the Density of the Earth. 
5°9 
On the Method of computing the Density of the Earth from these 
Experiments. 
I shall first compute this, on the supposition that the arm 
and copper rods have no weight, and that the weights exert 
no sensible attraction, except on the nearest ball; and shall 
then examine what corrections are necessary, on account of 
the arm and rods, and some other small causes. 
The first thing is, to find the force required to draw the 
arm aside, which, as was before said, is to be determined by 
the time of a vibration. 
The distance of the centres of the two balls from each other 
is 73,3 inches, and therefore the distance of each from the centre 
of motion is 36,65, and the length of a pendulum vibrating se- 
conds, in this climate, is 39,14; therefore, if the stiffness of the 
wire by which the arm is suspended is such, that the force which 
must be applied to each ball, in order to draw the arm aside by 
the angle A, is to the weight of that ball as the arch of A to the 
radius, the arm will vibrate in the same time as a pendulum 
whose length is 36,65 inches, that is, in seconds ; and 
therefore, if the stiffness of the wire is such as to make it vibrate 
in N seconds, the force which must be applied to each ball, in 
order to draw it aside by the angle A, is to the weight of the 
ball as the arch of A x x to the radius. But the ivory 
scale at the end of the arm is 38,3 inches from the centre 
of motion, and each division is ~ of an inch, and therefore 
subtends an angle at the centre, whose arch is ; and there- 
fore the force which must be applied to each ball, to draw f he 
