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CHAPTER V. 



THE MOTION OF A PENDULUM. 



1. Some general considerations. 



2. Motion in vacuo, Newton xxiv. 



3. The properties of a pendulum. 



4. Motion in a resisting medium Modern method of considering the 



perturbations of a pendulum, the Newtonian method. 



5. Newton s experiments to discover the law of resistance. 



1. THE importance of the pendulum can hardly be over 

 rated. It ministers to our comforts in a variety of ways. 

 But what is more to our present purpose, it is a powerful 

 engine of discovery. It can be made to test the laws of 

 impact, it teaches us the law of resistance by which fluids 

 retard the motion of bodies moving in them. It enables 

 us to note the variations of gravity over the earth, and 

 thus reveals to us not only the form of the world, but also 

 the force with which it attracts external objects. It has 

 even been applied lately to prove ocularly the rotation of 

 the earth. There is no end to its applications. It is the 

 great accuracy with which the time of oscillation may be 

 observed that renders this instrument so useful. By 

 noting the time of any great number of oscillations, and 

 dividing that time by the number of oscillations, we can 

 find the time of any one with great accuracy. It is, there 

 fore, highly necessary for us to consider carefully the pro 

 perties of a pendulum. 



A pendulum is any solid body which oscillates about a 

 fixed horizontal axis. A simple pendulum consists of a 



