w = k {m (m'/81)} / (1081)^{2};

from which we find by division--

w = (W / 81) (3963 / 1081)^{2} = (W / 6) (approximately).

The cubic yard of rock, which upon the earth weighs two tons, would, if transported to the moon, weigh only one third of a ton, and would have only one sixth as much influence in compressing the rocks below it as it had upon the earth. Note that this rock when transported to the moon would be still attracted by the earth and would have weight toward the earth, but it is not this of which we are speaking; by its weight in the moon we mean the force with which the moon attracts it. Making due allowance for the difference in compression produced by weight, we may say that in general, so far as density goes, the moon is very like a piece of the earth of equal ma.s.s set off by itself alone.

97. ALBEDO.--In another respect the lunar stuff is like that of which the earth is made: it reflects the sunlight in much the same way and to the same amount. The contrast of light and dark areas on the moon's surface shows, as we shall see in another section, the presence of different substances upon the moon which reflect the sunlight in different degrees. This capacity for reflecting a greater or less percentage of the incident sunlight is called _albedo_ (Latin, whiteness), and the brilliancy of the full moon might lead one to suppose that its albedo is very great, like that of snow or those ma.s.ses of summer cloud which we call thunderheads. But this is only an effect of contrast with the dark background of the sky. The same moon by day looks pale, and its albedo is, in fact, not very different from that of our common rocks--weather-beaten sandstone according to Sir John Herschel--so that it would be possible to build an artificial moon of rock or brick which would shine in the sunlight much as does the real moon.

The effect produced by the differences of albedo upon the moon's face is commonly called the "man in the moon," but, like the images presented by glowing coals, the face in the moon is anything which we choose to make it. Among the Chinese it is said to be a monkey pounding rice; in India, a rabbit; in Persia, the earth reflected as in a mirror, etc.

98. LIBRATIONS.--We have already learned that the moon turns always the same face toward the earth, and we have now to modify this statement and to find that here, as in so many other cases, the thing we learn first is only approximately true and needs to be limited or added to or modified in some way. In general, Nature is too complex to be completely understood at first sight or to be perfectly represented by a simple statement. In Fig. 55 we have two photographs of the moon, taken nearly three years apart, the right-hand one a little after first quarter and the left-hand one a little before third quarter. They therefore represent different parts of the moon's surface, but along the ragged edge the same region is shown on both photographs, and features common to both pictures may readily be found--e. g., the three rings which form a right-angled triangle about one third of the way down from the top of the cut, and the curved mountain chain just below these. If the moon turned exactly the same face toward us in the two pictures, the distance of any one of these markings from any part of the moon's edge must be the same in both pictures; but careful measurement will show that this is not the case, and that in the left-hand picture the upper edge of the moon is tipped toward us and the lower edge away from us, as if the whole moon had been rotated slightly about a horizontal line and must be turned back a little (about 7) in order to match perfectly the other part of the picture.

This turning is called a _libration_, and it should be borne in mind that the moon librates not only in the direction above measured, north and south, but also at right angles to this, east and west, so that we are able to see a little farther around every part of the moon's edge than would be possible if it turned toward us at all times exactly the same face. But in spite of the librations there remains on the farther side of the moon an area of 6,000,000 square miles which is forever hidden from us, and of whose character we have no direct knowledge, although there is no reason to suppose it very different from that which is visible, despite the fact that some of the books contain quaint speculations to the contrary. The continent of South America is just about equal in extent to this unknown region, while North America is a fair equivalent for all the rest of the moon's surface, both those central parts which are constantly visible, and the zone around the edge whose parts sometimes come into sight and are sometimes hidden.

An interesting consequence of the peculiar rotation of the moon is that from our side of it the earth is always visible. Sun, stars, and planets rise and set there as well as here, but to an observer on the moon the earth swings always overhead, shifting its position a few degrees one way or the other on account of the libration but running through its succession of phases, new earth, first quarter, etc., without ever going below the horizon, provided the observer is anywhere near the center of the moon's disk.

[Ill.u.s.tration: FIG. 54.--Ill.u.s.trating the moon's rotation.]

99. CAUSE OF LIBRATIONS.--That the moon should librate is by no means so remarkable a fact as that it should at all times turn very nearly the same face toward the earth. This latter fact can have but one meaning: the moon revolves about an axis as does the earth, but the time required for this revolution is just equal to the time required to make a revolution in its...o...b..t. Place two coins upon a table with their heads turned toward the north, as in Fig. 54, and move the smaller one around the larger in such a way that its face shall always look away from the larger one. In making one revolution in its...o...b..t the head on this small coin will be successively directed toward every point of the compa.s.s, and when it returns to its initial position the small coin will have made just one revolution about an axis perpendicular to the plane of its...o...b..t. In no other way can it be made to face always away from the figure at the center of its...o...b..t while moving around it.

We are now in a position to understand the moon's librations, for, if the small coin at any time moves faster or slower in its...o...b..t than it turns about its axis, a new side will be turned toward the center, and the same may happen if the central coin itself shifts into a new position. This is what happens to the moon, for its...o...b..tal motion, like that of Mercury (Fig. 17), is alternately fast and slow, and in addition to this there are present other minor influences, such as the fact that its rotation axis is not exactly perpendicular to the plane of its...o...b..t; in addition to this the observer upon the earth is daily carried by its rotation from one point of view to another, etc., so that it is only in a general way that the rotation upon the axis and motion in the orbit keep pace with each other. In a general way a cable keeps a ship anch.o.r.ed in the same place, although wind and waves may cause it to "librate" about the anchor.

How the moon came to have this exact equality between its times of revolution and rotation const.i.tutes a chapter of its history upon which we shall not now enter; but the equality having once been established, the mechanism by which it is preserved is simple enough.

The attraction of the earth for the moon has very slightly pulled the latter out of shape (-- 42), so that the particular diameter, which points toward the earth, is a little longer than any other, and thus serves as a handle which the earth lays hold of and pulls down into its lowest possible position--i. e., the position in which it points toward the center of the earth. Just how long this handle is, remains unknown, but it may be shown from the law of gravitation that less than a hundred yards of elongation would suffice for the work it has to do.

100. THE MOON AS A WORLD.--Thus far we have considered the moon as a satellite of the earth, dependent upon the earth, and interesting chiefly because of its relation to it. But the moon is something more than this; it is a world in itself, very different from the earth, although not wholly unlike it. The most characteristic feature of the earth's surface is its division into land and water, and nothing of this kind can be found upon the moon. It is true that the first generation of astronomers who studied the moon with telescopes fancied that the large dark patches shown in Fig. 55 were bodies of water, and named them oceans, seas, lakes, and ponds, and to the present day we keep those names, although it is long since recognized that these parts of the moon's surface are as dry as any other. Their dark appearance indicates a different kind of material from that composing the lighter parts of the moon, material with a different albedo, just as upon the earth we have light-colored and dark-colored rocks, marble and slate, which seen from the moon must present similar contrasts of brightness. Although these dark patches are almost the only features distinguishable with the unaided eye, it is far otherwise in the telescope or the photograph, especially along the ragged edge where great numbers of rings can be seen, which are apparently depressions in the moon and are called craters. These we find in great number all over the moon, but, as the figure shows, they are seen to the best advantage near the _terminator_--i. e., the dividing line between day and night, since the long shadows cast here by the rising or setting sun bring out the details of the surface better than elsewhere. Carefully examine Fig. 55 with reference to these features.

[Ill.u.s.tration: FIG. 55.--The moon at first and last quarter. Lick Observatory photographs.]

Another feature which exists upon both earth and moon, although far less common there than here, is ill.u.s.trated in the chain of mountains visible near the terminator, a little above the center of the moon in both parts of Fig. 55. This particular range of mountains, which is called the Lunar Apennines, is by far the most prominent one upon the moon, although others, the Alps and Caucasus, exist. But for the most part the lunar mountains stand alone, each by itself, instead of being grouped into ranges, as on the earth. Note in the figure that some of the lunar mountains stretch out into the night side of the moon, their peaks projecting up into the sunlight, and thus becoming visible, while the lowlands are buried in the shadow.

A subordinate feature of the moon's surface is the system of _rays_ which seem to radiate like spokes from some of the larger craters, extending over hill and valley sometimes for hundreds of miles. A suggestion of these rays may be seen in Fig. 55, extending from the great crater Copernicus a little southwest of the end of the Apennines, but their most perfect development is to be seen at the time of full moon around the crater Tycho, which lies near the south pole of the moon. Look for them with an opera gla.s.s.

Another and even less conspicuous feature is furnished by the rills, which, under favorable conditions of illumination, appear like long cracks on the moon's surface, perhaps a.n.a.logous to the canons of our Western country.

101. THE MAP OF THE MOON.--Fig. 55 furnishes a fairly good map of a limited portion of the moon near the terminator, but at the edges little or no detail can be seen. This is always true; the whole of the moon can not be seen to advantage at any one time, and to remedy this we need to construct from many photographs or drawings a map which shall represent the several parts of the moon as they appear at their best. Fig. 56 shows such a map photographed from a relief model of the moon, and representing the princ.i.p.al features of the lunar surface in a way they can never be seen simultaneously. Perhaps its most striking feature is the shape of the craters, which are shown round in the central parts of the map and oval at the edges, with their long diameters parallel to the moon's edge. This is, of course, an effect of the curvature of the moon's surface, for we look very obliquely at the edge portions, and thus see their formations much foreshortened in the direction of the moon's radius.

[Ill.u.s.tration: FIG. 56.--Relief map of the moon's surface.--After NASMYTH and CARPENTER.]

The north and south poles of the moon are at the top and bottom of the map respectively, and a mere inspection of the regions around them will show how much more rugged is the southern hemisphere of the moon than the northern. It furnishes, too, some indication of how numerous are the lunar craters, and how in crowded regions they overlap one another.

The student should pick out upon the map those features which he has learned to know in the photograph (Fig. 55)--the Apennines, Copernicus, and the continuation of the Apennines, extending into the dark part of the moon.

[Ill.u.s.tration: FIG. 57.--Mare Imbrium. Photographed by G. W. RITCHEY.]

102. SIZE OF THE LUNAR FEATURES.--We may measure distances here in the same way as upon a terrestrial map, remembering that near the edges the scale of the map is very much distorted parallel to the moon's diameter, and measurements must not be taken in this direction, but may be taken parallel to the edge. Measuring with a millimeter scale, we find on the map for the diameter of the crater Copernicus, 2.1 millimeters. To turn this into the diameter of the real Copernicus in miles, we measure upon the same map the diameter of the moon, 79.7 millimeters, and then have the proportion--

Diameter of Copernicus in miles : 2,163 :: 2.1 : 79.7,

which when solved gives 57 miles. The real diameter of Copernicus is a trifle over 56 miles. At the eastern edge of the moon, opposite the Apennines, is a large oval spot called the Mare Crisium (Latin, _ma-re_ = sea). Measure its length. The large crater to the northwest of the Apennines is called Archimedes. Measure its diameter both in the map and in the photograph (Fig. 55), and see how the two results agree. The true diameter of this crater, east and west, is very approximately 50 miles.

The great smooth surface to the west of Archimedes is the Mare Imbrium.

Is it larger or smaller than Lake Superior? Fig. 57 is from a photograph of the Mare Imbrium, and the amount of detail here shown at the bottom of the sea is a sufficient indication that, in this case at least, the water has been drawn off, if indeed any was ever present.

[Ill.u.s.tration: FIG. 58.--Mare Crisium. Lick Observatory photographs.]

Fig. 58 is a representation of the Mare Crisium at a time when night was beginning to encroach upon its eastern border, and it serves well to show the rugged character of the ring-shaped wall which incloses this area.

With these pictures of the smoother parts of the moon's surface we may compare Fig. 59, which shows a region near the north pole of the moon, and Fig. 60, giving an early morning view of Archimedes and the Apennines. Note how long and sharp are the shadows.

[Ill.u.s.tration: FIG. 59.--Ill.u.s.trating the rugged character of the moon's surface.--NASMYTH and CARPENTER.]

103. THE MOON'S ATMOSPHERE.--Upon the earth the sun casts no shadows so sharp and black as those of Fig. 60, because his rays are here scattered and reflected in all directions by the dust and vapors of the atmosphere (-- 51), so that the place from which direct sunlight is cut off is at least partially illumined by this reflected light. The shadows of Fig. 60 show that upon the moon it must be otherwise, and suggest that if the moon has any atmosphere whatever, its density must be utterly insignificant in comparison with that of the earth. In its motion around the earth the moon frequently eclipses stars (_occults_ is the technical word), and if the moon had an atmosphere such as is shown in Fig. 61, the light from the star _A_ must shine through this atmosphere just before the moon's advancing body cuts it off, and it must be refracted by the atmosphere so that the star would appear in a slightly different direction (nearer to _B_) than before. The earth's atmosphere refracts the starlight under such circ.u.mstances by more than a degree, but no one has been able to find in the case of the moon any effect of this kind amounting to even a fraction of a second of arc.

While this hardly justifies the statement sometimes made that the moon has no atmosphere, we shall be entirely safe in saying that if it has one at all its density is less than a thousandth part of that of the earth's atmosphere. Quite in keeping with this absence of an atmosphere is the fact that clouds never float over the surface of the moon. Its features always stand out hard and clear, without any of that haze and softness of outline which our atmosphere introduces into all terrestrial landscapes.

[Ill.u.s.tration: FIG. 60.--Archimedes and Apennines. NASMYTH and CARPENTER.]

104. HEIGHT OF THE LUNAR MOUNTAINS.--Attention has already been called to the detached mountain peaks, which in Fig. 55 prolong the range of Apennines into the lunar night. These are the beginnings of the Caucasus mountains, and from the photograph we may measure as follows the height to which they rise above the surrounding level of the moon: Fig. 62 represents a part of the lunar surface along the boundary line between night and day, the horizontal line at the top of the figure representing a level ray of sunlight which just touches the moon at _T_ and barely illuminates the top of the mountain, _M_, whose height, _h_, is to be determined. If we let _R_ stand for the radius of the moon and _s_ for the distance, _T M_, we shall have in the right-angled triangle _M T C_,

R^{2} + s^{2} = (R + h)^{2},

and we need only to measure _s_--that is, the distance from the terminator to the detached mountain peak--to make this equation determine _h_, since _R_ is already known, being half the diameter of the moon--1,081 miles. Practically it is more convenient to use instead of this equation another form, which the student who is expert in algebra may show to be very nearly equivalent to it:

_h_ (miles) = s^{2} / 2163, or _h_ (feet) = 2.44 s^{2}.

The distance _s_ must be expressed in miles in all of these equations.

In Fig. 55 the distance from the terminator to the first detached peak of the Caucasus mountains is 1.7 millimeters = 52 miles, from which we find the height of the mountain to be 1.25 miles, or 6,600 feet.

[Ill.u.s.tration: FIG. 61.--Occultations and the moon's atmosphere.]

[Ill.u.s.tration: FIG. 62.--Determining the height of a lunar mountain.]

Two things, however, need to be borne in mind in this connection. On the earth we measure the heights of mountains _above sea level_, while on the moon there is no sea, and our 6,600 feet is simply the height of the mountain top above the level of that particular point in the terminator, from which we measure its distance. So too it is evident from the appearance of things, that the sunlight, instead of just touching the top of the particular mountain whose height we have measured, really extends some little distance down from its summit, and the 6,600 feet is therefore the elevation of the lowest point on the mountains to which the sunlight reaches. The peak itself may be several hundred feet higher, and our photograph must be taken at the exact moment when this peak appears in the lunar morning or disappears in the evening if we are to measure the alt.i.tude of the mountain's summit. Measure the height of the most northern visible mountain of the Caucasus range. This is one of the outlying spurs of the great mountain Calippus, whose princ.i.p.al peak, 19,000 feet high, is shown in Fig. 55 as the brightest part of the Caucasus range.

The highest peak of the lunar Apennines, Huyghens, has an alt.i.tude of 18,000 feet, and the Leibnitz and Doerfel Mountains, near the south pole of the moon, reach an alt.i.tude 50 per cent greater than this, and are probably the highest peaks on the moon. This falls very little short of the highest mountain on the earth, although the moon is much smaller than the earth, and these mountains are considerably higher than anything on the western continent of the earth.

The vagueness of outline of the terminator makes it difficult to measure from it with precision, and somewhat more accurate determinations of the heights of lunar mountains can be obtained by measuring the length of the shadows which they cast, and the depths of craters may also be measured by means of the shadows which fall into them.

105. CRATERS.--Fig. 63 shows a typical lunar crater, and conveys a good idea of the ruggedness of the lunar landscape. Compare the appearance of this crater with the following generalizations, which are based upon the accurate measurement of many such:

A. A crater is a real depression in the surface of the moon, surrounded usually by an elevated ring which rises above the general level of the region outside, while the bottom of the crater is about an equal distance below that level.

B. Craters are shallow, their diameters ranging from five times to more than fifty times their depth. Archimedes, whose diameter we found to be 50 miles, has an average depth of about 4,000 feet below the crest of its surrounding wall, and is relatively a shallow crater.

[Ill.u.s.tration: FIG. 63.--A typical lunar crater.--NASMYTH and CARPENTER.]

C. Craters frequently have one or more hills rising within them which, however, rarely, if ever, reach up to the level of the surrounding wall.