Mr, Knight on the Attraction of such Solids 
partial forces A, B, C will remain unchanged, as, consequently, 
will the total force, both in quantity and direction. 
For, if we put m x a for b, the expressions of the forces 
become <p ( i, m, r) — arc (tang. = Aj , % (i ,m, r), \p (1, m, r ) ; 
which are independent of the absolute values of a and b. It is 
scarcely necessary to observe, that arc (tang. — Aj is the 
arc, to the radius unity, corresponding to the angle rvm. 
Cor. 2. When r becomes infinite, the triangle rmv is changed 
into a parallelogram, infinitely extended in the direction rv ; 
in which case, the expressions of the forces become very 
simple, viz. A = arc (tang. = —), B = L. - : a , C = L. 
&+vVTfr~» 
a 
Prop. 2. 
Let vmu, fig. 2, be any triangle whatever, pm a line per- 
pendicular to the plane of the triangle, at the angular point m : 
from whence, let fall the perpendicular mr on the opposite 
side uv; moreover, let pg, po, be respectively parallel to 
mr, vu. 
It is required to find the actions of the triangle vmu on the 
point p, in the directions pm, pg, po. 
If we keep the same denominations as before, and put, be- 
sides, r'=tang. umr, it is plain from the last proposition, and 
because the action of the whole must necessarily equal the 
sum of the actions of its parts, that 
A =; <p (a,b,r) + <p (zz, 6 ,r , )~ arc (tang. = A) — arc (tang. — A j ; 
B = % (a,b,r) + x(a,b, r '); C = ^ (a t b , r) — (a, b, F). 
When umv is a right angle, we shall evidently have arc 
