Mr. Knight on the Attraction of such Solids 
when m = i. The curve is then transcendent, and has for its 
equation xjL . ( x 1 — j— y 2 — j- d j — xL . (x 2 — y 2 ) — j- Cci T o. 
Cor. 3, If the cylinder becomes infinitely long, [in being 
positive and greater than unity ) the equation of its base is 
— £ + C '=0; 
(**+y*)- =z 
let a be the value of x when y 
equation becomes 
0 ; then C' = 
—1 
and the 
(x'+y*? 
0. 
rn 
2, as in tlie case of nature, this becomes 
x % +y* 
so that the infinitely long cylinder of greatest attraction will be an 
infinitely long rectangle , with its edge turned to the attracted 
point. 
If m = 3, we have ax = x 1 -y 9 , the equation of a circle 
with the attracted point in its circumference. 
If m = 4, the equation is a 2 x = (x 2 -f-y 2 )f, which is Mr. 
Playfair’s curve of equal attraction. 
If we want the figure of the infinite cylinder of greatest 
attraction, when m = 1, we must have recourse to the last 
corollary ; where we found 
xL ( x" -j- y a -f* cC) — xL (x 2 -f-y 2 ) = C'. 
This, when d is infinite gives xL . dd=. C', or, x = const., the 
equation of a plane perpendicular to the axis of x. 
Cor. 4. If we would solve Proposition 34, but with this dif- 
ference, that the force is now inversely as the mth power of 
the distance, and the density, in the generating rectangle uvv'u, 
fig. 15, is, at any point, as its distance from rm ory ; we need 
only put f (x) (given by the nature of the curve pr) for d, in 
the equation here found, and we get that of pr, in the case of 
