THE PENDULUM. 71 



move more rapidly than they otherwise would. On the 

 other hand, the parts furthest from the centre of suspen- 

 sion tend to move more slowly than those nearer, and force 

 these to retard their individual rates of motion. Between 

 these there will be a particle moving, of its own accord, 

 at the average rate of all. The accelerating tendency of 

 the particles above it is compensated by the retarding ten- 

 dency of the particles below it. This molecule, there- 

 fore, ivill move as if it were vibrating alone, sup- 

 ported by a thread without weight. It fulfills all the 

 conditions of a simple pendulum. This point is called the 

 centre of oscillation. 



142. The Keal Length of a Pendulum. The 



laws of the simple pendulum are applicable to the com- 

 pound pendulum if we consider the length of the latter to 

 be the length of the equivalent simple pendulum, i. e., the 

 distance between the centres of suspension and 

 oscillation. We, therefore, may say that the real length 

 of a pendulum is the distance between the centre of sus- 

 pension and the centre of oscillation. The real length is 

 less than the apparent length except in the imaginary case 

 of the simple pendulum. 



143. First Law of the Pendulum. The vi- 

 brations of a given pendulum, at any given place, 

 are isochronous, i. e. y are performed in equal times, 

 whether the arc be long or short. Each pupil should 

 satisfy himself of the truth of this proposition, by the only 

 true scientific method, experiment. 



144. The Cycloidal Pendulum. TJie law 

 above given is strictly true only when the pendu- 



