Chap. XLII.] 



SIM PL E PEND UL UM. 



505 



multiplied by the square of the time, gives the 

 distance at the end of the time. Let s = the space, 

 the formula becomes 



s = $ g t 2 16-1 x t*. 



Thus, at the end of 2 seconds, s = 16 - 1 x 4 = 64 -4. 

 The rule, put in words, is, the spaces described are 

 proportional to the squares of the time employed in the 

 description. 



A third formula, v = \/2 gs, gives the velocity v 

 a body acquires by falling through a certain space s ; 

 thus the velocity acquired by a body falling 30 feet= 



v = \/64-4Tx~367 



The simple pendulum is formed by a weight 

 attached to the end of a fine inextensible thread, the 

 other end of the thread being fixed. The centre of 

 gravity is below the point of 

 suspension. If the weight be 

 pulled to one side of its posi- 

 tion of rest, and then be let go, 

 it will move towards its former 

 position by the force of gravity ; 

 but in moving it acquires 

 energy, and thus it does not 

 come to rest, but passes its 

 middle position to the other 

 side, moving upwards along a 

 small arc. It will move up 

 till it has expended all the 

 energy it acquired by its previous 

 downward movement. But it has now gained energy 

 of position which causes it to move backwards over 

 its former path. If it did not encounter resistance, 

 friction, etc., it would move back to its former posi- 

 tion. But energy is expended in overcoming resistance, 

 etc., and thus it gradually loses its energy, describing 

 movements, on each side of its position of rest, of ever 



Fig. 213. The Simple 

 Pendulum. 



