5*8 Mr. Cavendish’s Experiments to determine 
that the whole motion B b is greater than it would be if the 
attraction on the ball was the same in all places as it is at M, 
in the ratio of 1 -(- to one; and, therefore, does not depend 
sensibly on the place of the arm, in either position of the 
weights, but only on the quantity of its motion, by moving 
them. 
This variation in the attraction of the weight, affects also the 
time of vibration ; for, suppose the weights to be approached 
to the balls, let W be the centre of the nearest weight ; let B 
and A represent the same things as before ; and let x be the 
centre of the ball, at any point of its vibration ; let AB repre- 
sent the force with which the ball, when placed at B, is drawn 
towards A by the stiffness of the wire ; then, as B is the point 
of rest, the attraction of the weight thereon will also equal AB; 
and, when the ball is at x, the force with which it is drawn 
towards A, by the stiffness of the wire, = Ax, and that with 
which it is drawn in the contrary direction, by the attraction, 
AB x ; so that the actual force by which it is drawn to- 
wards A = Ax — = AB + Bx- AB X i + = 
Bx — — > very nearly. So that the actual force with 
which the ball is drawn towards the middle point of the vibra- 
tion, is less than it would be if the weights were removed, in 
2 AB 
the ratio of 1 — to one, and the square of the time of a 
2AB 
vibration is increased in the ratio of 1 to 1 — -^g-; which differs: 
very little from that of 1 -ff t0 lf which is the ratio in which 
the motion of the arm, by moving the weights from one near 
position to the other, is increased. 
