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 ............