218.] 



PLANE MOTION. 



119 



The constants C lt C 2 can be determined from the initial con- 

 ditions for which we shall now take = # and v = o when /=o; 

 this gives \ = > C 2 = o ; hence 



(37) 



The last equation gives for 0= the time 

 tion, or half the period T t 



of one oscilla- 



(38) 



The time of a small oscillation is thus seen to be indepen- 

 dent of the arc through which the pendulum swings ; in other 

 words, for all small arcs the times of oscillation of the same 

 pendulum are the same ; such oscillations are therefore called 

 isochronous. 



218. A pendulum whose length is so adjusted as to make it 

 perform at a certain place just one oscillation in a second is 

 called a seconds pendulum. 



Putting ^= i in (38) we find for the length / x of the seconds 

 pendulum at a place where the acceleration of gravity is g, 



(39) 



As the length of the pendulum can be determined with great 

 accuracy by measurement, the pendulum can be used to find 

 the value of g. 



The length of the seconds pendulum is very nearly a metre ; 

 it varies for points at sea level from ^=99.103 cm. at the equa- 

 tor to / 1 = 99.6io at the poles.* 



* Further numerical data for ^ and g will be found in J. D. EVERETT, C. G. S. 

 system of units, 1891, pp. 21-22. 



