THE SIMPLE PENDULUM 261 



This equation contains the complete solution of the problem. 

 We notice that the values of s continually repeat at intervals of 

 time t for which 



Thus the motion of the pendulum repeats itself indefinitely. 

 The interval between two instants at which the pendulum is in 

 the same position, namely t 0> given by 



' 



is called the period. 



207. Seconds pendulum. To construct a pendulum which is to 

 beat seconds, we choose a so that t shall be equal to two seconds, 

 for a seconds pendulum is one which takes one second to move 

 from left to right, and then one second more to move from right 

 to left. Thus we must have 



*r,- = 



In foot-second units we may take g 32.19 for London, and 



so obtain 



a = 39.14 inches, 



as the length of the seconds pendulum at London. 



We notice that the period of a pendulum varies as the square 

 root of its length. Thus, for a pendulum to beat half-seconds, its 

 length would have to be only a quarter of that of the seconds 

 pendulum, and therefore 9.78 inches at London. 



Since g varies from point to point on the earth's surface, the 

 length of the seconds pendulum will also vary. If we observe 

 the length of a pendulum and also measure its period with a 

 chronometer, we shall be able to calculate the value of g at 

 the place at which the experiment is performed; in fact, this 

 method affords the easiest and most accurate way of obtaining 

 the value of g at any point of the earth's surface. 



