by Sil- 
vabelle and Mr. Playfair. 
Cor. 2. If, on the other hand, we make d infinitely great, 
the equation is reduced toy 2 — ax — a: 2 , which is that of a circle 
whose diameter is a, the attracted point being in the circum- 
ference. Therefore, — of all infinitely long cylinders, having the 
areas of their bases, or transverse sections, equal, that which has a 
circle for the circumference of the said base , shall exert the greatest 
action on a point at its surface. 
Prop. 32. 
Let a given quantity of matter be fashioned into such a solid 
as was treated of at the beginning of the last section (in Pro- 
positions 24, 25, 26), viz. having its section perpendicular to 
the axis a regular polygon. The polygon being given in 
MDCCCXII. P p 
