the light of the moon and the changes of the moon were probably the first phenomena which led men to study the motions of the heavenly bodies. in our times, when most men live where artificial illumination is used at night, we can scarcely appreciate the full value of moonlight to men who cannot obtain artificial light. especially must moonlight have been valuable to the class of men among whom, according to all traditions, the first astronomers appeared. the tiller of the soil might fare tolerably well without nocturnal light, though even he,—as indeed the familiar designation of the harvest-moon shows us,—finds special value, sometimes, in moonlight. but to the shepherd moonlight and its changes must have been of extreme importance as he watched his herds and flocks by night. we can understand how carefully he would note the change from the new moon to the time when throughout the whole night, or at least of the darkest hours, the full moon illuminated the hills and valleys over which his watch extended, and thence to the time when the sickle of the fast waning moon shone but for a short time before the rising of the sun. to him, naturally, the lunar month, and its subdivision, the week, would be the chief measure of time. he would observe—or rather he could not help observing—the passage of the moon around the zodiacal band, some twenty moon-breadths wide, which is the lunar roadway among the stars. these would be the first purely astronomical observations made by man; so that we learn without surprise that before the present division of the zodiac was adopted the old chaldean astronomers (as well as the indian, persian, egyptian, and chinese astronomers, who still follow the practice) divided the zodiac into 28 lunar mansions, each mansion corresponding nearly to one day's motion of the moon among the stars.

it is easy to understand how the first rough observations of moonlight and its changes taught men the true nature of the moon, as an opaque globe circling round the earth, and borrowing her light from the sun. they perceived, first, that the moon was only full when she was opposite the sun, shining at her highest in the south at midnight when the sun was at his lowest beneath the northern horizon. before the time of full moon, they saw that more or less of the moon's disc was illuminated as he was nearer or farther from the position opposite the sun, the illuminated side being towards the west—that is, towards the sun; while after full moon the same law was perceived in the amount of light, the illuminated side being still towards the sun, that is, towards the east. they could not fail to observe the horned moon sometimes in the daytime, with her horns turned directly from the sun, and showing as plainly, by her aspect, whence her light was derived, as does any terrestrial ball lit up either by a lamp or by the sun.

the explanation they gave was the explanation still given by astronomers. let us briefly consider it. in doing so i propose to modify the ordinary text-book illustration which has always seemed to me ingeniously calculated (with its double set of diversely illuminated moons around the earth) to make a simple subject obscure.

in fig. 12, let e represent the earth one half in darkness, the other half illuminated by the rays of the sun s, which should be supposed placed at a much greater distance to the left,—in fact, about five yards away from e. to preserve the right proportions, also, the sun ought to be much smaller and the earth a mere point. i mention this to prevent the reader from adopting erroneous ideas as to the size of these bodies. in reality it is quite impossible to show in such figures the true proportions of the heavenly bodies and of their distances. next let m1, m2, m3, etc., represent the moon in different positions along her circuit around the earth at e.

fig. 12.—explaining the moon's changes.

fig. 13.—illustrating the moon's changes.

now, it is clear that when the moon is at m1, her illuminated face is turned from the earth, e. she therefore cannot be seen; and accordingly, in fig. 12, she is presented as a black disc at 1 to correspond with her invisibility when she is as at m1. she passes on to m2; and now from e a part of her illuminated half can be seen towards the sun, which would be towards the right, if we imagine an eye at e looking towards m2. her appearance then is as shown at 2, fig. 13. in any intermediate portion between m1 and m2, the sickle of light is visible but narrower. we see also that all this time the moon's place on the sky cannot be far from the sun's place, for the line from e to m2 is not greatly inclined to the line from e to s. when the moon has got round to m3, the observer on the earth sees as much of the dark half as of the bright half of the moon, the bright half being seen, of course, towards the sun. thus the moon appears as at 3, fig. 13, again as to position, the moon is now a quarter of a circuit of the heavens from the sun, for the line from e to m3 is square to the line from e to s. we see similarly that when at m4 the moon appears as shown at 4, fig. 13, for now the observer at e sees as small a part of the moon's dark side as he had seen of her bright side when she was at m2. when she is at m5 the observer at e sees her bright face only, the dark face being turned directly from him. she, therefore, appears as at 5, fig. 13. also being now exactly opposite the sun, as we see from fig. 12, she is at her highest when the sun is at his lowest, or at midnight; and at this time she rules the night as the sun rules the day.[10] as the moon passes on to m6, a portion of her dark half comes into view, the bright side being now towards the left, as we look at m5 from e, fig. 12. her appearance, therefore, is as shown at 5. when at m7 she is seen as at 7, half-bright and half-dark, as when she was at m3, but the halves interchanged. at m8 she appears as at 8, and, lastly, at m1 she is again undiscernible.

the ancient chaldean astronomers could have little doubt as to the validity of this explanation. in fact, while it is the explanation obviously suggested by observed facts, one cannot see how any other could have occurred to them.

but if they had had any doubts for a while, the occurrence of eclipses would soon have removed those doubts. they must early have noticed that at times the full moon became first partly obscured, then either wholly disappeared or changed in colour to a deep coppery red, and after a while reappeared. sometimes the darkening was less complete, so that at the time of greatest darkness a portion of the moon seemed eaten out, though not by a well defined or black shadow. these phenomena, they would find, occurred only at the time of full moon. and if they were closely observant, they would find that these eclipses of the moon only occurred when the full moon was on or near the great circle round the stellar heavens, which they had learned to be the sun's track. they could hardly fail to infer that these darkenings of the moon were caused by the earth's shadow, near which the moon must always pass when she is full, and through which she must sometimes pass more or less fully; in fact, whenever, at the time of full, she is on or near the plane in which the earth travels round the sun. solar eclipses would probably be observed later. for though a total eclipse of the sun is a much more striking phenomenon than a total eclipse of the moon, yet the latter are far more common. a partial eclipse of the sun may readily pass unnoticed, unless the sun's rays are so mitigated by haze or mist that it is possible to look at his disc without pain. whenever solar eclipses came to be noted, and we know from the chaldean discovery of the great eclipse period, called the saros, that they were observed at least two thousand years before the christian era, the fact that the moon is an opaque body circling round the earth, and much nearer to the earth than the sun is, must be regarded as demonstrated. not only would eclipses of the sun be observed to occur only when the moon was passing between the earth and the sun, but in an eclipse of the sun, whether total or partial, the round black body cutting off the sun's light wholly or partially would be seen to have the familiar dimensions of the lunar orb.

leaving solar and lunar eclipses for description on another occasion, i will now proceed to consider a peculiarity of moonlight which must very early have attracted attention,—i mean the phenomenon called the harvest-moon.

the moon circuits the heavens in a path but slightly inclined to that of the sun, called the ecliptic, and for our present purpose we may speak of the moon as travelling in the ecliptic. now we know that during the winter half of the year the sun is south of the equator, the circle of the heavenly sphere which passes through the east and west points of the horizon, and has its plane square to the polar axis of the heavens. during the other or summer half of the year he is north of the equator. in the former case the sun is above the horizon less than half the twenty-four hours, day being so much shorter as the sun is farther south of the equator; whereas in the latter case the sun is above the horizon more than twelve hours, day being so much the longer as the sun is farther north of the equator. precisely similar changes affect the moon, only, instead of taking place in a year (the time in which the sun circuits the stellar heavens), they occur in what is called a sidereal month, the time in which the moon completes her circuit of the stellar heavens. for about a fortnight the moon is above the horizon longer than she is below the horizon, while during the next fortnight she is below the horizon longer than she is above the horizon. now clearly when the length of what we may call the moon's diurnal path (meaning her path above the horizon) is lengthening most, the time of her rising on successive nights must change least. she comes to the south later and later each successive night by about 50? minutes, because she is always travelling towards the east at such a rate as to complete one circuit in about four weeks; and losing thus one day in 28, she losses about 50? minutes per day. if the interval between her rising and her arriving to the south were always the same, she would rise 50? minutes later night after night. but if the interval is lengthening, say by 10 minutes per night, she would of course rise only 40? minutes later: if the interval is lengthening 20 minutes per night, she would rise only 30? minutes later, and so forth. but the lunar diurnal arc is lengthening all the time she is passing from her position farthest south of the equator to her position farthest north, just in the same way as the solar day is lengthening from mid-winter to midsummer, only to a much greater degree. and as the solar day lengthens fastest at spring when the sun crosses the equator from south to north, so the time the moon is above the horizon lengthens most, day by day, when the moon is crossing the equator from south to north. it lengthens, then, from an hour to an hour and 20 minutes in one day, that is, the interval between moon-rise and moon-setting increases from 30 to 40 minutes. at this time, then, whenever it happens in each lunar month, the moon's time of rising changes least: instead of the moon rising night after night 50? minutes later, the actual difference varies only from 10 to 20 minutes.

now if this happens at a time when the moon is not nearly full, it is not specially noticed, because the moon's light is not then specially useful. but if it happens when the moon is nearly full, it is noticed, because her light is then so useful. a moon nearly full, afterwards quite full, and then for a day or two still nearly full, rising night after night at nearly the same time, remaining also night after night longer above the horizon, manifestly serves man for the time being in the most convenient way possible. but it is clear that as the full moon is opposite the sun, and as to fulfil the condition described we have seen that she must be crossing the equator from south to north, the sun, opposite to her, must be at the part of his path where he crosses the equator from north to south. in other words, the time of year must be the autumnal equinox. thus the moon which comes to "full" nearest to september 22 or 23 will behave in the convenient way described. at this time, moreover, when she rises night after night nearly at the same time, the nights are lengthening fastest while the time the moon is above the horizon is lengthening still more, and therefore, in all respects, the moon is then doing her best, so to speak, to illuminate the nights. at this season the moon is called the harvest-moon, from the assistance she sometimes renders to harvesters.

the moon which is full nearest to september 22-23 may precede or follow that date. in the former case only can it properly be called a harvest-moon. in the latter it is sometimes called the hunter's moon. the full moon occurring nearest to harvest time will always partake more or less of the qualities of a full moon occurring at the autumnal equinox: and similarly of a full moon following the autumnal equinox. so that, in almost every year, there may be said to be a harvest-moon and a hunter's moon. but, of course, it will very often happen that in any particular agricultural district the harvest has to be gathered in during the wrong half of the lunar month, that is, during the last and first, instead of the second and third quarters.

the reader must not fall into the mistake of supposing, as i have seen sometimes stated in text-books of astronomy, that we are more favoured in this respect than the inhabitants of the southern hemisphere. it is quite true that the same full moon shines on us as on our friends in new zealand, australia, and cape colony, and also that our autumn is their spring, and their spring our autumn. but the full moon we have in autumn behaves in the southern hemisphere not as with us, but as our spring full moon behaves; and the full moon of our spring, which is their autumn, behaves with them as our autumn moon behaves with us. it is, therefore, for them a harvest-moon if it occur before the equinox, and a hunter's moon if it occur after the equinox. a very little consideration will show why this is. in fact if, in the explanation given above, the words north and south be interchanged, and march 21-22 written for september 22-23, the explanation will be precisely that which i should have given respecting the harvest (or march) moon of the southern hemisphere, if i had been writing for southern readers.

having thus considered the moon as a light-giver, both in respect of her monthly changes and of that yearly change which causes her services to be most useful in harvest time, let us consider what science tells us of the orb which thus usefully reflects to us the solar rays.

the moon is a globe about 2159? miles in diameter, travelling round the earth at a mean distance of 238,818 miles. her path round the earth is not, however, a circle, but an ellipse, which itself is constantly varying in shape. the average eccentricity of the moon's path is such that her greatest and least distances, as she circuits round it, are 251,953 miles and 225,683 miles respectively; but when it is most eccentric, her greatest and least distances are 252,948 miles and 221,593 miles respectively; while, when it is least eccentric, they are respectively 250,324 miles and 227,312 miles. the earth's surface exceeds the moon's nearly 13? times, the actual number of square miles in the moon's surface amounting to 14,600,000. this is nearly equal to europe and africa together, or, more nearly still, to north and south america together, without their islands. in volume our earth exceeds the moon rather more than 49? times: or, more nearly, if the earth's volume be represented by 10,000, the moon's will be represented by 209. the materials of the moon's globe are either lighter or (more probably) they are less closely compacted than those forming our earth,—for, according to the best modern estimates, the earth exceeds the moon in mass nearly 81? times. assuming as the most probable value of the earth's mean density about 5-7/10 times the density of water, the moon's mean density is equal to 3-46/100 times that of water. gravity at her surface is accordingly much less than at the surface of the earth; a quantity of matter weighing six pounds at the surface of the earth would weigh almost exactly one pound at the surface of the moon.

the moon circuits once round the earth in 27d. 7h. 43m. 11.5s. this is the time in which, viewed from the earth, she seems to complete one circuit round the stellar heavens, and is therefore called a sidereal month. but as the earth is all the time travelling the same way round the sun, the lunar month is longer. thus, suppose s (fig. 14) to be the sun, e the earth at the beginning of a lunar month, m1 m2 m3 m4 the moon's path, and m1 the moon's place on the line joining e and s. if the earth remained at rest while the moon went round the path m1 m3, then after completing one circuit the moon would again be at m1 on the line joining e and s, or it would be new moon again. but the earth is moving onwards along the arc ee′ of her circuit round the sun. so that when the moon has completed one circuit she is at m4 (e′m1 drawn parallel to em1) and has still to travel some distance before she gets round to m′ on the line joining s and e′. the lunation, or interval between successive new moons, has an average duration of 29d. 12h. 44m. 38s., exceeding a sidereal month by 2d. 5h.

fig. 14.—explaining the difference between a sidereal lunar month and a common lunar month or lunation.

it would not, however, be correct to regard the earth as the true centre of the moon's motion. the moon is in reality a planet circling round the sun, but largely perturbed by the attraction of its companion planet the earth. if the moon's path in the course of a year were carefully drawn to scale, or, better, were modelled by means of a fine wire, it would scarcely be distinguishable from a similar picture or model of the earth's path round the sun. or thus, the entire width of the moon's track is about 477,636 miles, while the diameter of the orbit along which she and the earth both travel is nearly 104,000,000 miles, or 385 times as great. if we draw then a circle 3-85/100 inches in diameter to represent the earth's path round the sun, somewhat eccentrically placed, and the circular line is 1-100th of an inch wide, the moon's track would be fairly represented by a curve touching alternately the inside and the outside edge of this circular line, at equidistant points dividing the circle into about 24? parts.

regarding the moon as a planet, she may be said to have a year, and seasons, and day and night, as the earth has, but very unlike our seasons and days. her axis is inclined only 1? degrees from uprightness to her path, whereas our earth's axis is inclined 23? degrees. the sun's range of mid-day altitude is in fact not quite equal to the range of our sun in mid-day height, from four days before to four days after either spring or autumn. the lunar day lasts a lunar month, daytime and night-time each lasting rather more than a fortnight. the lunar year of seasons is not, as is commonly stated, the same in length as ours. she goes round the sun in the same time, so that her sidereal year is the same as ours; but owing to the swaying round of her axis her year of seasons or tropical year is shorter. our tropical year is also shorter than the sidereal year, but very little shorter, because the earth's axis sways round once only in 25,868 years. the moon's axis sways round once in 18? years, and accordingly the year of seasons is much more effectively shortened. it lasts, in fact, only 346d. 14h. 34m. of our time; and contains only 11? lunar days. so that i cannot altogether agree with sir w. herschel's statement, that "the moon's situation with respect to the sun is much like that of our earth, and by a rotation on its axis it enjoys an agreeable variety of seasons, and of day and night."

when the moon is examined with a telescope her surface is seen to be marked by many irregularities. there are large dark regions which were formerly thought to be seas, but are now known to be land-surfaces. some of these regions are singularly level, and have been thought to be old sea-bottoms. mountains and mountain ranges are another important feature of the moon's surface. some, like our rocky mountains and andes, form long continuous chains; others form elevated plateaus whence ridges extend in various directions. a very striking form is that of narrow ridges little raised above the general level, but reaching over enormous areas of the moon's globe. it is a system of this kind, radiating from a great lunar crater called tycho, which gives to small photographs of the moon the appearance of a peeled orange. they are supposed to indicate the action of tremendous forces of upheaval, in past ages, bursting open portions of the moon's crust.

but the most characteristic of all the lunar features are the crater mountains, which exist on a scale not only much larger relatively to the moon's globe than the scale on which terrestrial craters are formed, but much larger absolutely. they are also far more numerous. some parts of the moon's surface, especially in the bright south-western quarter of her face, are literally crowded with craters of various dimensions.

there are few signs of the former emission of lava from the lunar craters. within some of them recent changes have been suspected. a remarkable instance is that of the crater linné, marked in m?dler's map as a deep, well-walled crater, some four miles in diameter. at present only a small crater can be seen in its place. the surrounding region is rather conspicuously bright. it is not necessary to infer that there has been any volcanic disturbance, however. far more probably the walls have been thrown down through the long-continued action of that alternate expansion and contraction, which must affect the moon's crust as the long fortnightly day proceeds, and then the equally long lunar night.

there are many well-marked valleys on the moon, besides clefts and ravines. the features called rilles are among the most perplexing objects on the moon's surface. webb, in his charming and most useful little book, "celestial objects for common telescopes," thus describes them: "these most singular furrows pass chiefly through levels, intersect craters (proving a more recent date), reappear beyond obstructing mountains, as though carried through by a tunnel, and commence and terminate with little reference to any conspicuous feature of the neighbourhood. the idea of artificial formation is negatived by their magnitude; they have been more probably referred to cracks in a shrinking surface." some observations would seem to show that they have been formed from rows of closely-adjacent small craters. faults, also, or closed cracks where the surface is higher on one side than on the other, have been recognised from the careful study of the shadows on the moon's disc.

from measurements of the shadows of lunar mountains, it appears that their average height is about five miles. in comparing this elevation with that assigned to terrestrial mountains, it must be remembered that these are measured from the sea-level; if the average height of terrestrial mountains were determined with reference to the sea-bottom it would be far greater. still, even taking this circumstance into account, the average height of the lunar mountains bears a far greater ratio to the diameter of the globe on which they stand than the average height of our mountains to the earth's diameter.

several circumstances agree in showing that the moon's atmosphere must be exceedingly rare. the shadows of lunar mountains are either actually black or nearly so. when the moon hides the sun in total eclipse, no sign can be seen of any refractive effort exerted on the sun's rays. when a star is hidden (or occulted) by the moon, the star vanishes in an instant and reappears with equal suddenness. it is certain from these phenomena that the moon has either no air, or air exceedingly tenuous. it is equally clear that she has no water, for if she had we should undoubtedly be able to recognise the occasional formation or dissipation of mist and vapour over parts of the moon's surface. no signs of such phenomena have ever been observed. the moon is certainly at present a waterless globe, so far at least as her surface is concerned.

it has been thought that though there is no water and very little air on the side of the moon turned towards the earth, there may be both water and air on the farther unseen side. the theory has been long since given up, but the reasoning on which it depends is worth noting. owing to the strange circumstance that the moon rotates on her axis in the same time in which she revolves round the earth, she always presents the same face towards the earth, or very nearly so. if her axis were exactly square to the path in which she circuits the earth, and if she revolved at a uniform rate, we should have exactly the same side constantly turned towards us. but as the axis is inclined about 6?° from uprightness to the path round the earth (which, be it remembered, is not in the same plane as the path round the sun, but inclined 5° 8′ to it), the northern and southern parts of the moon are alternately swayed over by about 6?° into view. this apparent swaying is called a libration, and the libration just described is called the libration in latitude. again, as the moon does not travel at a uniform rate round the earth, but faster than her mean rate when nearer to us, and slower when farther from us, she alternately gains and loses in her motion of revolution as compared with her motion of rotation, by a quantity varying between 5° and 7?°, to which varying extent the parts east and west of her mean disc are alternately swayed into view. this is called the libration in longitude. thus we see, beyond the edge of the mean half turned towards us, a considerable fringe of the other half. if a globe, as pap′b, fig. 15, were divided into two halves to represent the farther and nearer halves of the moon, and held so that that dividing circle were seen as pep′ in the figure, then ppep′p′ would represent the part brought into view at different times by the apparent swaying described above; while ppep′p′ would represent the parts swayed out of view. the regions thus alternately in view and out of view have their greatest breadth, not at the poles or east and west, but at mmm and m′m′m′, where the two librations act together. the narrow fringe bordering these regions is that brought into or out of view by changes in the place of the observer on earth, due to the earth's rotation. it is called the parallactic fringe, any change in the apparent position of a heavenly body, or part of one, on account of the earth's rotation, being termed parallax.

fig. 15.—illustrating lunar libration.

lastly, let us return to the consideration of moonlight, as depending on the condition of the moon's surface, to one who observes the moon as seen on the sky, her light appears white; but it must not be supposed that she is a white body. careful estimates of the quantity of light she reflects show that she is more nearly black than white, though in reality she is neither one nor the other. it has been said, and truly, that if the surface of the moon were covered with black velvet she would still appear white; for even black velvet reflects some light, and whatever light the moon reflected would show her by contrast with the blackness of the sky, as a luminous body or white. it follows from the observations made by z?llner that if the moon's surface were covered with white snow she could give us about 4? times as much light as she actually does. if she were covered with white paper she would give more than 4 times as much light as she does. if she had a surface of white sandstone her light would be nearly half as great again as it is. she gives rather more light than she would if her surface consisted entirely of weathered grey sandstone, or of clay marl, and more than twice as much light as she would give if her surface were of moist earth, or dark grey syenite. as some parts of her surface are obviously much brighter than others, we must infer that some parts shine with much more, and others with much less, brightness than weathered grey sandstone. probably some parts are much brighter than white sandstone, and some much darker than dark grey syenite. from the degree in which her lustre changes with her changing aspect, z?llner infers that her mountains have an average slope of about fifty-two degrees.