the Density of the Earth. 
6~'| 1 
of the earth thereon, as 10,64 x ,9779 x g-gj to 41800000 D 
: : 1 to 8739000 D. 
It is shewn, therefore, that the force which must be applied 
to each ball, in order to draw the arm one division out of its 
natural position, is of the weight of the ball ; and, if the 
mean density of the earth is to that of water as D to 1, the at- 
traction of the weight on the ball is g 7 ~ ~ — g of the weight of 
that ball ; and therefore the attraction will be able to draw the 
arm out of its natural position by g 739000 ' g or —gg-yp divisions ; 
and therefore, if on moving the weights from the midway to a 
near position the arm is found to move B divisions, or if it 
moves 2 B divisions on moving the weights from one near po- 
sition to the other, it follows that the density of the earth, or D, 
• N a 
^ 10683 B * 
We must now consider the corrections which must be ap- 
plied to this result ; first, for the effect which the resistance of 
the arm to motion has on the time of the vibration : 2d, for 
the attraction of the weights on the arm : 3d, for their attrac- 
tion on the farther ball : 4th, for the attraction of the copper 
rods on the balls and arm : 5th, for the attraction of the case 
on the balls and arm : and 6th, for the alteration of the attrac- 
tion of the weights on the balls, according to the position of 
the arm, and the effect which that has on the time of vibration. 
None of these corrections, indeed, except the last, are of much 
signification, but they ought not entirely to be neglected. 
As to the first, it must be considered, that during the vibra- 
tions of the arm and balls, part of the force is spent in accele- 
