19. The same Principle of Coincidence or Interference is applied to the exact measurement of the length of time occupied in the oscillation of a pendulum. If a detached pendulum, of such a length as to swing in little less than a second, be placed before the seconds' pendulum of a clock, and if the two pendulums begin to move together, the former will gain upon the latter, and in a little while their motions will be quite discordant. But if we go on watching, we shall find them, after a time, to agree again exactly; namely, when the detached pendulum has gained one complete oscillation (back and forwards,) upon the clock pendulum, and again coincides with it in its motion. If this happen after 5 minutes, we know that the times of oscillation of the two pendulums are in the proportion of 300 to 302, and therefore the detached pendulum oscillates in 150/151 of a second. The accuracy which can be obtained in the measure of an oscillation by this means is great; for the clock can be compared (by {158} observing transits of the stars or otherwise) with the natural standard of time, the sidereal day. And the moment of coincidence of the two pendulums may, by proper arrangements, be very exactly determined. We have hitherto spoken of methods of measuring time and space, but other elements also may be very precisely measured by various means. 20. (VI.) _Measurement of Weight._--Weight, like space and time, is a quantity made up by addition of parts, and may be measured by similar methods. The principle of repetition is applicable to the measurement of weight; for if two bodies be simultaneously put in the same pan of a balance, and if they balance pieces in the other pan, their weights are exactly added. There may be difficulties of practiced workmanship in carrying into effect the mathematical conditions of a perfect balance; for example, in securing an exact equality of the effective arms of the beam in all positions. These difficulties are evaded by the _Method of double weighing_; according to which the standard weights, and the body which is to be weighed, are successively put in the _same_ pan, and made to balance by a third body in the opposite scale. By this means the different lengths of the arms of the beam, and other imperfections of the balance, become of no consequence[8\3]. [Note 8\3: For other methods of measuring weights accurately, see Faraday's _Chemical Manipulation_, p. 25.] 21. There is no natural _Standard_ of weight. The conventional weight taken as the standard, is the weight of a given bulk of some known substance; for instance, a _cubic foot of water_. But in order that this may be definite, the water must not contain any portion of heterogeneous substance: hence it is required that the water be _distilled_ water.