as are terminated by Planes , &c. 259 
into four equal triangular pyramids ; and, using for each of 
them the notation of Prop . 7, we have for the action of the 
whole rhomboidal pyramid, on a point at its vertex, 
A == 4-rp ( 1 , m, r ) -f 4 X(p ( 1 , m, f) — Q7TX. 
The other attractions evidently destroy each other. 
It is not necessary, in the above proposition, that the per- 
pendicular pm should fall within the base ; if it falls without, 
we shall however have occasion for the following problem. 
Prop. 9. 
Let umv, fig. 3, be any triangle whatever, p a point any 
how situated with respect to it; join pm, pu, pv.* It is re- 
quired to find the attraction of the oblique pyramid pumv, 
whose base is the triangle umv, on a point at the vertex p. 
Let fall, from p, the perpendicular pm' on the plane of the 
base umv, draw the lines m'm, m'u, m'v. Find, by Prop. 7, 
the attractions of the pyramids pm'uv, pm'um, pm'vm, whose 
bases are m'uv, m'um, m'vm, and their common vertex p. 
Resolve these attractions into others in the directions of any 
rectangular co-ordinates, and when thus resolved let the ac- 
tions of the pyramids 
f pm'uv . . fA , B , C 1 
in the directions of these „ 
< pm'um > , < A' , B' , C' >. 
1 I co-ordinates be 1 _ 1 
[pm'vm J [A", B", C"j 
It is plain, that the actions of the pyramid pumv, on the point p, 
in the directions of the same co-ordinates, will be A — A'— A"; 
B — B' — B"; C — C' — C". 
* I have not actually drawn the lines, to avoid confusion in the figure, 
