82 THE PENDULUM. 



vibrate seconds at the equator, must be somewhat 

 shorter than at the poles. 



When we consider a simple pendulum, or a ball 

 suspended by a string having no sensible weight, 

 we suppose the whole weight of the ball to be col- 

 lected in its centre of gravity; and the length of 

 the pendulum is the distance from the centre of 

 gravity to the point of suspension. 



But when a pendulum consists of a ball, or any 

 other figure, suspended by a metallic or wooden 

 rod, the length of the pendulum is the distance 

 from the point of suspension to a point in the pen- 

 dulum called the centre of oscillation, which does 

 not exactly coincide with the centre of gravity of 

 the ball. The centre of oscillation is that point in 

 the pendulum in which all its force is collected, 

 and to which, if an obstacle were applied, all motion 

 would cease, and would be received by the 

 obstacle. 



A single pendulum, consisting of a ball and a 

 thread, whose length is two-thirds of the length of 

 a bar without a ball, will be found to perform its 

 oscillations in equal times with the bar. Hence, a 

 point taken one-third of the length of the bar from 

 the lower end is its centre of oscillation. 



The pendulums of clocks usually vibrate in the 

 arcs of circles. It had formerly been thought an 

 advantage to make them vibrate in the arcs of cy- 

 cloids; but the difficulties that attend the practical 

 application of this principle are such, that there is 

 good reason to think that they produce greater 

 errors in the measurement of time than those they 

 are intended to remedy. 



As heat expands, and cold contracts all metals, a 

 pendulum-rod is longer in warm than in cold wea- 



