5io Mr. Cavendish's Experiments to determine 
arm aside by one division, is to the weight of the ball as 
F&tn 5 Ijirf t0 or as stin^ to »• 
The next thing is, to find the proportion which the attraction 
of the weight on the ball bears to that of the earth thereon, 
supposing the ball to be placed in the middle of the case, that 
is, to be not nearer to one side than the other. When the 
weights are approached to the balls, their centres are 8,85 
inches from the middle line of the case ; but, through inadver- 
tence, the distance, from each other, of the rods which support 
these weights, was made equal to the distance of the centres of 
the balls from each other, whereas it ought to have been some- 
what greater. In consequence of this, the centres of the weights 
are not exactly opposite to those of the balls, when they are ap- 
proached together ; and the effect of the weights, in drawing the 
arm aside, is less than it would otherwise have been, in the tri- 
plicate ratio of — ~ to the chord of the angle whose sine is 
or in the triplicate ratio of the cosine of ~ this angle to 
the radius, or in the ratio of ,9779 to 1. 
Each of the weights weighs 2439000 grains, and therefore 
is equal in weight to 1 0,64 spherical feet of water ; and there- 
fore its attraction on a particle placed at the centre of the ball, 
is to the attraction of a spherical foot of water on an equal par- 
to 1. The 
tide placed on its surface, as 10,64 x ,9779 x g-gj 
mean diameter of the earth is 41800000 feet;* and therefore, 
if the mean density of the earth is to that of water as D to one, 
the attraction of the leaden weight on the ball will be to that 
* In strictness, we ought, instead of the mean diameter of the earth, to take the 
diameter of that sphere whose attraction is equal to the force of gravity in this cli- 
mate ; but the difference is not worth regarding. 
