as are terminated by Planes , &c. 2 53 
(tang. = yj -j- arc (tang. = A-J ~ -j> v being the number 
3,1415, &c. : this makes the expression for A somewhat sim- 
pler, in that case. 
If it is the triangle vmu' whose attraction we seek, we have, 
putting r' = tang, u'mr, 
A = <p ( a,b,r ) — <p - arc (tang. = ~) + arc ( tang. = ~] ; 
B = — %(a,6,r'); C = 4 / (fl, 6, r) — 4 / (a,b,r’). 
Cor. 1. As a rhombus may be divided, from its centre, into 
four equal triangles, like that in fig. 2, but right angled at m, 
the angle lying at the centre ; if b represent a perpendicular 
from the centre of a rhombus on one of its sides, and r and r 7 
the tangents of the angles, that this perpendicular makes, at 
the centre, with the semi-diameters of the figure, we shall 
have for the action of the rhombus, on a point situated per- 
pendicularly over its centre, at the distance a, 
A = 4 <p (a, b, r) + 4 <p (#, ft, r') — 2 tt. 
Cor. 2. As any plane, terminated by right lines, may be 
divided into triangles from a point within it, we may find, by 
means of this proposition, the attraction of such a plane, on a 
point above it, both in quantity and direction. Let, for ex- 
ample, uvuVu, fig. 6 , be the plane, p the attracted point; let 
fall the perpendicular pm on the plane, and from m draw right 
lines to the angles u, v, u', x'; the plane will thus be divided 
into triangles, situated, with respect to the point p, like that 
in the proposition. 
The attraction may still be found, if the perpendicular should, 
fall without the figure ; as in 
MDCCCXII. 
LI 
