as are terminated by Planes , 283 
circle at the quadrantal points o and t ; and, I say, that the 
action, on the point p, of the infinitely long cylinder, whose 
base is the parabolic area owpvtco, is to the attraction of the 
furthest half of the infinite circular cylinder, exactly as 2 to 1. 
For the latter action has been shewn to be 2^ ; and if in the 
expression, obtained in Cor. 2, Prop. 27, we make » and x both 
= k , it is reduced to A = 4T 
5. In fig. 18, draw fug perpendicular to pu at u ; and from 
p, through o and t, the lines pof, ptg. The attraction, on the 
point p, of the infinitely long prism whose base is the triangle 
pfg, is equal to the attraction of the infinitely long circular 
cylinder. For the action of the prism is 4 x pu x arc. fpu (by 
Prop. 20) = 8k x ~ = 2^7 r ; and this has been already shewn. 
to be the attraction of the circular solid, 
§■ V. ■ 
Of Solids of greatest Attraction , 
The subject of this section has occupied the attention of' Mr.- 
Playfair,* in the same paper I have before noticed ; it had 
previously been treated of by Silvabelle. Frisi also, in the 
third volume of his works, gives a solution of the same pro- 
blem as that which is first considered by Mr. Playfair, but 
his result is an erroneous one. None of these writers have 
pursued the matter any further than what relates to the figure 
of a homogeneous solid of revolution. My manner of treat- 
# The problems which I investigate are similar to the first of Mr. Playfair^*, 
where the equation of a curve is sought; nor do I at all meddle with that other class 
of problems which he, treats of in the subsequent part of the paper. 
