derably elongated from the Sun, it is then out of the way of this reflection. 5. The time between two conjunctions, or two oppositions, called a lunation, and synodic month, is greater than the time of a revolution in the orbit, or the time of return to the fixed star. Because, when' the latter time is completed, the Moon has to move a farther space to overtake the Sun. = Let S period of Sun's apparent motion round the Earth. P=period of Moon's motion about the Earth. L= period between conjunction and conjunction, or of a lunation. Then S: P:: 4 right angles: angle described by Sun in the Moon's periodic time = angle gained by the Moon in the time L-P. But the angles gained by the Moon are as the times of gaining them. Therefore, 4 right angles: angle gained by Moon in time L - P :: L:L-P. Hence, S: P::L: L-P, or S: S - P : : L : P, therefore 6. In 19 solar years, of 365 days, there are 235 lunations and one hour. Therefore, considering only the mean motion, at the end of 19 years, the full moon falls again upon the same days of the nonth, and only one hour sooner. This is called the Metonic cycle, from Meton, who published it at the Olympic Games, in the year 433, before the Christian era. This period of 19 years has been always in much estimation for its use in forming the calendar; and from that circumstance, the numbers of this cycle have been called the golden number.. Golden One of the earliest attempts upon record to discover the distance of the sun from the earth, was from observing when the moon was exactly halved or dichotomised. At that time the angle at the moon, formed by lines drawn from the moon to the sun and earth, is exactly a right angle; therefore, if the elongation of the moon from the sun be exactly observed, the distance of the sun from the earth will be had, that of the moon being known, by the solution of a right angled triangle; that is, sun's distance: moon's distance:: radius: cosine moon's elongation. The uncertainty in observing when the moon was exactly dichotomised, rendered this method of little value to the ancients. However, by the assistance of micrometers, it may be performed with considerable accuracy. Vendelinus, observing at Majorca, the climate of which is well adapted to observation, determined in 1650, the sun's distance, by this method, very considerably nearer than had been done at that time by any other method. of This method is particularly worthy of attention, being the first attempt for the solution of the important problem finding the sun's distance. It was used by Aristarchus of Samos, who observed at Alexandria, about 280 years before the commencement of the christian era. 7. Viewing the moon with a telescope, several curious phenomena offer themselves. Great variety is exhibited on her disc. There are spots differing very considerably in degrees of brightness. Some are almost dark. Many of the dark spots must necessarily be excavations on the surface or valleys between mountains, from the circumstances of the shades of light which they exhibit. There is no reason to suppose that there is any large collection of water in the moon; for if there were, when the boundary of light and darkness passes through it, it must necessarily exhibit a regular curve, which is never observed. The non-existence of large collections of water is also probable, from the circumstance of no change being observed on the moon's surface; such as would be produced by vapours or clouds; for, although, as will be remarked, the atmosphere of the moon is comparatively of small extent, yet it is probable that an atmosphere does exist. 8. That there are lunar mountains is strikingly apparent, by a variety of bright detached spots almost always to be seen on the dark part, near the separation of light and darkness.. These are tops of eminences enlightened by the sun, while their lower parts are in darkness. But sometimes light spots have been seen at such a distance from the bright part, that they could not arise from the light of the sun. Dr. Herschel has particularly taken notice of such at two or three different times. These, he supposes, are volcanoes. He measured the diameter of one, and found it equal to 3", which answers to four miles on the surface of the moon. The heights of lunar mountains may be ascertained by measuring with a micrometer the distance between the top of the mountain, at the instant it first becomes illuminated, and the circle of light and darkness. This measurement is to be made in a direction perpendicular to the line, joining the extremities of the horns. See Dr. Brinkley's Elements of Astronomy. According to Ricciolus, the top of the hill, called St Catherine's, is nearly 8 miles in height. But later astrono mers are not inclined to allow of so great an elevation to any of the lunar mountains. Dr. Herschel investigated the height of a great many; and he thinks that, a few excepted, they generally do not exceed halt a mile. But there seems to be little doubt that there are mountains on the surface of the moon, which must exceed those on the surface of our earth, taking into consideration the relative magnitudes of the moon and earth. Schroeter determined the height of one, called Leibnitz, to be 25,000 feet, whereas the height of Chimborazo is not 22,000 feet; so that taking into consideration the relative magnitudes of the earth and moon, this lunar mountain will be five times higher than any of the terrestrial mountains. 9. It is not the least remarkable circumstance of the moon, that it always exhibits nearly the same face to us. We always observe nearly the same spots, and that they are always nearly in the same position with respect to the edge of the moon. Therefore as we are certain of the motion of the moon round the earth, we conclude that this must revolve on an axis nearly perpendicular to the plane of his orbit, in the same time that she performs her synodic revolution. This must necessarily take place in order that the same face may be continually turned towards the earth during a whole revolution in her orbit. The motion of the moon in her orbit is not equable, therefore if the rotation on her axis be equable, there must be parts in her eastern and western edges, which are only occasionally seen. These changes, called the moon's libration in longitude, are found to be such as would agree with an equable motion of rotation. There are parts about her poles only occasionally visible. This, called her libration in latitude, arises from her axis being constantly inclined to the plane of her orbit in an angle of 860. A diurnal libration also takes place; at rising, a part of the western edge is seen, that is invisible at setting, and the contrary takes place with respect to the easterr. edge. This is occasioned by the change of place in the spectator, on account of the earth's rotation. 10. At the full moon nearest the autumnal equinox, the moon is observed to rise nearly at sun-set, for several nights together. This moon, for its uses in lengthening the day, at a time when a continuance of light is most desirable to assist the husbandman in securing the fruits of his agricultural labour, is called the harvest moon. The rising and setting of the moon is most interesting at and near full moon. At full moon, it is in or near that part of the ecliptic, opposite to the sun. Hence, at full moon, at mid-summer, it is in or near the most southern part of the ecliptic, and consequently appears but for a short time above the horizon; and so there is little moon-light in summer, when it would be useless. In mid-winter, at full, it is near or in the northernmost part of the ecliptic, and therefore remains long above the horizon, and the quantity of moon-light is then greatest when it is most wa wanted; and this is the more remarkable, the nearer the place is to the north pole. There at mid-winter the moon does not set. for 15 solar days together, namely, from the first to the last quarter. The moon, by its motion from west to east, rises later every day, but the retardations of rising are very unequal. In northern latitudes, when the moon is near the vernal equinox, or the beginning of the sign Aries, the retardation of rising is least, and when near the beginning of Libra, greatest. This will appear by considering that when Aries is rising, the part of the ecliptic below the horizon makes the least angle with the horizon, and when Libra is rising, the greatest. This may be satisfactorily illustrated by the celestial globe. The variation of the retardation of rising, according as the moon is in or near different parts of the ecliptic, being understood, the explanation of the harvest moon is very easy. The moon, at full, being near the part of the ecliptic, opposite to the sun, and at the autumnal equinox the sun being in Libra; consequently the moon must be then near Aries, when, from what has been stated, the retardation of her rising amounts only to a few minutes; and as the moon at full always rises at sun-set, the cause of the whole phenomenon is still more striking, and there it is of greater use where the changes of seasons are much more rapid. In some years the phenomenon of the harvest moon is much more perceptible than in others, even although the moon should be full on the same day, or in the same point of her orbit. This is owing to a variation in the angle which the moon's orbit makes with the horizon of the place where the phenomenon is observed. If the moon moved exactly in the ecliptic, this angle would always be the same at the same time of the year. But as the moon's orbit intersects the ecliptic, and makes an angle with it of 509', the angle formed by the moon's orbit and the horizon of any place is not exactly the same as that made by the ecliptic and horizon. When the ascending node happens to be in Aries, the harvest moon will appear to the greatest advantage; but, when the descending node is in Aries, the phenomenon will be the least remarkable. At places near the equator, this phenomenon does not happen; for every point of the ecliptic, and nearly every point of the moon's orbit, makes the same angle with the horizon, both at rising and setting, and therefore equal portions of it will rise and set in equal times. As the moon's nodes make a complete circuit of the ecliptic in about 18 years and 225 days, it is evident, that when the ascending node is in the first point of Aries at any given time, the descending node must be in the same points about 9 years and 112 days afterwards; consequently, there will be a regular interval of about 9 years between the most beneficial and least beneficial harvest moons. 11. The moon, when at, or near, the horizon, appears much larger than when at, or near, the zenith; and yet it can be demonstrated that the |