the Density of the Earth. 513 
and wire is proportional to f -i. 1 - the fluent of which, 
generated while x flows from c to d, = x — -”=3 5°» 
so that the force required to accelerate each half of the deal rod 
and wire, is the same as is required to accelerate 350 grains 
placed at d. 
The resistance to motion of each of the pieces de, is equal to 
that of 48 grains placed at d; as the distance of their centres of 
gravity from C is 38 inches. The resistance of the brass work 
at the centre may be disregarded ; and therefore the whole force 
required to accelerate the arm, is the same as that required to 
accelerate 398 grains placed at each of the pointy D and d. 
Each of the balls weighs 1 1262 grains, and they are placed at 
the same distance from the centre as D and d ; and therefore, the 
force required to accelerate the balls and arm together, is the 
same as if each ball weighed 1 1660, and the arm had no weight; 
and therefore, supposing the time of a vibration to be given, the 
force required to draw the arm aside, is greater than if the arm 
had no weight, in the proportion of 11660 to 11262, or of 
E0353 to 1. 
_ To find the attraction of the weights on the arm, through d 
draw the vertical plane dwh perpendicular to D d, and let w 
be the centre of the weight, which, though not accurately in this 
plane, may, without sensible error, be considered, as placed 
therein, and let b be the centre of the ball; then w b is horizontal 
and = 8,85, and d b is vertical and — 5,5 ; let w a — a, w b — 
b, and let j~, or 1 — x '= % ; then the attraction of the weight 
on a particle of matter at x , in the direction d zv, is to its attrac- 
— 3 _ 
tion on the same particle placed at b : : b 3 : a x -f- z % /*% or is pro- 
su 
MDCCXCVIII. 
