743 MONSOON. which is also sometimes the case in Java and the Lesser Sunda Islands. The direction of the monsoons in the vicinity of the land is frequently changed by the direction of the coast, especially when a mountain range extends along the shores. The most remarkable instance of this phenomenon is observed on the south-western coast of the island of Sumatra. The south-west monsoon is felt at Acheen Head, its most northern point; but, being opposed by the range of high mountains running along the south-western coast, it is changed into a north-west wind, which blows as far south as 1° N. lat. South of the equator the wind is not south-west, but south-east, and may be considered as the trade-wind, which, as already observed, extends as far north as 3° S. lat. when the sun is in the northern hemisphere. During this period that part of the island which lies north of the equator has its rainy season, When the sun is in whilst the southern districts have dry weather. the northern hemisphere the southern portion has abundant rains, with frequent thunder-storms; and the northern enjoys a serene sky. In that season of the year the wind blows in the southern part from north west, and is that wind which is generally called the north-west monsoon; but the northern districts are under the influence of the north-east monsoon. north-east monsoon. It is not easy to explain the origin of these periodical winds. It is admitted on all hands that they are only a modification of the tradewinds, produced by the peculiar form of the countries lying within and around the Indian Ocean. This modification, it is said, is produced by the difference of temperature to which the high table-lands of Asia and Africa are subject during the two great divisions of the year. When the sun is in the northern hemisphere the heat causes such a rarefaction of the atmosphere on the table-land of Asia as to make the air flow rapidly from the colder region near the equator to that quarter; When, on the contrary, the sun, and this is the south-west monsoon. during its stay in the southern hemisphere, heats the air on the tableland of southern Africa, the contrary effect takes place, and that is the This explanation however is hardly satisfactory. It is a fact that on the high table lands the air is always in a state of rarefaction, compared with that of low countries, and that the summerheat is never such as to cause a degree of rarefaction sufficient to produce a motion in the air from the lower countries towards the tablelands. Besides this, the Himalaya mountains, with their immensely high masses, lie in the line in which the south-west monsoon blows, and its effects are not observed to be sensible in the higher part of that range. The table-lands of Beloochistan and Arabia cannot be considered as affecting the direction of the wind, for in that case the wind would rather blow from the south-east than from the south-west. We think therefore that the cause of this modification of the trade-wind must be sought for in less remote localities. As for the north-east monsoon, we are inclined to consider it entirely as a continuation of the north-east trade-wind, which is only interrupted by the two peninsulas stretching southward into the Indian Ocean; and this interruption is the cause why it is commonly less constant and regular than the trade-wind itself. The question therefore is only why this trade-wind is interrupted by a wind blowing in an opposite direction when the sun is in the northern hemisphere. In this part of the year the tradewind in the northern hemisphere retires thirteen degrees from the equator. If this fact is applied to the Indian Ocean, only the most northern recesses of the three gulfs, the Arabian Sea, the Bay of Bengal, and the Chinese Sea, would fall within its limits, and the remainder would be within the region of calms. In such a state of indiference a less powerful agency may produce a great effect. The south-east trade-wind, which, when the sun is on the north of the equator, extends to the vicinity of the equator, is prevented by the elevated table-land of Africa from proceeding in its direction, and is It follows the winding of the therefore diverted from its course. coast to the north-east; but as the coast of Africa, as well as that of Arabia, is skirted by very high mountains, it finds no way to escape in a western direction. It would however probably not acquire that degree of constancy and force by which it is characterised, if it did not blow towards a country in which a considerable rarefaction of the air is produced by the sun's approaching to the northern tropic. This is the Indian Desert, called Thurr, in which the heat in summer rises to an excessive degree, on account of its small elevation above the sea, its sandy soil, and the almost complete want of vegetation. The rarefaction produced by this heat gives strength and constancy to the south-west monsoon, and carries it to the very base of the Himalaya mountains, though the desert itself does not partake of the fertilising rains which this monsoon brings to all the coast whose mountains oppose its progress. This, we think, is sufficient to explain the south-west monsoon in the Arabian Sea, where it is most constant and regular. The south-east trade-wind, not extending to the north of the equator, cannot be considered as contributing to produce the south-west monsoon in the Bay of Bengal; and this wind therefore seems to owe its existence merely to the rarefaction of the air produced by the summerheat in the wide plain of the Ganges; but as this plain is partly covered with trees (Sunderbund and Terai) and nearly everywhere with vegetation, the effect of the heat on the temperature of the air is less regular; and thus it may be explained that the south-west The vegetation monsoon in this sea is less regular and constant, MONTH. rains brought by the monsoon are distributed over its whole extent, The origin of the south monsoon in the Chinese Sea is more difficult As for the monsoons of the Java Sea and of the seas between the MONT DE PIETE' (MONTE DI PIETA', in Italian), is the title This institution was introduced into other countries, especially into When the French under Bonaparte invaded Italy in 1796-7, they MONTEM CUSTOM, the ancient custom of a procession of the This ceremony has been frequently honoured with the presence of the sovereign and the royal family, whose liberal contributions added to those of many of the nobility and others who had been educated at Eton, so far augmented the general collection that it has been known to amount to near 1000l. The sum so collected was given to the captain of the school, or senior scholar, who was going off to Cambridge, for his support at the university. It would be in vain, perhaps, to trace the origin of all the circumstances of this singular custom, particularly that of collecting money for salt, which had been in use from time immemorial. The procession itself seems to have been coeval much probability, that it was that of the Bairn, or Boy-bishop. It with the foundation of the college, and it has been conjectured, with the patron of children, being the day on which it was customary at originally took place on the 6th of December, the festival of St. Nicholas, elect the Boy-bishop from among the children belonging to the catheSalisbury, and in other places where the ceremony was observed, to dral. It is only since 1759 that the time of the celebration of the Eton Montem was changed, and in 1778 it appears to have been held biennially. It was formerly a part of the ceremony that a boy dressed MONTH. [MOON; YEAR.] in a clerical habit, with a wig, should read prayers. In a day or two (depending on the state of the weather) from the time called in the almanacs "the new moon," a thin silver crescent is seen with its horns turned from the sun and placed to the eastward of the sun, after which it soon sets. Its distance from the sun increases, the horns at the same time growing fuller, until, in 7 days, it is at ninety degrees (or as far as from the horizon to the zenith) distant from the sun, and the crescent has become a semicircle of white light. The distance still increases, until the moon is 180° distant from the sun, or in the opposite part of the heavens, by which time the light part has become a full circle: this happens in somewhat more than 14 days from the new moon. The satellite still continues its revolution among the stars, becoming westward of the sun after the full moon, and, decreasing by the same steps as it increased, is lost a day or two before the time which the almanacs point out as the next new moon. The whole of this process takes up what is called a lunation, or a lunar month: the lunar months are slightly unequal, but their average period is 29 days, 12 hours, 44 minutes, 2 seconds, or 29-5305887215 mean solar days. To show the irregularity of the lunations, we give the times of all the new moons which take place ir the years 1860 and 1861, with the intervals. NEW MOONS. 1860, 1861. Excess of Interval over 29 days, h m 19 23 phenomenon occurred only 705 instead of 730 (twice 365) times. Now the motion of the moon round the heavens is found to take place (one time with another) in 27-32166142 solar days (we shall presently see why this is not a lunation), which gives 13° 10' 35" increase of right ascension in each solar day, or 13° 8' 23" in a sidereal day, or actual revolution of the earth. Hence the meridian of the spectator, between two times at which the moon is on the visible side of that meridian, must make so much more revolution as is necessary to overtake a body which revolves through 13° 8' 23" while it revolves through 360°; which gives 24h 55m of a revolution of the earth for each lunar day, or 12 274 for its half. Now the year contains 3661 sidereal days, or simple revolutions of the earth; and it will be found that 12h 274m is contained 705 times and a fraction in 3661d. As every reader may not be acquainted with the distinction of sidereal and solar time, we may here simply state (referring to SUN and TIME for detail) that the common day is not the simple revolution of the earth, but includes the additional time in which the meridian overtakes the sun, which has moved forward about a degree. Thus it appears, that even on a single year the coincidence of half a lunar day and the interval between two times of high water is sufficiently apparent. It may be said that we have assumed the question by counting the times of high water from an almanac constructed on the supposition which we wished to establish. This would be true if we had talked of the year 1860; but we may consider an almanac for 1858 as now a verified prediction: it would have made no small noise in the public papers if there had been a tide more or less in the Thames than was predicted in the almanacs. The theory of the tides is the most difficult in astronomy, owing to the disturbing action of winds, channels, &c., as well as its intrinsic mathematical difficulties; but this one phenomenon has never had its exception in open sea-that every transit of the moon over (either side of) the meridian is followed by the rise of the water, though so high a wind has been known as to prevent the tide coming up a river. We return to the phenomena of the phases (Greek for appearances), as they are called, of the moon, namely, the changes in the quantity of its illuminated part. These may be immediately explained on the supposition that the moon is not luminous itself, but receives its light from the sun. To show how this may be, suppose a ball, illuminated by another ball at a great distance in the direction ES, to be carried round the spectator at E. This ball may be always subdivided into a visible and in 18 21 15 49 13 1 10 37 8 56 8 0 7 50 Sept. 15 8 27 9 59 12 12 14 50 16 38 17 32 17 19 16 11 12 34 10 41 K 9 18 8 45 9 7 10 13 1861. Jan. 11 H F B It appears then not only that the lunar month varies, but that there is no yearly cycle of variation. Before however we make any remark on the preceding, we shall place by its side materials for confidence in the almanac from whence the preceding times were quoted. Taking at hazard a volume of astronomical observations, and opening the part where the results of the lunar observations are found, we took the first right ascensions [ASCENSIONS] of the moon which we came to, opposite to which, for comparison, were written the predicted right ascensions of the moon for the same times. The dates matter nothing, since it is only the accordance of prediction with observation which is to be noticed. (Camb. Obs., 1835.) The lunar theory then, resting upon the Newtonian doctrine, enables astronomers to find the position of the moon within a part of the heavens answering to a second of diurnal revolution, while the rough observations with which astronomy must always commence would not give the length of a lunation within an hour. It is also confidently expected that the lunar tables recently computed by Professor Hausen of Gotha, in accordance with his lunar theory, and printed at the expense of the British government, will, from their superiority, ensure a degree of accuracy of prediction hitherto unprecedented. Taking the lunar phenomena in the order of discovery, we next notice that this planet writes its mark on the earth in terms which have been understood from the earliest ages of astronomical inquiry. The alternate rise and fall of the waters, called the tides, is found to follow its motions, so that high water always found to succeed the time when the moon comes on the meridian, whether on the visible or invisible side of it. At first sight it would appear that there is high water twice a-day (that is, in the common solar day), but it is found on further examination that the interval between high water and high water is a little more than twelve hours; so that in the year 1858 that visible half, since one-half must hide the other in all positions. But it may also be divided into an illuminated and unilluminated half. At a the visible half is all unilluminated, and though we have called it the visible half (meaning in a position to be seen, if there were light), it will not be seen. But when the ball arrives at B, a small portion of the illuminated half is in the visible half, as much as is intercepted between the arrows. At D a larger portion of the illuminated part is visible, and at F a full half of the visible surface is illuminated. A little consideration of this scheme (which is moreover explained in all popular works) will show not only the occurrence of phases precisely similar to those of the moon, but also that the circular boundary of the enlightened part is towards the illuminating body. We copy from Riccioli his collection of the Latin and Greek terms used with respect to the different phases : A Novilunium, luna silens, Conjunctio, Congressus cum sole, Neomenia, Synodus, Lunæ accensio. H, K, L, I, Luna Gibba, gibbosa; H primus, πασμένα Luna crescens ab A per F in M, Luna descrescens ƒ σeλývŋ avžavoμévn seu senescens ab M per G in A. If the moon moved in the plane of the ecliptic, or of the sun's motion, as in the figure, there would be an eclipse of the sun at every new moon (A), and of the moon at every full moon (M); since in the former case the moon would hide the sun, and in the latter the earth would intercept the sun's light. The moon however is generally a little on one side or the other of the ecliptic, not enough to introduce any sensible error into the preceding explanation of the phases, but enough to hinder the eclipses from taking place, except now and then : we shall see more of this presently. Again, if the sun remained in the line E s, the lunation, or complete cycle of phases, would be of the same duration as the actual revolution of the moon round the heavens. Since however the sun moves slowly forward in the same direction as the moon, the latter does not alter its phases so rapidly as in the figure, nor is the cycle of phases complete until the moon has overtaken the sun. It is usual to divide the whole lunation into four quarters, the first from new moon to increasing half moon, the second from half moon to full moon, the third from full moon to waning half moon, the fourth from half moon to new moon. Each of these is called the change of the moon, and it is a very common belief that a change of weather and wind is to be expected, if not at every change of the moon, at least much oftener at the changes than in the intervals. This opinion, when not absolutely received as true, is usually treated as the extreme of absurdity. It is in truth neither one thing nor the other, as the following considerations will show. The atmosphere is continually undergoing a slight alteration from At new and full moon (or rather a little after the effects of the tide. these phenomena) there are those great tides called the spring-tides, arising from the action of both luminaries; at the two quarters the same luminaries oppose each other, and the quarters are followed by the smaller floods, called neap-tides. What effect may be produced by this succession of smaller and greater oscillations of the sea, which must produce oscillations of the atmosphere, it is impossible to say beforehand. Again, we know nothing of the electric action of either luminary upon the earth, or whether any and what electric state may depend upon their relative position. We have therefore abundant grounds à priori to abstain from forming any opinion upon the effect of the heavenly bodies upon the weather; and we shall now state the results of such facts as observation has furnished. M. Arago collected the evidence on this subject in an article published in the Annuaire for 1833; the general conclusion derived from them is, that upon the whole there is a little more rain during the second quarter than during either of the others; but that there is no evidence to confirm the common notion that a change of the moon is accompanied by change of weather. It has also been observed that the height of the barometer is, one time with another, less in the middle of the second quarter than in that of either of the others; and that it is somewhat greater at new and full moon than at the quarters. With regard to a great many other asserted effects of the moon upon animal and vegetable life, it can only be said that there is no conclusive evidence for or against them; nothing but a long series of observations can settle such points, and this is not likely to be made (or if made, to be made fairly) by those who have predetermined the questions in one way or the other. The moon's age is usually reckoned from the new moon, and the rules by which Easter is found depend, or should depend, upon a correct knowledge of this age at the beginning of the year, called the EPACT. But all readers should remember that the sun and moon by which Easter is found are not the real bodies, but fictitious ones, moving not with the real but the average motions, and therefore sometimes before and sometimes behind the real bodies. It should then be no matter of surprise if, as will happen, Easter Sunday should sometimes be seven days sooner or later than it would be if the real bodies were employed. [EASTER, METHOD OF FINDING.] We now come to the actual motion of the moon round the earth, which is the most complicated question in astronomy. Roughly speaking, it may be said that the moon's motion is circular, which is sufficient for the explanation of the phases; it is somewhat, but very little, more correct to say it is elliptical. If the moon's orbit were actually exhibited in space, an ellipse might be found which would nearly fit one of its convolutions; but the succeeding convolutions would depart further and further from such an ellipse, and it would be nineteen years before a convolution would again occur which is situated in space near to the ellipse with which we started. And though astronomers have found a way of simplifying the question, by supposing the moon MOON. to move in an ellipse which itself moves in space, yet we may better explain the subject by arriving at that ellipse from the real motion than by beginning with it. When the motion of the moon is watched in the heavens with instruments fitted to measure her apparent diameter, it is soon found that she changes her distance from the earth, becoming alternately larger and smaller. Her path is not very much inclined to the eclipt e, so that she is never 51° from some one of the positions which the sun F has had or will have in the course of the year. We may explain the We may notice, then, five distinct species of months:-1. The average lunation, common month, or interval between two conjunctions average sidereal month, or complete circuit of the heavens. 2. The If we compare the lunation with the common year, we shall find that 235 lunations make 6939-69 days, while 19 years make 6939 or 6940 days, according as there are four or five leap-years in the number. Neither is wrong by a day; consequently in 19 years the new and full moons are restored to the same days of the year. This does not absolutely follow, either from the preceding or from the method which gave it, since neither is the coincidence exact, nor are the months exactly equal. But it will generally so happen; and this is the foundation of the Metonic Cycle. [CALIPPUS and METON, in BIOG. DIV.] Again, 223 lunations make 6585-322 days, and 242 nodical revolutions make 6585-357 days, so that there is only 035 of a day, or 50 minutes, difference between the two. This period of 223 lunations is the SAROS, a celebrated Chaldean period, and contains in round numbers of days 18 years and 10 days, or 18 years and 11 days, according as there are five or four leap-years. It may be worth while to express these numbers of lunations in terms of the other months. Metonic Cycle.-235 lunations make 253-999 sidereal months, 251.852 anomalistic months, and 255-021 nodical months. Saros.-223 lunations make 241.029 sidereal months, 238.992 anomalistic months, and 241 999 nodical months. The rate at which the moon moves is different in different parts of the orbit. We may speak either of the rate at which she changes longitude, latitude, or distance from the earth; and owing to the smallness of the inclination of her path to the ecliptic, her motion in longitude is nearly the same thing as her motion in her own orbit. The quickest motion is at or near the perigee, and the slowest at or near the apogee. The moon's rate of motion follows no easily obtain able law in its changes, which are different in different months. The rate of change of latitude is greatest near the nodes, and the rate of change of distance from the earth is least at the apogee and perigee, and greatest at and about the intermediate points. We have hitherto considered the apparent path of the moon among the stars: we now pass to the real orbit in space. Her average distance from the earth is 29-982175 times the equatorial diameter of the earth, which makes about 60 radii of the earth, or 237,000 miles. But the radius of the sun's body is 111 times the radius of the earth: so that a large sphere, which, having its centre in the earth, should contain every part of the moon's orbit, would not be a quarter of the size of the sun. Again, the sun's distance is 23,984 radii of the earth, or nearly 400 times the moon's average distance. A good idea of the relative magni. tudes of the distances may be obtained as follows:-Take a ball one inch in diameter to be the sun, and another of half an inch in diameter to be the sphere which envelopes the moon's real orbit; place these nine feet apart, and a proper idea of the distance of the sun, compared with its size and that of the moon's orbit, will be obtained. To form a sufficient notion of the real orbit, imagine another body, directly under the moon on the plane of the ecliptic, to accompany her in her motion. Let ssss represent the plane of the ecliptic, in which the sun must be, and ALB a part of the real orbit, from an ascending to a descending node; L being a position of the moon, P is the projected body on the plane of the ecliptic; and the motion of P will be very nearly that of L, owing to the smallness of the rise of ALB above the plane of the ecliptic. The motion of the projected body will then be of the kind of which the following diagram is an exaggeration. Suppose the moon to set out from 1 on the left, being then in apogee, and also at a node: the projected body will then describe 111, &c., until it comes to its perigee at the first 2, which is in advance of the point opposite to the apogee. But the real moon will have come to the plane of the ecliptic before it is opposite to the first 1, so that at the first 2 the moon will be below the projected orbit. The projected body then describes 2 2 2 ... up to the next apogee 3, and so on; the 15 10 16 12 the first; in the moon's orbit the number of folds is unlimited. The real relation between the greatest and least distances is slightly variable in the different folds; one with another it may be thus stated: 5 per cent. being added to the mean distance will give the greatest or apogean distance, and subtracted, the least or perigean distance. Taking the fiction of the moving ellipse for the moon's orbit, its eccentricity is '0548442. In the article GRAVITATION will be found a sketch of the producing causes of the inequality of the lunar motions, showing that they arise from the effect of the sun's unequal attraction of the earth and moon; were it not for which, the latter would describe an ellipse round the former. In the present article we intend only to describe the motions themselves. We have pointed out both the apparent orbit in the heavens, and the real orbit: It remains to ask, In which manner is the real orbit described? At a given time, how is the moon's place in the heavens to be ascertained? Returning again to the apparent orbit, we first consider motion in longitude only; that is we ask how to find the moon's longitude at the end of a given time. Let us suppose then that, Q being the apparent place of the moon in the heavens, we draw QM on the sphere perpendicular to the ecliptic, so that м has the same longitude as q. To connect this figure with the last, suppose that the moon was at L when it was projected in the heavens to Q, and let P be the projection of L on the ecliptic: then P will be thrown upon м in the heavens. The average motion of м will be that of the moon, or a circuit in 27 32166 days. If then we were to suppose a fictitious moon setting out from M, and moving with this average motion, it would never be far from the point M; which last, from the irregularity of the real moon's motion, would be sometimes before and sometimes behind the fictitious moon. If we could observe the fictitious moon, thus regularly moving in the ecliptic (say every day at midnight), and also the real moon, we might take a long series of years' observations, and sum all the excesses of M's longitude over that of the fictitious body, when there are excesses, and all the defects when there are defects. We might expect to find the one sum equal to the other; but we are taught by the theory (which, as before seen, is exact enough to find the moon's place within a second) that the equality of these sums will not be absolutely attained in any series of years, however great, if we take the commencing point, at which м is to coincide with the fictitious body, at our own caprice. Wherever Q may be, there is a proper place for this fictitious moon, before or behind M, from which if we allow the former to start, the longer we go on with the series of supposed observations, the more nearly will the excesses balance the defects; supposing always that our series of observations stops at the end of a complete number of circuits, and not in the middle of one. This position is called the mean place of the moon, as distinguished from Q, its real place. Let us suppose it to be at v; then if the average moon start from v, with the moon's average motion, it will at every instant of time point out what is called the mean place of the moon corresponding to the then real place. At the commencement of the present century, that is, when it was 12 o'clock at Greenwich on the night of December 31, 1800, the longitude of the average moon, or the moon's mean longitude, was (according to Burckhardt) 118° 17′3′′; and the mean longitude at any other time is found by adding in the proportion of 4809-38468 for every 365 days, and making the necessary additive allowance for the precession of the equinoxes. [PRECESSION.] In the same way the node and perigee of the moon have their mean places, and, as we have seen, their mean motions. The mean longitude of the perigee, at the commencement of the century, was 266° 10′7′′-5; that of the ascending node 13° 53′ 22′′-2. To the above must be added that these average motions, as they are called, are subject to a slight acceleration, which hardly shows itself in a century; that of the longitude was detected by Halley from the comparison of some Chaldean eclipses with those of modern times. This acceleration would, in a century, increase the mean longitude of the moon by 11", that of the perigee by 50", and that of the ascending node by 7". The mean longitude being ascertained for the given time, the true longitude is found by applying a large number of corrections, as they are called, some determined from the theory of gravitation, but the larger ones, as might be supposed, detected by observation before that theory was discovered, and since confirmed by it. Into this subject it will be impossible to enter at length; we shall therefore merely instance a few of the principal corrections for the longitude, observing that the latitude, the distance, &c., are all determined by adding or subtracting a number of corrections from the results of the supposition that the moon moves uniformly in the ecliptic at her average distance from the earth. The first correction is one which brings the motion nearer to an elliptical one, and is called the equation of the centre. It depends upon the moon's distance from her perigee, called the anomaly. The mean anomaly is the distance of the moon's mean place from that of the perigee. The mathematical expression is (we give only rough constants)— 6° 17′ x sin (mean anomaly). which actually come into use may be represented by straight lines. Let the centre of the moon be at E when that of the shadow is at c; and let the hourly motions of the sun (that is, of the shadow) and of the moon be CF and EG. If then we communicate to the whole system a motion equal and contrary to CF [MOTION], the shadow will be reduced to rest, and the relative motion of the moon with respect to it will remain unaltered. Take EH equal to CF, and contrary in direction; then EL will represent the quantity and direction of the hourly motion of the moon relatively to the shadow at rest. By geometrical construction therefore, M, N, and P may be ascertained, the positions of the moon's centre at the beginning, middle, and end of the eclipse; and EM, EN, and E P, at the rate of EL to an hour, represent the times elapsed between that of the moon being at E and the phenomena in question. Such is the geometrical process: the one employed in practice is algebraical, and takes in several minor circumstances which it is not worth while here to notice. An eclipse of the moon is a universal phenomenon, since the moon actually loses her light, in whole or in part; while in an eclipse of the sun, the moon hides the sun from one part of the earth, but not from another. The former can only take place when the conjunction (or sameness of longitude) of the moon and earth's shadow, that is, the opposition of the sun and moon, or the full moon, happens when the moon is near her node. [ECLIPSE; SUN; SAROS.] For the phenomena of the occultation of a star by the moon, see OCCULTATION. By the harvest-moon is meant a phenomenon observed in our latitudes at the time of the full moon nearest to the autumnal equinox. when it happens for a few days that the moon, instead of rising fiftytwo minutes later every day, rises for several days nearly at the same time. Something of the same sort takes place always when the moon is near her node; but the circumstance is most remarkable when it happens at the time of greatest moonlight. The reason is that the increase of declination (which is most rapid when the moon is near the equator, which she must be when full moon comes nearly at the time of the equinox) compensates the retardation which would other The second correction, known as the erection, and discovered by wise arise from her orbital motion. [SPHERE.] See the treatise above Ptolemy, iscited, pp. 80, 81. 1°16′ × sin { 2 (C o) -- mean anomaly} where and stand for the mean longitudes of the moon and sun. The variation and the annual equation (discovered by Tycho Brahé) are represented by 39' x sin 2 (-O) and 11'x sin (O's mean anomaly.) Many such corrections (but those which remain, of less amount) must be added to or subtracted from the mean longitude before the true longitude can be determined. Having thus noticed the actual motions of the moon, we proceed to the phenomena of eclipses, and of the harvest-moon, as it is called. An eclipse of the moon has now lost most of its astronomical importance, and can only be useful as an occasional method of finding longitude, when no better is at hand. Eclipses of the sun, observed in a particular way, may be made useful in the correction of the theory both of the sun and moon; in this case matter is absolutely hid from view by matter, and the moment of disappearance can be distinctly perceived. But in the case of the moon, which is eclipsed by entering the shadow of the earth, the deprivation of light is gradual; so that it is hardly possible to note, with astronomical exactness, the instant at which the disappearance of the planet's edge takes place. to be repre In a lunar eclipse the first thing to be ascertained is the diameter of the earth's shadow at the distance of the moon. Suppose this shadow, that is, its section at the distance of the moon, sented by the circle whose centre is c: it is directly opposite to the sun, its centre is on the ecliptic, and moves in the direction of the sun's general motion, or from west to east. The discovery of the telescope, and the examination of the moon which followed, soon showed that the planet always turns the same face towards the earth, or very nearly. From hence it immediately follows that the moon must revolve round an axis in the same time as that axis revolves round the earth. If any one should walk round a circle without turning himself round, that is, keeping his face always in the same direction, he would present alternately his front and back to the interior of the circle. But if he desires to turn his face always inwards, he must turn round in the same direction as he walks round. [MOTION, DIRECTION OF.] If the moon moved uniformly round in her orbit, and had a uniform rotation of the same duration, then if her axis were perpendicular to the plane of the orbit, and the spectator were always at the earth's centre, the face of the moon 1. The motion in the orbit is irregular, while the rotation is uniform would be always actually the same. None of these suppositions are true. and exactly the sidereal month: the consequence will be that when the moon is moving quicker than the average, a little of the western side be disappearing, and rice versa. 2. The axis of the moon is not perwill be coming into view, and a small portion of the eastern side will pendicular to her orbit, but is out of the perpendicular by an angle of 5° 8' 49"; the consequence is, that as she revolves in her orbit, the north and south poles of the moon will alternately become invisible, the earth's axis, which will slightly vary the part seen of the moon in each during half a revolution. 3. The spectator is in motion round the course of the day. These effects are called librations: (1) the libration in longitude, (2) the libration in latitude, (3) the diurnal libration. The second will be elucidated in SEASONS, CHANGE OF, and the third in PRECESSION and NUTATION. The way in which we know that the face presented is always nearly the same, is by observation of that face, which is varied by numberless spots and streaks. The following cut represents the general appearance of the moon at full, being a view of its average face in the mean state of libration, that is to say, no part of the present edge is ever hidden by libration without as much of the opposite edge being hidden at some other time. It may here be mentioned that photography has been applied to the production of views of the lunar surface with great success. Among these, the beautiful photographs by Professor Bond in America, and Mr. Warren De La Rue in this country, hold a distinguished place. Indeed the stereoscopic views of the moon in different states by the latter gentleman, leave but little to be done by succeeding photogra phers, their effect being such as to excite the surprise and admiration of all by whom they are viewed. For particulars respecting the spots on the moon, the reader is referred to a work lately published by the Rev. T. W. Webb, entitled 'Celestial Objects for Common Telescopes.' In this little work, which contains a vast amount of information on practical subjects, a map of the moon is given, exhibiting the places and delineations of 404 of the principal craters and other appearances on the lunar surface carefully reduced from the large map published by Beer and Mädler, and verified for the most part by actual observation. Casual observers of the lunar surface must however bear in mind, |