THE PENDULUM. 



73 



weight. The investment of a little time and ingenuity in simple 

 experiments will pay large dividends. 



146. Third Law of the Pendulum. The vibra- 

 tions of pendulums of different lengths are performed in 

 different times. The lengths are directly proportional 

 to the squares of the times of vibration, or in- 

 versely proportional to the squares of the numbers 

 of vibrations in a given time. 



Note. Be careful to distinguish clearly between the expressions 

 "times of vibration" and "numbers of vibration." The greater 

 the time, the less the number. You may easily 

 verify by experiment the three laws already 

 given for the pendulum. 



147. The Second's Pendulum. 



At the equator, the length of a second's 

 pendulum, at the level of the sea, is 

 39 inches ; near the poles, 39.2 ; in this 

 latitude about 39.1 inches or 993.3 

 mm. As such a pendulum would be 

 inconveniently long, use is generally made 

 of one one-fourth as long, which, con- 

 sequently, vibrates half seconds. The 

 length and time of vibration of this 

 pendulum being thus known, the 

 length of any other pendulum may be 

 found when the time of vibration is 

 given ; or the time of vibration may be 

 found when the length is given. The 

 third law is applicable to such a problem. 



148. Use of the Pendulum in 

 Time-pieces. The motion of a* clock is due to the 

 force of gravity acting upon the weights, or to the elastic- 



FIG. 34. 



