51 6 Mr. Cavendish’s Experiments to determine 
the middle division, the attractions of the opposite sides of the 
case balance each other, and have no power to draw the arm 
either way. When the arm is removed from this division, it is 
attracted a little towards the nearest side, so that the force re- 
quired to draw the arm aside is rather less than it would other- 
wise be^ but yet, if this force is proportional to the distance of 
the arm from the middle division, it makes no error in the re- 
sult; for, though the attraction will draw the arm aside more 
than it would otherwise do, yet, as the accelerating force by 
which the arm is made to vibrate is diminished in the same 
proportion, the square of the time of a vibration will be in- 
creased in the same proportion as the space by which the arm 
is drawn aside, and therefore the result will be the same as if 
the case exerted no attraction ; but, if the attraction of the case 
is not proportional to the distance of the arm from the middle 
point, the ratio in which the accelerating force is diminished is 
different in different parts of the vibration, and the square of 
the time of a vibration will not be increased in the same pro- 
portion as the quantity by which the arm is drawn aside, and 
therefore the result will be altered thereby. 
On computation, I find that the force by which the attrac- 
tion draws the arm from the centre is far from being propor- 
tional to the distance, but the whole force is so small as not to 
be worth regarding ; for, in no position of the arm does the at- 
traction of the case on the balls exceed that of -fth of a spheric 
inch of water, placed at the distance of 1 inch from the centre 
of the balls; and the attraction of the leaden weight equals that 
of 10,6 spheric feet of water placed at 8,85 inches, or of 234 
spheric inches placed at 1 inch distance; so that the attraction 
of the case on the balls can in no position of the arm exceed 
