$02 THE PRINCIPLES OF SCIENCE. [CHAP. 



schel l effected the comparison by using the full moon as 

 an intermediate unit. Wollaston ascertained that the sun 

 gave 801,072 times as much light as the full moon, and 

 Herschel determined that the light of the latter exceeded 

 that of a Centauri 27,408 times, so that we find the ratio 

 between the light of the sun and star to be that of about 

 22,000,000,000 to i. 



The Pendulum. 



By far the most perfect and beautiful of all instruments 

 of measurement is the pendulum. Consisting merely of a 

 heavy body suspended freely at an invariable distance from 

 a fixed point, it is most simple in construction ; yet all the 

 highest problems of physical measurement depend upon its 

 careful use. Its excessive value arises from two circum- 

 stances. 



(1) The method of repetition is eminently applicable 

 to it, as already described (p. 290). 



(2) Unlike other instruments, it connects together three 

 different 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, ofwhatever kind. 

 The whole theory of the pendulum is contained in the 

 formula, first given by Iluygens in his Horologium Oscil- 

 latorium. 



Time of oscillation = 3-14159 X A/length of 



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 will be invariable. 

 Thus a pendulum of invariable length suspended at the 

 same place, where the force of gravity may be considered 

 constant, furnishes a measure of time. The same invari- 

 able pendulum being made to vibrate at different points of 



1 Herschel's Astronomy, 817, 4th. ed. p. 553 



