A pendulum, vibrating freely, in small and equal arcs, may be so adjusted in its length, as, by its vibrations, to make this division of the earth's motion into 86,400 equal parts, called seconds of mean time.
Such a pendulum, then, becomes itself a measure of determinate length, to which all others may be referred to as to a standard.
But even a pendulum is not without its uncertainties.
1. The difficulty of ascertaining, in practice, its centre of oscillation, as depending on the form of the bob, and its distance from the point of suspension; the effect of the weight of the suspending wire towards displacing the centre of oscillation; that centre being seated within the body of the bob, and therefore inaccessible to the measure, are sources of considerable uncertainty.
2. Both theory and experience prove that, to preserve its isochronism, it must be shorter towards the equator, and longer towards the poles.
3. The height of the situation above the common level, as being an increment to the radius of the earth, diminishes the length of the pendulum.
4. The pendulum being made of metal, as is best, it varies its length with the variations in the temperature of the atmosphere.
5. To continue small and equal vibrations, through a sufficient length of time, and to count these vibrations, machinery and a power are necessary, which may exert a small but constant effort to renew the waste of motion; and the difficulty is so to apply these, as that they shall neither retard or accelerate the vibrations.
1. In order to avoid the uncertainties which respect the centre of oscillation, it has been proposed by Mr. Leslie, an ingenious artist of Philadelphia, to substitute, for the pendulum, a uniform cylindrical rod, without a bob.
Could the diameter of such a rod be infinitely small, the centre of oscillation would be exactly at two-thirds of the whole length, measured from the point of suspension. Giving it a diameter which shall render it sufficiently inflexible, the centre will be displaced, indeed; but, in a second rod not the [(1)] six hundred thousandth part of its length, and not the hundredth part as much as in a second pendulum with a spherical bob of proper diameter. This displacement is so infinitely minute, then, that we may consider the centre of oscillation, for all practical purposes, as residing at two-thirds of the length from the centre of suspension. The distance between these two centres might be easily and accurately ascertained in practice. But the whole rod is better for a standard than any portion of it, because sensibly defined at both its extremities.