The pendulum is the most perfect of all instruments, chiefly because it admits of almost endless 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, 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 pendulums, 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, embodying the principle of repetition in perfection, was employed with wonderful skill by Sir George Airy, in his experiments 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 carried 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.[185] [185] *Philosophical Transactions*, (1856) vol. 146, Part i. p. 297.