292 Mr, Knight on the Attraction of such Solids 
infinite in the third, the result would be the equation of the 
base of the infinitely long cylinder of greatest attraction ; which 
however is by no means the case ; for that was found to be a 
circle, whereas the equation we get here is 
x ~C (.T+y s ) 0, 
and if we make a infinitely great in the first example, the 
equation becomes C' = ■£*-{- y% or the line pr is a circle with 
its centre at the attracted point. 
We might resolve this problem, on a variety of hypotheses 
respecting the density; or we might add other conditions of 
a different kind; for instance, not only the mass of the solid, 
but the area of the section, passing through the required curve 
pr and axis pm, might be supposed constant. But I pass on 
to other suppositions respecting the force of attraction ; which 
will be treated with as much brevity as possible. 
Lemma 3. 
To find the attraction of the triangle vrm, fig. 1, on the 
point p, in the direction pm, supposing the force to be inversely 
as the mth power of the distance. 
Keeping the same notation as in Prop. 1, we have, for the 
attraction of an element at q, JL; which being re- 
T*-f a) e 
solved, gives, for the force of the whole triangle, in the direction 
pm, A ~ ff - — ; the fluent is to be taken from 
t = 0 to t = rT, and we have 
A = « 5 1 _ ( 2 - m ) 
(«*+:r»)(a*+ (i+r a ) T l ) 2 t 
U— «) Trader- &c -h 
+ ( 2 — m) 
