&g6 Mr. Knight on the Attraction of such Solids 
where t must be made rT or y‘ accordingly as the action of a 
triangle or rectangle is required. 
From this simple case, we may not only arrive at some 
curious results, connected with the particular hypothesis of 
density, but may find with equal ease the figure of a homoge- 
neous solid of revolution of greatest attraction, as will just now 
be seen. 
If the density was to be a function of a and T only, it would 
be sufficient to multiply the values found in the lemma, by 
that function, see lemma 1. 
Prop. 35. 
Let Prop. 31 be again proposed, but with this difference, 
that the force is inversely as the mth power of the distance, 
and that the density of any particle of the cylinder is as its 
distance (/) from that middle section (parallel to the ends of 
the cylinder) which passes through the attracted point. 
In the expression we just now found, in the preceding scho- 
lium, put x for a, and d (half the length of the cylinder) for t. 
The action of the cylinder is 
A = 4 ff\ 
t (m— 1 
— xxT 
™ + 
xxT 
1 1 9 
1 )(x*+T*+d*)^ (|»— !)(**+ r* 
its quantity of matter is 4 JffxTit = sjjxft*; so that we have,, 
for the equation of the curve bounding the base, 
c^+r)- 
( **+y 4 + d a . 
4. C d q = 0. 
m — i 0 
Cor. s. When d is infinitely small, this becomes 
m— 1 
(* a +y 
"L— + Gf, or — i-rr + C ' — o. 
Let a be the value of x when y ^0, then C' =3 — ™ ; and 
