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this most interesting application of astronomy, in ascertaining the date of a papyrus, sent from Egypt by Mr. Salt, in the hieroglyphical researches of the late Dr. Thomas Young, whose profound and varied acquirements do honour to his country and to the age in which he livedi The manuscript was found in a mummy-case; it proved to be a horoscope of the age of Ptolemy, , and its antiquity was determined from the configuration of the heavens at the time of its construction.
The form of the earth furnishes a standard of weights and measures for the ordinary purposes of life, as well as for the determination of the masses and distances of the heavenly bodies. The length of the pendulum vibrating seconds of mean solar time, in the latitude of London, forms the standard of the British measure of extension. Its length oscillating in vacuo at the temperature of 62° of Fahrenheit, and reduced to the level of the sea was determined, by Captain Kater, to be 39-1392 inches. The weight of a cubic inch of water at the temperature of 62° of Fahrenheit, barometer 30 inches, was also determined in parts of the imperial troy pound, whence a standard both of weight and capacity is deduced. The French have adopted the metre equal to 362808992 English feet for their unit of linear measure, which is the ten-millionth part of that quadrant of the meridian passing through Formentera and Greenwich, the middle of which is nearly in the fortyfifth degree of latitude. Should the national standards of the two countries be lost in the vicissitude of human affairs, both may be recovered, since they are derived from natural standards presumed to be invariable. The length of the pendulum would be found again with more facility than the metre; but as no measure is mathematically exact, an error in the original standard may at length become sensible in measuring a great extent, whereas the error that must necessarily arise in measuring the quadrant of the meridian is rendered totally insensible by subdivisions, in taking its ten-millionth part. The French have adopted the decimal division, not only in time, but in their degrees, weights, and measures, on account of the very great facility it affords in computation. It has not been adopted by any other people, though nothing is more desirable than that all nations should concur in using the same division and standards, not only on account of convenience, but as affording a more definite idea of quantity.
It is singular that the decimal division of the day, of degrees, weights, and measures, was employed in China 4000 years ago; and that at the time Ibn Junis made his observations at Cairo, about the year 1000 of the Christian era, the Arabs were in the habit of employing the vibrations of the pendulum in their astronomical observations as a measure of time.
One of the most immediate and remarkable effects of a gravitating force external to the earth, is the alternate rise and fall of the surface of the sea twice in the course of a lunar day, or 24h 50m 48* of mean solar time. As it depends upon the action of the sun and moon, it is classed among astronomical problems, of which it is by far the most difficult and its explanation the least satisfactory. The form of the surface of the ocean in equilibrio, when revolving with the earth round its axis, is an ellipsoid flattened at the poles; but the action of the sun and moon, especially of the moon, disturbs the equilibrium of the ocean. If the moon attracted the centre of gravity of the earth and all its particles with equal and parallel forces, the whole system of the earth and the waters that cover it would yield to these forces with a common motion, and the equilibrium of the seas would remain undisturbed. The difference of the forces, and the inequality of their directions alone, trouble the equilibrium.
It is proved by daily experience, as well as by strict mathematical reasoning, that if a number of waves or oscillations be excited in a fluid by different forces, each pursues its course, and has its effect independently of the rest. Now in the tides there are three distinct kinds of oscillations, depending on different causes, and producing their effects independently of each other, which may therefore be estimated separately.
The oscillations of the first kind, which are very small, are independent of the rotation of the earth; and as they depend upon the motion of the disturbing body in its orbit, they are of long periods. The second kind of oscillations depends upon the rotation of the earth, therefore their period is nearly a day; and the oscillations of the third kind vary with an angle equal to twice the angular rotation of the earth; and consequently happen twice in twenty-four hours. The first afford no particular interest, and are extremely small; but the difference of two consecutive tides depends upon the second. At the time of the solstices, this difference, which ought to be very great, according to Newton's theory, is hardly sensible on our shores. La Place has shown that this discrepancy arises from the depth of the sea, and that if the depth were uniform there would be no difference in the consecutive tides but that which is occasioned by local circumstances; it follows, therefore, that as this difference is extremely small, the sea, considered in a large extent, must be nearly of uniform depth, that is to say, there is a certain mean depth from which the deviation is not great. The mean depth of the Pacific Ocean is supposed to be about four miles, that of the Atlantic only three. From the formulæ which determine the difference of the consecutive tides, it is also proved, that the precession of the equinoxes, and the nutation of the earth's axis, are the same as if the sea formed one solid mass with the earth.
Oscillations of the third kind are the semidiurnal tides, so remarkable on our coasts; they are occasioned by the combined action of the sun and moon, but as the effect of each is independent of the other, they may be considered separately.
The particles of water under the moon are more attracted than the centre of gravity of the earth, in the inverse ratio of the square of the distances ; hence they have a tendency to leave the earth, but are retained by their gravitation, which is diminished by this tendency. On the contrary, the moon attracts the centre of the earth more powerfully than she attracts the particles of water in the hemisphere opposite to her; so that the earth has a tendency to leave the waters, but is retained by