THE PENDULUM. 



FIG. 32. 



lum vibrates in a cyeloidal arc. A cycloid is the 



curve traced by a point 

 in the circumference 

 of a circle rolling along 

 a straight line. The 

 pendulum may be 

 made to move in such 

 an arc by suspending 

 a small heavy ball by 

 a thread between two 

 cheeks upon which the 



thread winds as the pendulum vibrates. The cheeks must 

 be the two halves of a cycloid; each cheek must have the 

 same length as the thread. The path of the ball will be 

 a cycloid, identical with that to which the cheeks belong. 



(a.) The cyeloidal pendulum is of little practical use. If the 

 amplitude of an ordinary pendulum does not exceed five degrees, 

 the circular arc, thus described, will not vary much from the true 

 cyeloidal arc, and the pendulum will be practi- 

 cally isochronous. If from the centre of sus- 

 pension, with radius equal to the length of the 

 string, a circular arc be described, the two 

 curves will sensibly coincide for at least five 

 degrees. This is why the pendulums of "reg- 

 ulator " clocks have a small swing or amplitude. 



145. Second Law of the Pen- 

 dulum. %e time of vibration is 

 independent of the weight or mate- 

 rial of the pendulum, depending only 

 upon the length of the pendulum, and 

 the intensity of the force of gravity at 

 any given place. 



(a.) Each pupil should try the experiment, 

 at home, with balls of equal size but different FIG. 33. 



