12$ THE 



tions of the shorter pendulum are performed in th( 

 same time as one vibration of the longer. 

 The time of vibration of a pendulum depends on its 

 length. If a pendulum is to vibrate in twice as long a 

 time as another pendulum, it must be made 2x2=4 

 times as long; if in three times as long a time, it must 

 be 3 x 3 = 9 times as long, and so on : The lengths of 

 different pendulums are proportional to the squares of the 

 time' of their vibrations^ The time of vibration of a pen- 

 dulum may hence be varied by varying its length in 

 accordance with this law. By c time of vibration ' we 

 understand the time required for a whole oscillation to 

 and fro; thus the time of vibration of the pendulum a 

 (fig. 93), is the time required for moving from a through 

 c to 5, and back again through c to a. This may also 

 be called a complete period of the pendulum's motion. 

 What is commonly called the time of vibration, or the 

 time of a single vibration, is the half of a complete 

 period. A pendulum which for such a single vibration, 

 that is, for half a complete period, requires precisely 

 one second of time, is called a seconds pendulum. The 

 length of the simple seconds pendulum, that is, the 

 distance from the point of suspension of the thread to 

 the centre of the small bullet, is O m *994, which differs 

 only 6 mm from a metre. 



The pendulums which are used for regulating the 

 motion of clocks consist essentially of a heavy rod and a 

 lens-shaped body, the 'bob.' In such a compound 

 pendulum the time of vibration depends not on the 

 length alone, but also upon its form, size, and the rela- 

 tive weight of its component parts. In a simple pen- 

 dulum the thread is so light that its weight exerts n< 



