tion good, it will verify the accuracy of modern tables, and will show to how many centuries they may be extended without the fear of error. A few examples will show the importance of the subject. At the solstices the sun is at his greatest distance from the equator ; consequently his declination at these times is equal to the obliquity of the ecliptic (N. 152), which was formerly determined from the meridian length of the shadow of the stile of a dial on the day of a solstice. The lengths of the meridian shadow at the summer and winter solstices are recorded to have been observed at the city of Layang, in China, 1100 years before the Christian era. From these the distances of the sun from the zenith (N. 153) of the city of Layang are known. Half the sum of these zenith distances determines the latitude, and half their difference gives the obliquity of the ecliptic at the period of the observation; and, as the law of the variation of the obliquity is known, both the time and place of the observations have been verified by computations from modern tables. Thus the Chinese had made some advances in the science of astronomy at that early period. Their whole chronology is founded on the observations of eclipses, which prove the existence of that empire for more than 4700 years. The epoch of the lunar tables of the Indians, supposed by Bailly to be 3000 years before the Christian era, was proved by La Place, from the acceleration of the moon, not to be more ancient than the time of Ptolemy, who lived in the second century after it. The great inequality of Jupiter and Saturn, whose cycle embraces 918 years, is peculiarly fitted for marking the civilization of a people. The Indians had determined the mean motions of these two planets in that part of their periods when the apparent mean motion of Saturn was at the slowest, and that of Jupiter the most rapid. · The periods in which that happened were 3102 years before the Christian era, and the year 1491 after it. The returns of comets to their perihelia may possibly mark the present state of astronomy to future ages. The places of the fixed stars are affected by the precession of the equinoxes; and, as the law of that variation is known, their positions at any time may be computed. Now Eudoxus, a contemporary of Plato, mentions a star situate in the pole of the equator, and it appears from computation that Draconis was a not very far from that place about 3000 years ago; but, as it is only about 2150 years since Eudoxus lived, he must have described an anterior state of the heavens, supposed to be the same that was mentioned by Chiron about the time of the siege of Troy. Thus every circumstance concurs in showing that astronomy was cultivated in the highest ages of antiquity. It is possible that a knowledge of astronomy may lead to the interpretation of hieroglyphical characters. Astronomical signs are often found on the ancient Egyptian monuments, probably employed by the priests to record dates. The author had occasion to witness an instance of 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 lived. The manuscript was found in a mummy case; it proved to be a horoscope of the age of Ptolemy, and its date was determined from the configuration of the heavens at the time of its con. struction. 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 approximate length oscillating in vacuo at the temperature of 620 of Fahrenheit, and reduced to the level of the sea (N. 154), was determined by Captain Kater to be 39.1393 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 was deduced. The French have adopted the mètre, equal to 3.2808992 English feet, for their unit of linear measure, which is the ten-millionth part of the arc of the meridian which extends from the equator to the pole, as deduced from the measures of the separate arc extending from Formentera, the most southern of the Balearic Islands, to Dunkirk. Should the national standards of the two countries ever be lost, both may be recovered, since they are derived from natural and invariable ones. The length of the measure deduced from that of the pendulum would be found again with more facility than the mètre. 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 (N. 155) is rendered totally insensible by subdivision in taking its ten-millionth part. The French have adopted the decimal division, not only in time, but also 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 country, though nothing is more desirable than that all nations should concur in using the same 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 space, 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. SECTION XIII. Tides - Forces that produce them Origin and Course of Tidal Wave Its Speed — Three kinds of Oscillations in the Ocean - The Semidiurnal Tides Equinoctial Tides Effects of the Declination of the Sun and Moon Theory insufficient without Observation Direction of the Tidal Wave Height of Tides Mass of Moon obtained from her Action on the Tides - Interference of Undulations Impossibility of a Universal Inundation - Currents. 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 28% 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 disturb the equilibrium. 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 distance. 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 gravitation, which is again diminished by this tendency. Thus the waters immediately under the moon are drawn from the earth, at the same time that the earth is drawn from those which are diametrically opposite to her, in both instances producing an elevation of the ocean of nearly the same height above the surface of equilibrium ; for the diminution of the gravitation of the particles in each position is almost the same, on account of the distance of the moon being great in comparison of the radius of the earth. Were the earth entirely covered by the sea, the waters thus attracted by the moon would assume the form of an oblong spheroid whose greater axis would point towards the moon ; since the columns of water under the moon, and in the direction diametrically opposite to her, are rendered lighter in consequence of the diminution of their gravitation ; and, in order to preserve the equilibrium, the axes 90° distant would be shortened. The elevation, on account of the smaller space to which it is confined, is twice as great as the depression, because the contents of the spheroid always remain the same. If the waters were capable of assuming the form of equilibrium instantaneously, that is, the form of the spheroid, its summit would always point to the moon notwithstanding the earth's rotation. But, on account of their resistance, the rapid motion produced in them by rotation prevents them from assuming at every instant the form which the equilibrium of the forces acting upon them requires. Hence, on account of the inertia of the waters, if the tides be considered relatively to the whole earth and open seas, there is a meridian about 300 eastward of the moon, where it is always high water both in the hemisphere where the moon is and in that which is opposite. On the west side of this circle the tide is flowing, on the east it is ebbing, and on every part of the meridian at 90° distant it is low water. This great wave, which follows all the motions of the moon as far as the rotation of the earth will permit, is modified by the action of the sun, the effects of whose attraction are in every respect like those produced by the moon, though greatly less in degree. Consequently a similar wave, but much smaller, raised by the sun, tends to follow his motions, which at times combines with the lunar wave, and at others opposes it, according to the relative positions of the two luminaries ; but as the lunar wave is only modified a little by the solar, the tides must necessarily happen twice in a day, since the rotation of the earth brings the same point twice under the meridian of the moon in that time, once under the superior and once under the inferior meridian. |