The sequence to be derived from all the foregoing considerations is, that the whole decrease of gravitation from the equator to the poles is 0.005.1449, which subtracted from the 1/155.2 gives the amount of compression of the earth to be nearly 1/285.26. But this form of the earth would give the excess of the equatorial axis over the polar about 26¹⁄₂ miles. The measurement is confirmed by Mr. Ivory in his investigations on the five principal measurements of arcs of the meridian in Peru, India, France, England, and Lapland. He found that the law required an ellipsoid of revolution whose equatorial radius should be 3,962.824 miles, and the polar 3,949.585 miles; the difference is 13.239 miles; this quantity multiplied by two gives 26.478 as the excess of one diameter over the other. Thus, by two different processes the figure of the earth has been determined; but another remains that is the result of pure analysis, derived from the nutation and precession of the equinoxes—for, as explained before, these effects are caused by the excess of matter at the earth’s equator. The calculation does not lead us to certainty, but it does show the compression to be comprised between the two fractions ¹⁄₂₇₀ and ¹⁄₅₇₃. There is this advantage in the lunar theory, that it takes the earth as a whole, disregarding any irregularities of surface, or the local attractions that influence the pendulum—the difficulties of measuring an arc of the meridian being an obstacle to perfect accuracy.
The form of the earth has, however, a value confined not alone to those interested in horology—it furnishes us with a standard of weights and measures. In England and the United States, the pendulum is the unit of mensuration, or at least the common standard from which measurement is derived. It has been shown that, deducting the effects of nutation, the axis of the earth’s rotation is always in the same plane. Now, the mass being the same constant quantity, a pendulum oscillating seconds at the Greenwich Observatory, has been adopted by the English Government as its standard of length. Oscillating in vacuo at the level of the sea, at 62° Fahr., Captain Kater found its approximate length to be 39.1393 inches; as this must be invariable under the same circumstances, it becomes a standard for all time. The French deduced their standard from the measurement of the ten-millionth part of a quadrant of the meridian passing through Formentera and Greenwich. They have also adopted the decimal system; yet it seems to prove that nothing under the sun is new, for over forty centuries ago the Chinese used the decimal system in the division of degrees, weights, and measures.
The antiquity of the pendulum is also shown by the fact that the Arabs were in the habit of dividing the time in observations, by its oscillations, when Ibn Junis, in the year one thousand, was making his astronomical researches. Before we lose sight of the influence of the form of the earth on the pendulum, it may be well to state another source of disturbance, arising from the combined influence of the earth’s rotation and the fact that a body moving in its own plane seeks to maintain that plane. It will be seen from the very beautiful experiment showing the rotation of the earth, that if a body like a pendulum be suspended so as to be free in every direction, and not be influenced by the motion of the earth when set in oscillation in any plane, that that plane will preserve its line of motion, while the earth in its motion beneath the body can be seen to slowly move, as though the minute hand of a watch were made stationary while the dial revolved. The same principle is the one that maintains the spinning-top in a parallel position to the horizon, or the gyrascope in its apparently anomalous defiance of all the laws of gravitation. In the pendulum this tendency to preserve the same plane of motion becomes a cause of error—slight, it is true, but can be very easily remedied by so placing it that the plane of oscillation shall be parallel to the equator. It will be readily seen that this precaution will become more important as we recede from the equator; for if we were to suspend a pendulum at the pole in a true line with the axis of rotation, and if the plane of vibration remained constant, the earth would turn once around that plane in the diurnal period. During this time there would be a continuous torsion on the point of suspension, that would in time materially affect the accuracy of the instrument. The reasoning holds good for every latitude—degree of influence being the only difference.
Having given the action of the earth’s form, mass, and rotation on the pendulum, there remain the disturbances due to expansion and contraction, owing to changes of temperature and those of atmospheric causes. The astronomical points to be observed are somewhat too fully laid down, but it must be remembered that an exact science requires the premises to be fully established before a sequence can be drawn.
As the standard of time depends on the passage of a star or the sun, or any known celestial object, at a certain time across the meridian of the place where the observation is taken, it was absolutely necessary to give the modes of calculation, together with the disturbing causes. Moreover, a full appreciation of the indebtedness of horology to astronomy could not be obtained without a general knowledge of the change of the position of the major axis of the orbit described by the earth around the sun. Also, the difference between mean and apparent solar time was required to illustrate the use of the tables of equated time, the necessity of which will become patent when the use of the transit instrument for the establishment of time, or a fixed standard, is introduced. Also, the disturbing effects of the sun and moon collectively and relatively as to position, could not be passed, as they produce the precession of the equinoxes and the nutation of the pole—essential elements in the computation of time.
Watch and Chronometer Jewelling.
NUMBER ONE.
This whole subject is well worthy an article both in a scientific and mechanical sense, whether we consider the delicacy of the operations or the intractable character of the material operated on—for there has been no improvement in the horological trade of more importance to accuracy and durability of time-keepers.