THE EXACT MEASUREMENT OF PHENOMENA. 339 



applicable to moving objects like the heavenly bodies, so 

 that its use is confined to important trigonometrical 

 surveys. 



The pendulum is the most perfect of all instruments, 

 chiefly because it naturally admits of almost indefinite 

 repetition. Since the force of gravity never ceases, one 

 swing of the pendulum is no sooner ended than the other 

 is begun, so that the juxtaposition of successive units is 

 absolutely perfect. Provided that the oscillations be equal, 

 then one thousand oscillations will occupy exactly one 

 thousand times as great an interval of time as one oscil- 

 lation. Not only is the subdivision of time entirely de- 

 pendent on this fact, but in the accurate measurement of 

 gravity, and many important determination it is of 

 the greatest service. In the deepest mine, we could not 

 observe the rapidity of fall of a body for more than a 

 quarter of a minute, and the measurement of its velocity 

 would be difficult, and subject to uncertain errors from 

 resistance of air, &c. In the pendulum, we have a body 

 which can be kept rising and falling for many hours, in 

 a medium entirely under our command or if desirable in 

 a vacuum. Moreover, the comparative force of gravity at 

 different points, at the top and bottom of a mine for 

 instance, can be determined with wonderful precision, by 

 comparing the oscillations of two exactly similar pendu- 

 lums, with the aid of electric clock signals. To ascertain 

 the comparative lengths of vibration of two pendulums, it 

 is only requisite to swing them one in front of the other, 

 to record by a clock the moment when they coincide in 

 swing, so that one hides the other, and then count the 

 number of vibrations until they again come to similar 

 coincidence. If one pendulum makes m vibrations and 

 the other n, we at once have our equation pn = qm ; 

 which gives the length of vibration of either pendulum in 

 terms of the other. This method of coincidence, embody- 



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