506 PHYSIOLOGICAL PHYSICS. [Chap. XLII. 



diminishing extent till it finally comes to rest. If the 

 pendulum be at B' (Fig. 213), the force urging it towards 

 B is that of gravity acting in the direction B'G, and 

 equal to the energy gained in falling through the dis- 

 tance CB. But this force can be resolved into two 

 others, namely, fi'e, in the line of the thread which is 

 counterbalanced by the thread, and By, which acts 

 along a tangent to the arc, and is that part of the 

 force which is effective in moving B' to B. 



The movement of the weight from B' to B" a.nd 

 back to B' is a complete vibration, and the time occu- 

 pied is called the periodic time. The distance from 

 the position of rest B to either extreme B' or B" is the 

 amplitude of vibration, and is usually measured by 

 the angle BAB'. 



The time of oscillation of a pendulum is usually 

 estimated, not by the time of a complete vibration, 

 but the time occupied in travelling from the middle 

 position to the extreme, and then back to the middle 

 position ; or, what is the same thing, the time of 

 travelling from one extreme, to another B' to B", the 

 time of an oscillation. When the oscillations of the 

 pendulum do not exceed a certain extent the time 

 of vibration is independent of the amplitude. The time 

 t is obtained by the formula 



where I = the length of the pendulum, g = the 

 acceleration due to gravity, and -* = the ratio of the 

 circumference of a circle to the diameter = 3-14159. 

 From this formula the length of the pendulum can be 

 estimated if t be given ; thus, 



7T 2 



Where the length is known, the intensity of gravity 



