the Density of the Earth. 
5*7 
yyj~o of that of the weight. The computation is given in the 
Appendix. 
It has been shewn, therefore, that the force required to 
draw the arm aside one division, is greater than it would be if 
the arm had no weight, in the ratio of 1,0353 to 1, and therefore 
*>°353 
of the weight of the ball ; and moreover, the attrac- 
tion of the weight and copper rod on the arm and both balls 
together, exceeds the attraction of the weight on the nearest ball, 
in the ratio of 1,0199 to 1, and therefore ==i 1 of the 
8739000 D 
8 i 8 
weight of the ball; consequently D is really equal to 
x -o - 1?01 — - 5 -, or — S- 4 i , instead of — as by the former 
computation. It remains to be considered how much this is 
affected by the position of the arm. 
Suppose the weights to be approached to the balls; let W, 
(fig. 7.) be the centre of one of the weights ; let M be the centre 
of the nearest ball at its mean position, as when the arm is at 
20 divisions ; let B be the point which it actually rests at ; and 
let A be the point which it would rest at, if the weight was re- 
moved; consequently, AB is the space by which it is drawn 
aside by means of the attraction ; and let M /3 be the space by 
which it would be drawn aside, if the attraction on it was the 
same as when it is at M. But the attraction at B is greater 
than at M, in the proportion of WM a : WB 1 ; and therefore, 
AB = M /3 x 
WM 1 
2MB 
X l + -f-jw, very nearly. 
WB* 1 MW 
Let now the weights be moved to the contrary near position, 
and let w be now the centre of the nearest weight, and h the 
point of rest of the centre of the ball ; then A b = M /3 x 1 + 
.zM b 
MW 
, and B h 
. zMfi . 2MB 
x2 + mW + ■ 
MW 
2 M /3 X 1 + 
B b 
MW 
SO 
