THE EXACT MEASUREMENT OF PHENOMENA. 353 



merely of a heavy body suspended freely at an invari- 

 able distance from a fixed point, it is the most simple 

 in construction ; and yet all the highest problems of phy- 

 sical measurement depend upon its careful use. Its 

 excessive value arises from two circumstances, which 

 render it at once most accurate and indispensable. 



(1) The method of repetition is eminently applicable 

 to it, as already described (p. 339.) 



(2) Unlike any other instrument, it connects together 

 three different variable quantities, those of space, time, 

 and force. 



In most works on natural philosophy it is shown, that 

 when the oscillations of the pendulum are infinitely small, 

 the square of the time occupied by an oscillation is directly 

 proportional to the length of the pendulum, and indirectly 

 proportional to the force affecting it, of whatever kind. 

 The whole theory of the pendulum is contained in the 

 formula, first given by Huyghens in his Horologium Oscil- 

 latorium, 



time Of OScillation= 3-14159. . / length of pendulum 



V force. 



The quantity 3-14159 is the constant ratio of the circum- 

 ference and radius of a circle, and is of course known with 

 accuracy. Hence, any two of the three quantities con- 

 cerned being given, the third may be found ; or any two 

 being maintained invariable, the third wiU be invariable. 

 Thus a pendulum of invariable length suspended at the 

 same place, where the force of gravity may be considered 

 uniform, furnishes a theoretically perfect measure of time. 

 The same invariable pendulum being made to vibrate at 

 different points of the earth's surface, and the time of 

 vibration being astronomically determined, the force of 

 gravity becomes accurately known. Finally, with a known 

 force of gravity, and time of vibration ascertained by refer- 

 ence to the stars, the length is determinate. 



A a 



