Part 7

The least retardations for full moon occur when the moon is near the vernal equinox at full: the sun must then be near the autumnal equinox. Hence the least retardations for full moon occur in the months of August, September, and October. The retardation is, of course, least for September; and the full moon of this month rises night after night less than half an hour later than the previous night. The full moon of September is called the "Harvest Moon," and that of October the "Hunter's Moon."

105. _The Rotation of the Moon._--A careful examination of the spots on the disc of the moon reveals the fact that she always presents the same side to the earth. In order to do this, she must rotate on her axis while making a revolution around the earth, or in about twenty-seven days.

106. _Librations of the Moon._--The moon appears to rock slowly to and fro, so as to allow us to see alternately a little farther around to the right and the left, or above and below, than we otherwise could. This apparent rocking of the moon is called _libration_. The moon has three librations:--

(1) _Libration in Latitude._--This libration enables us to see alternately a little way around on the northern and southern limbs of the moon.

This libration is due to the fact that the axis of the moon is not quite perpendicular to the plane of her orbit. The deviation from the perpendicular is six degrees and a half. As the axis of the moon, like that of the earth, maintains the same direction, the poles of the moon will be turned alternately six degrees and a half toward and from the earth.

(2) _Libration in Longitude._--This libration enables us to see alternately a little farther around on the eastern and western limbs of the moon.

It is due to the fact that the moon's axial motion is uniform, while her orbital motion is not. At perigee her orbital motion will be in advance of her axial motion, while at apogee the axial motion will be in advance of the orbital. In Fig. 119, _E_ represents the earth, _M_ the moon, the large arrow the direction of the moon's motion in her orbit, and the small arrow the direction of her motion of rotation. When the moon is at _M_, the line _AB_, drawn perpendicular to _EM_, represents the circle which divides the visible from the invisible portion of the moon. While the moon is passing from _M_ to _M'_, the moon performs less than a quarter of a rotation, so that _AB_ is no longer perpendicular to _EM'_. An observer on the earth can now see somewhat beyond _A_ on the western limb of the moon, and not quite up to _B_ on the eastern limb. While the moon is passing from _M'_ to _M''_, her axial motion again overtakes her orbital motion, so that the line _AB_ again becomes perpendicular to the line joining the centre of the moon to the centre of the earth. Exactly the same side is now turned towards the earth as when the moon was at _M_. While the moon passes from _M''_ to _M'''_, her axial motion gets in advance of her orbital motion, so that _AB_ is again inclined to the line joining the centres of the earth and moon. A portion of the eastern limb of the moon beyond _B_ is now brought into view to the earth, and a portion of the western limb at _A_ is carried out of view. While the moon is passing from _M'''_ to _M_, the orbital motion again overtakes the axial motion, and _AB_ is again perpendicular to _ME_.

(3) _Parallactic Libration._--While an observer at the centre of the earth would get the same view of the moon, whether she were on the eastern horizon, in the zenith, or on the western horizon, an observer on the surface of the earth does not get exactly the same view in these three cases. When the moon is on the eastern horizon, an observer on the surface of the earth would see a little farther around on the western limb of the moon than when she is in the zenith, and not quite so far around on the eastern limb. On the contrary, when the moon is on the western horizon, an observer on the surface of the earth sees a little farther around on the eastern limb of the moon than when she is in the zenith, and not quite so far around on her western limb.

This will be evident from Fig. 120. _E_ is the centre of the earth, and _O_ a point on its surface. _AB_ is a line drawn through the centre of the moon, perpendicular to a line joining the centres of the moon and the earth. This line marks off the part of the moon turned towards the centre of the earth, and remains essentially the same during the day. _CD_ is a line drawn through the centre of the moon perpendicular to a line joining the centre of the moon and the point of observation. This line marks off the part of the moon turned towards _O_. When the moon is in the zenith, _CD_ coincides with _AB_; but, when the moon is on the horizon, _CD_ is inclined to _AB_. When the moon is on the eastern horizon, an observer at _O_ sees a little beyond _B_, and not quite to _A_; and, when she is on the western horizon, he sees a little beyond _A_, and not quite to _B_. _B_ is on the western limb of the moon, and _A_ on her eastern limb.

Since this libration is due to the point from which the moon is viewed, it is called _parallactic_ libration; and, since it occurs daily, it is called _diurnal_ libration.

107. _Portion of the Lunar Surface brought into View by Libration._--The area brought into view by the first two librations is between one-twelfth and one-thirteenth of the whole lunar surface, or nearly one-sixth of the hemisphere of the moon which is turned away from the earth when the moon is at her state of mean libration. Of course a precisely equal portion of the hemisphere turned towards us during mean libration is carried out of view by the lunar librations.

If we add to each of these areas a fringe about one degree wide, due to the diurnal libration, and which we may call the _parallactic_ fringe, we shall find that the total area brought into view is almost exactly one-eleventh part of the whole surface of the moon. A similar area is carried out of view; so that the whole region thus swayed out of and into view amounts to two-elevenths of the moon's surface. This area is shown in Fig. 121, which is a side view of the moon.

108. _The Moon's Path through Space._--Were the earth stationary, the moon would describe an ellipse around it similar to that of Fig. 113; but, as the earth moves forward in her orbit at the same time that the moon revolves around it, the moon is made to describe a sinuous path, as shown by the continuous line in Fig. 122. This feature of the moon's path is greatly exaggerated in the upper portion of the diagram. The form of her path is given with a greater degree of accuracy in the lower part of the figure (the broken line represents the path of the earth); but even here there is considerable exaggeration. The complete serpentine path of the moon around the sun is shown, greatly exaggerated, in Fig. 123, the broken line being the path of the earth.

The path described by the moon through space is much the same as that described by a point on the circumference of a wheel which is rolled over another wheel. If we place a circular disk against the wall, and carefully roll along its edge another circular disk (to which a piece of lead pencil has been fastened so as to mark upon the wall), the curve described will somewhat resemble that described by the moon. This curve is called an _epicycloid_, and it will be seen that at every point it is concave towards the centre of the larger disk. In the same way the moon's orbit is _at every point concave towards the sun_.

The exaggeration of the sinuosity in Fig. 123 will be more evident when it is stated, that, on the scale of Fig. 124, the whole of the serpentine curve would lie _within the breadth_ of the fine circular line _MM'_.

109. _The Lunar Day._--The lunar day is twenty-nine times and a half as long as the terrestrial day. Near the moon's equator the sun shines without intermission nearly fifteen of our days, and is absent for the same length of time. Consequently, the vicissitudes of temperature to which the surface is exposed must be very great. During the long lunar night the temperature of a body on the moon's surface would probably fall lower than is ever known on the earth, while during the day it must rise higher than anywhere on our planet.

It might seem, that, since the moon rotates on her axis in about twenty-seven days, the lunar day ought to be twenty-seven days long, instead of twenty-nine. There is, however, a solar, as well as a sidereal, day at the moon, as on the earth; and the solar day at the moon is longer than the sidereal day, for the same reason as on the earth. During the solar day the moon must make both a _synodical rotation_ and a _synodical revolution_. This will be evident from Fig. 125, in which is shown the path of the moon during one complete lunation. _E_, _E'_, _E''_, etc., are the successive positions of the earth; and 1, 2, 3, 4, 5, the successive positions of the moon. The small arrows indicate the direction of the moon's rotation. The moon is full at 1 and 5. At 1, _A_, at the centre of the moon's disk, will have the sun, which lies in the direction _AS_, upon the meridian. Before _A_ will again have the sun on the meridian, the moon must have made a synodical revolution; and, as will be seen by the dotted lines, she must have made more than a complete rotation. The rotation which brings the point _A_ into the same relation to the earth and sun is called a _synodical_ rotation.

It will also be evident from this diagram that the moon must make a synodical rotation during a synodical revolution, in order always to present the same side to the earth.

110. _The Earth as seen from the Moon._--To an observer on the moon, the earth would be an immense moon, going through the same phases that the moon does to us; but, instead of rising and setting, it would only oscillate to and fro through a few degrees. On the other side of the moon it would never be seen at all. The peculiarities of the moon's motions which cause the librations, and make a spot on the moon's disk seem to an observer on the earth to oscillate to and fro, would cause the earth as a whole to appear to a lunar observer to oscillate to and fro in the heavens in a similar manner.

It is a well-known fact, that, at the time of new moon, the dark part of the moon's surface is partially illumined, so that it becomes visible to the naked eye. This must be due to the light reflected to the moon from the earth. Since at new moon the moon is between the earth and sun, it follows, that, when it is new moon at the earth, it must be _full earth_ at the moon: hence, while the bright crescent is enjoying full sunlight, the dark part of its surface is enjoying the light of the full _earth_. Fig. 126 represents the full earth as seen from the moon.

The Atmosphere of the Moon.

111. _The Moon has no Appreciable Atmosphere._--There are several reasons for believing that the moon has little or no atmosphere.

(1) Had the moon an atmosphere, it would be indicated at the time of a solar eclipse, when the moon passes over the disk of the sun. If the atmosphere were of any considerable density, it would absorb a part of the sun's rays, so as to produce a dusky border in front of the moon's disk, as shown in Fig. 127. In reality no such dusky border is ever seen; but the limb of the moon appears sharp, and clearly defined, as in Fig. 128.

If the atmosphere were not dense enough to produce this dusky border, its refraction would be sufficient to distort the delicate cusps of the sun's crescent in the manner shown at the top of Fig. 125; but no such distortion is ever observed. The cusps always appear clear and sharp, as shown at the bottom of the figure: hence it would seem that there can be no atmosphere of appreciable density at the moon.

(2) The absence of an atmosphere from the moon is also shown by the absence of twilight and of diffused daylight.

Upon the earth, twilight continues until the sun is eighteen degrees below the horizon; that is, day and night are separated by a belt twelve hundred miles in breadth, in which the transition from light to darkness is gradual. We have seen (66) that this twilight results from the refraction and reflection of light by our atmosphere; and, if the moon had an atmosphere, we should notice a similar gradual transition from the bright to the dark portions of her surface. Such, however, is not the case. The boundary between the light and darkness, though irregular, is sharply defined. Close to this boundary the unillumined portion of the moon appears just as dark as at any distance from it.

The shadows on the moon are also pitchy black, without a trace of diffused daylight.

(3) The absence of an atmosphere is also proved by the absence of refraction when the moon passes between us and the stars. Let _AB_ (Fig. 129) represent the disk of the moon, and _CD_ an atmosphere supposed to surround it. Let _SAE_ represent a straight line from the earth, touching the moon at _A_, and let _S_ be a star situated in the direction of this line. If the moon had no atmosphere, this star would appear to touch the edge of the moon at _A_; but, if the moon had an atmosphere, a star behind the edge of the moon, at _S'_, would be visible at the earth; for the ray _S'A_ would be bent by the atmosphere into the direction _AE'_. So, also, on the opposite side of the moon, a star might be seen at the earth, although really behind the edge of the moon: hence, if the moon had an atmosphere, the time during which a star would be concealed by the moon would be less than if it had no atmosphere, and the amount of this effect must be proportional to the density of the atmosphere.

The moon, in her orbital course across the heavens, is continually passing before, or _occulting_, some of the stars that so thickly stud her apparent path; and when we see a star thus pass behind the lunar disk on one side, and come out again on the other side, we are virtually observing the setting and rising of that star upon the moon. The moon's apparent diameter has been measured over and over again, and is known with great accuracy; the rate of her motion across the sky is also known with perfect accuracy: hence it is easy to calculate how long the moon will take to travel across a part of the sky exactly equal in length to her own diameter. Supposing, then, that we observe a star pass behind the moon, and out again, it is clear, that, if there is no atmosphere, the interval of time during which it remains occulted ought to be exactly equal to the computed time which the moon would take to pass over the star. If, however, from the existence of a lunar atmosphere, the star disappears too late, and re-appears too soon, as we have seen it would, these two intervals will not agree; the computed time will be greater than the observed time, and the difference will represent the amount of refraction the star's light has sustained or suffered, and hence the extent of atmosphere it has had to pass through.

Comparisons of these two intervals of time have been repeatedly made, the most extensive being executed under the direction of the Astronomer Royal of England, several years ago, and based upon no less than two hundred and ninety-six occultation observations. In this determination the measured or telescopic diameter of the moon was compared with the diameter deduced from the occultations; and it was found that the telescopic diameter was greater than the occultation diameter by two seconds of angular measurement, or by about a thousandth part of the whole diameter of the moon. This discrepancy is probably due, in part at least, to _irradiation_ (91), which augments the apparent size of the moon, as seen in the telescope as well as with the naked eye; but, if the whole two seconds were caused by atmospheric refraction, this would imply a horizontal refraction of one second, which is only one two-thousandth of the earth's horizontal refraction. It is possible that an atmosphere competent to produce this refraction would not make itself visible in any other way.

But an atmosphere two thousand times rarer than our air can scarcely be regarded as an atmosphere at all. The contents of an air-pump receiver can seldom be rarefied to a greater extent than to about a thousandth of the density of air at the earth's surface; and the lunar atmosphere, if it exists at all, is thus proved to be twice as attenuated as what we commonly call a vacuum.

The Surface of the Moon.

112. _Dusky Patches on the Disk of the Moon._--With the naked eye, large dusky patches are seen on the moon, in which popular fancy has detected a resemblance to a human face. With a telescope of low power, these dark patches appear as smooth as water, and they were once supposed to be seas. This theory was the origin of the name _mare_ (Latin for _sea_), which is still applied to the larger of these plains; but, if there were water on the surface of the moon, it could not fail to manifest its presence by its vapor, which would form an appreciable atmosphere. Moreover, with a high telescopic power, these plains present a more or less uneven surface; and, as the elevations and depressions are found to be permanent, they cannot, of course, belong to the surface of water.

The chief of these plains are shown in Fig. 130. They are _Mare Crisium_, _Mare Foecunditatis_, _Mare Nectaris_, _Mare Tranquillitatis_, _Mare Serenitatis_, _Mare Imbrium_, _Mare Frigoris_, and _Oceanus Procellarum_. All these plains can easily be recognized on the surface of the full moon with the unaided eye.

113. _The Terminator of the Moon._--The terminator of the moon is the line which separates the bright and dark portions of its disk. When viewed with a telescope of even moderate power, the terminator is seen to be very irregular and uneven. Many bright points are seen just outside of the terminator in the dark portion of the disk, while all along in the neighborhood of the terminator are bright patches and dense shadows. These appearances are shown in Figs. 131 and 132, which represent the moon near the first and last quarters. They indicate that the surface of the moon is very rough and uneven.

As it is always either sunrise or sunset along the terminator, the bright spots outside of it are clearly the tops of mountains, which catch the rays of the sun while their bases are in the shade. The bright patches in the neighborhood of the terminator are the sides of hills and mountains which are receiving the full light of the sun, while the dense shadows near by are cast by these elevations.

114. _Height of the Lunar Mountains._--There are two methods of finding the height of lunar mountains:--

(1) We may measure the length of the shadows, and then calculate the height of the mountains that would cast such shadows with the sun at the required height above the horizon.

The length of a shadow may be obtained by the following method: the longitudinal wire of the micrometer (19) is adjusted so as to pass through the shadow whose length is to be measured, and the transverse wires are placed one at each end of the shadow, as shown in Fig. 133. The micrometer screw is then turned till the wires are brought together, so as to ascertain the length of the arc between them. We may then form the proportion: the number of seconds in the semi-diameter of the moon is to the number of seconds in the length of the shadow, as the length of the moon's radius in miles to the length of the shadow in miles.

The height of the sun above the horizon is ascertained by measuring the angular distance of the mountain from the terminator.

(2) We may measure the distance of a bright point from the terminator, and then construct a right-angled triangle, as shown in Fig. 134. A solution of this triangle will enable us to ascertain the height of the mountain whose top is just catching the level rays of the sun.

_B_ is the centre of the moon, _M_ the top of the mountain, and _SAM_ a ray of sunlight which just grazes the terminator at _A_, and then strikes the top of the mountain at _M_. The triangle _BAM_ is right-angled at _A_. _BA_ is the radius of the moon, and _AM_ is known by measurement; _BM_, the hypothenuse, may then be found by computation. _BM_ is evidently equal to the radius of the moon _plus_ the height of the mountain.

By one or the other of these methods, the heights of the lunar mountains have been found with a great degree of accuracy. It is claimed that the heights of the lunar mountains are more accurately known than those of the mountains on the earth. Compared with the size of the moon, lunar mountains attain a greater height than those on the earth.

115. _General Aspect of the Lunar Surface._--A cursory examination of the moon with a low power is sufficient to show the prevalence of crater-like inequalities and the general tendency to _circular_ shape which is apparent in nearly all the surface markings; for even the large "seas" and the smaller patches of the same character repeat in their outlines the round form of the craters. It is along the terminator that we see these crater-like spots to the best advantage; as it is there that the rising or setting sun casts long shadows over the lunar landscape, and brings elevations into bold relief. They vary greatly in size; some being so large as to bear a sensible proportion to the moon's diameter, while the smallest are so minute as to need the most powerful telescopes and the finest conditions of atmosphere to perceive them.

The prevalence of ring-shaped mountains and plains willbe evident from Fig. 135, which is from a photograph of a model of the moon constructed by Nasmyth.

This same feature is nearly as marked in Figs. 131 and 132, which are copies of Rutherfurd's photographs of the moon.