512 Mr. Cavendish's Experiments to determine 
rating the arm; and therefore, in order to find the force re- 
quired to draw them out of their natural position, we must find 
the proportion which the forces spent in accelerating the arm 
and balls bear to each other. 
Let EDC e d c (fig. 4.) be the arm. B and b the balls. C s 
the suspending wire. The arm consists of 4 parts ; first, a deal 
rod D cd, 73,3 inches long; 2d, the silver wire DC d, weigh- 
ing 170 grains ; 3d, the end pieces DE and e d, to which the 
ivory vernier is fastened, each of which weighs 45 grains ; and 
4th, some brass work C c, at the centre. The deal rod, when 
dry, weighs 2320 grains, but when very damp, as it commonly 
was during the experiments, weighs 2400 ; the transverse sec- 
tion is of the shape represented in fig 5; the thickness BA, and 
the dimensions of the part DE ed, being the same in all parts ; 
but the breadth B b diminishes gradually, from the middle to 
the ends. The area of this section is ,33 of a square inchat the 
middle, and ,146 at the end ; and therefore, if any point x (fig. 
4.) is taken in c d , and — is called x, this rod weighs — 
^ ’ c d 0 73,3 x >230 
per inch at the middle; at the end, and x 
1 73,3 X 3238 71.1 .2*8 
73-3 
,238 
= HdfL — iiilf a t x ; and therefore, as the weight of the wire is 
73-3 b 
per inch, the deal rod and wire together may be considered 
as a rod whose weight at x '= per inch. 
But the force required to accelerate any quantity of matter 
placed at x> is proportional to x z ; that is, it is to the force re- 
quired to accelerate the same quantity of matter placed at d as 
x % to 1 ; and therefore, if c d is called /, and x is supposed to 
flow, the fluxion of the force required to accelerate the deal rod 
i 
