xiii.] MEASUREMENT OF PHENOMENA. 291 



perfect. Provided that the oscillations be equal, one 

 thousand oscillations will occupy exactly one thousand 

 times as great an interval of time as one oscillation. 

 Not only is the subdivision of time entirely dependent 

 on this fact, but in the accurate measurement of gravity, 

 and many other important determinations, 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 times 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 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- 

 ing the principle of repetition in perfection, was employed 

 with wonderful skill by Sir George Airy, in his experi- 

 ments on the Density of the Earth at the Harton Colliery, 

 the pendulums above and below being compared with 

 clocks, which again were compared with each other by 

 electric signals. So exceedingly accurate was this method 

 of observation, as earned out by Sir George Airy, that he 

 was able to measure a total difference in the vibrations at 

 the top and bottom of the shaft, amounting to only 2*24 

 seconds in the twenty-four hours, with an error of less 

 than one hundredth part of a second, or one part in 

 8,640,000 of the whole day. 1 



The principle of repetition has been elegantly applied 



1 Philosophical Transactions, (1856) vol. 146, Part i. p. 297. 



U 2 



