322

NEW EXPERIMENTS

TRACT 34<.

vibrations made in s seconds, and l the length of the se-'conds pendulum, then it is well known that n 1 : s'- :: li-the distance from the axis of motion to the centre of oscil-lation. And here if 5 be 60 seconds, or one minute, and nthe number of vibrations performed in 1 minute, as found bydividing the whole number of vibrations, actually performed,by the whole number of minutes ; then is n 1 : 60 z : : l :the distance to the centre of oscillation. But, by the bestobservations on the vibration of pendulums, it is found thatl — 39-j inches, is the length of the seconds pendulumfor the latitude of London, or of Woolwich ; and therefore-- or- = o, will be the distance, in inches, or

n n nn

__ j 1137 5 f eet 0 f t | le cen tre of oscillation below the axis.

n n ’

And by this rule the place of that centre was found for eachday of the experiments.

Of the Rule for Computing the Velocity of the Ball.

21. Having described the methods of obtaining the neces-sary dimensions and weights, proceed we now to the inves-tigation of the theorem by which the velocity of the ball isto be computed : and first by means of the pendulum.

The several weights and measures being found, letb denote the weight of the ball,p the weight of the pendulum,g the distance to its centre of gravity,

0 the distance to its centre of oscillation,

1 the distance to the point of impact, or point struck,c the chord of the arch described by the pendulum,

r its radius, or distance to the tape or arch,v the initial or original velocity of the ball, at the impact.

Then, from the nature of oscillatory motion, bii willexpress the sum of the forces of the ball acting at thedistance i from the axis, and pg o the sum of the forces, ofthe pendulum, and consequently pgofbii the sum for