as are terminated by Planes , &c\ ogs 
Cor. 1. For a polygon of sides, these expressions must 
be multiplied by 2 n as usual ; and when m is greater than 3, 
A = 2 nfaTq* [a, m, T, rT), if in this we make n infinitely 
great and r infinitely small, it ought to enter into the general 
case of the attraction of a circle given in Cor. 1, to the first 
part of the lemma : and in fact we get 
A = j 1 i, —P-Zs- _ 4. j_ , 
Lm — i ” (rn~ i( (m— 3) i (m — 1) (??i — 3) m — 5) ' 
(m—2) ( in— a . ) 3 
(m— 1) (m— 3) 2 
(w — 2) (i»-4) ........ 3 7 f znarTf } 
■T ( m-i) ( m-3) 2 } 3 
cause the quantity between the brackets is plainly equal to unity , 
becomes A = \J *- • 
znraTT 
(a 2 -f T 2 ) 
which is the same form as was 
found before for the general case. 
Cor. 2. When r becomes infinite, and the triangle rmv is 
changed into an infinitely extended rectangle, we have for its 
attraction 
A 3-5-7 (m-z) p aPr 
2, 4- 6 ( m — 0 2 (« 2 -f T 2 )ZJ 
2 
except when m—i. in which case, A = f — 
J 2 vV+T* 
Scholium. 
This lemma has been treated on the supposition that the 
density is the same at every part of the triangle rmv, fig. i ; 
but there are other hypotheses which render the solution 
easier: for instance, we may conceive the density of a particle 
at q to be as its distance ( t ) from the line rm, in which case 
A =iT; 
aTtt 
(«*+ t z + rpPt, 
2 
^ f (m-i) 
■ aT 
(a 2 + T 2 + t z )~- 
m — 1 
aT 
(w-i) (a a -f T % i 
Qq a 
a 
