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direction, and force it to move from east to west, so that the equinoctial points have a slow retrograde motion on the plane of the ecliptic of 50".37572 annually. The direct tendency of this action is to make the planes of the equator and ecliptic coincide, but it is balanced by the tendency of the earth to return to stable rotation about the polar diameter, which is one of its principal axes of rotation; therefore the inclination of the two planes remains constant, as a top spinning preserves the same inclination to the plane of the horizon. Were the earth spherical, this effect would not be produced, and the equinoxes would always correspond with the same points of the ecliptic, at least as far as this kind of motion is concerned. But another and totally different cause which operates on this motion has already been mentioned. The action of the planets on one another and on the sun occasions a very slow variation in the position of the plane of the ecliptic, which affects its inclination to the plane of the equator, and gives the equinoctial points a slow but direct motion on the ecliptic of 0.15272 annually, which is entirely independent of the figure of the earth, and would be the same as if it were a sphere. Thus the sun and moon, by moving the plane of the equator, cause the equinoctial points to retrograde on the ecliptic, and the planets, by moving the plane of the ecliptic, give them a direct motion, though much less than the former; consequently, the difference of the two is the mean precession, which is proved, both by theory and observation, to be about 50'.223 annually.
As the longitudes of all the fixed stars are increased by this quantity, the effects of precession are soon detected; it was accordingly discovered by Hipparchus, in the year 128 before Christ, from a comparison of his own observa
tions with those of Timocharis, 155 years before. In the time of Hipparchus, the entrance of the sun into the constellation Aries was the beginning of spring, but since that time the equinoctial points have receded 30°, so that the constellations called the signs of the zodiac are now at a considerable distance from those divisions of the ecliptic which bear their names. Moving at the rate of 50' 223 annually, the equinoctial points will accomplish a revolution in 25805 years; but as the precession varies in different centuries, the extent of this period will be slightly modified. Since the motion of the sun is direct, and that of the equinoctial points retrograde, he takes a shorter time to return to the equator than to arrive at the same stars; so that the tropical year of 365-242219 mean solar days must be increased by the time he takes to move through an arc of 50"223, in order to have the length of the sidereal year. By simple proportion, it is the 0.014154th part of a day, so that the siderial year contains 365-256373 mean solar days.
The mean annual precession is subject to a secular variation; for, although the change in the plane of the ecliptic, in which the orbit of the sun lies, be independent of the form of the earth, yet, by bringing the sun, moon, and earth into different relative positions, from age to age, it alters the direct action of the two first on the prominent matter at the equator: on this account, the motion of the equinox is greater by 0" 455 now than it was in the time of Hipparchus; consequently, the actual length of the tropical year is about 4.21 shorter than it was at that time. The utmost change that it can experience from this cause amounts to 43 seconds.
Such is the secular motion of the equinoxes; but it is
sometimes increased and sometimes diminished by periodic variations, whose periods depend upon the relative positions of the sun and moon with regard to the earth, and which are occasioned by the direct action of these bodies on the equator. Dr. Bradley discovered that by this action the moon causes the pole of the equator to describe a small ellipse in the heavens, the diameters of which are 16" and 20". The period of this inequality is 19 years, the time employed by the nodes of the lunar orbit to accomplish a revolution. The sun causes a small variation in the description of this ellipse; it runs through its period in half a year. This nutation in the earth's axis affects both the precession and obliquity with small periodic variations; but, in consequence of the secular variation in the position of the terrestrial orbit, which is chiefly owing to the disturbing energy of Jupiter on the earth, the obliquity of the ecliptic is annually diminished by 0'445, or, according to Bessel, by 0'457. This variation in the course of ages may amount to ten or eleven degrees; but the obliquity of the ecliptic to the equator can never vary more than 2°42′ or 3°, since the equator will follow in some measure the motion of the ecliptic.
It is evident that the places of all the celestial bodies are affected by precession and nutation, and therefore all observations of them must be corrected for these inequalities.
The densities of bodies are proportional to their masses divided by their volumes; hence, if the sun and planets be assumed to be spheres, their volumes will be as the cubes of their diameters. Now, the apparent diameters of the sun and earth, at their mean distance, are 1922''8 and 17" 154, and the mass of the earth is the 354936th
part of that of the sun taken as the unit: it follows, therefore, that the earth is nearly four times as dense as the sun; but the sun is so large, that his attractive force would cause bodies to fall through about 334.65 feet in a second; consequently, if he were habitable by human beings, they would be unable to move, since their weight would be thirty times as great as it is here. A man of moderate size would weigh about two tons at the surface of the sun, whereas, at the surface of the four new planets, he would be so light, that it would be impossible to stand steady, since he would only weigh a few pounds. All the planets and satellites appear to be of less density than the earth. The motions of Jupiter's satellites show that his density increases towards his centre; were his mass homogenous, his equatorial and polar axes would be in the ratio of 41 to 36, whereas they are observed to be only as 41 to 38. The singular irregularities in the form of Saturn, and the great compression of Mars, prove the internal structure of these two planets to be very far from uniform.
Astronomy has been of immediate and essential use in affording invariable standards for measuring duration, distance, magnitude, and velocity. The sidereal day, measured by the time elapsed between two consecutive transits of any star at the same meridian, and the sidereal year, are immutable units with which all great periods of time are compared; the oscillations of the isochronous pendulum measure its smaller portions. By these invariable standards alone, we can judge of the slow changes that
other elements of the system may have undergone in the lapse of ages.
The returns of the sun to the meridian, and to the same equinox or solstice, have been universally adopted as the measure of our civil days and years. The solar or as
tronomical day is the time that elapses between two consecutive noons or midnights; it is consequently longer than the sidereal day, on account of the proper motion of the sun during a revolution of the celestial sphere; but, as the sun moves with greater rapidity at the winter than at the summer solstice, the astronomical day is more nearly equal to the sidereal day in summer than in winter. The obliquity of the ecliptic also affects its duration, for in the equinoxes the arc of the equator is less than the corresponding arc of the ecliptic, and in the solstices it is greater. The astronomical day is therefore diminished in the first case, and increased in the second. If the sun moved uniformly in the equator at the rate of 59′ 8′′.3 every day, the solar days would be all equal; the time, therefore, which is reckoned by the arrival of an imaginary sun at the meridian, or of one which is supposed to move uniformly in the equator, is denominated mean solar time, such as is given by clocks and watches in common life; when it is reckoned by the arrival of the real sun at the meridian, it is apparent time, such as is given by dials. The difference between the time shown by a clock and a dial is the equation of time given in the Nautical Almanac, sometimes amounting to as much as sixteen minutes. The apparent and mean time coincide four times in the year.
The astronomical day begins at noon, but in common reckoning the day begins at midnight. In England it is divided into twenty-four hours, which are counted by