as are terminated by Planes, &c. 
26 1 
A = 2 nx arc (tang. = - vA 4. ( 1+ d) ml) - (n — 2) vx. 
Hitherto, I have considered the action of a pyramid, only 
on a point at its vertex ; the case which next presents itself, is 
that of the attraction on a point p' (fig. 5 and 6) any where 
in the produced axis mpp'. It would be easy to give a direct 
solution to this problem, but I choose rather to make it depend 
on the propositions that have been already established : and 
to shew that the functions <p (a, b, r) % (a, b, r ) $ (a, b, r), of 
which so much use has been made, in the preceding inves- 
tigations, are sufficient in all cases of the attraction of bodies 
bounded by planes. 
Prop. 12. 
Let pumv (fig. 5) represent the same pyramid as in Prop. 7; 
to find its attraction on a point p' in the produced axis. 
Suppose p'u, p'v joined, the attraction of the pyramid pumv, 
on the point p', is the difference of the attractions of the pyra- 
mids p'umv, p'upv on the same point ; which point being at 
the common vertex of these two pyramids, their attractions 
are found by Propositions 7 and 9 ; and the problem is solved. 
Prop. 13. 
Let it now be the action of the pyramid pumv, fig. 7, (where 
the plane of the base umv is not perpendicular to the line rnpp') 
on the point p', that is required. 
The attraction sought for will still be the difference of the 
actions of the two pyramids p'umv, p'upv, but these must now 
both be found by Prop. 9. 
MDCCCXH. 
M m 
