IV. A new Demonstration of the Parallelogram of 
Forces. 
By JOSHUA K'ING, Esq. M.A. 
FELLOW AND TUTOR OF QUEEN’S COLLEGE, 
[Read April 14, 1823.] 
Ler two equal forces, each of which is represented by p, act 
upon a material point inclined to each other at an angle 20, 
and let r be their resultant; which will evidently bisect the 
angle 20; for there is no reason why it should be inclined to 
one force at a greater angle than to the other. 
Now for every value of 6, r will vanish when p vanishes, but 
only upon that supposition. Again, for every value of p, r will 
30 5a 2n+1 
vanish when 0 = +“, or + Q> OF +> or &es es) bat 
2 
ae 
upon no other supposition: Hence the factors p, 
? 
2 92 
Qa -2*) &c. will enter into the expression for r, but no other, 
except quadratic factors having impossible roots: we may there- 
fore suppose 
r=k.p.(1-=%). 0-29) A - oe &e. 
=k.p. cos. 0. 
