THE PENDULUM. 81 



The body P acquires a velocity in falling through 

 the arch P A, that has a tendency, when it arrives 

 at the point A, to carry it off in the tangent A D ; 

 but being prevented from moving in a straight line 

 by the string which continually draws it towards the 

 centre, it is forced to describe the curve A E, which, 

 provided the pendulum were not affected by the 

 resistance of the air, or the friction at the centre, 

 would be exactly similar to the arch P A; that is, 

 it would rise to the same height as it fell from. 

 Having arrived at E, it will fall back again to A, 

 and go on with its acquired velocity to P, and so 

 on, continually backwards and forwards. 



Each swing that it makes, is called a vibration, 

 or oscillation. 



If the pendulum vibrated in vacuo, and there 

 was no friction at the point of suspension, the vi- 

 brations would not only be all equal, but they 

 would continue for ever; but as this is not the case, 

 the vibrations become less and less, till at last the 

 motion totally ceases. 



The longer a pendulum is, the slower are its vi- 

 brations, and the contrary; consequently, if a 

 pendulum be required to vibrate seconds, it must 

 have a determinate length. This length is found 

 to be 39.13 inches in Britain. 



Pendulums of the same length vibrate slower, 

 the nearer they are brought to the equator; because 

 the semi-diameter of the earth's equator is about 

 seventeen miles longer than the axis of the earth, 

 consequently gravity is less at the equator than at 

 the poles ; and because the centrifugal force at the 

 equator, arising from the diurnal motion of the 

 earth, being greater than that at the poles, lessens 

 gravity by T fo part. A pendulum, therefore, to 



vol. i. g 



