Chapter II: The Moon

Distance, Size, and Motions.

87. _The Distance of the Moon._--The moon is the nearest of the heavenly bodies. Its distance from the centre of the earth is only about sixty times the radius of the earth, or, in round numbers, two hundred and forty thousand miles.

The ordinary method of finding the distance of one of the nearer
heavenly bodies is first to ascertain its horizontal parallax. This
enables us to form a right-angled triangle, the lengths of whose
sides are easily computed, and the length of whose hypothenuse is
the distance of the body from the centre of the earth.

Horizontal parallax has already been defined (32) as the
displacement of a heavenly body when on the horizon, caused by its
being seen from the surface, instead of the centre, of the earth.
This displacement is due to the fact that the body is seen in a
different direction from the surface of the earth from that in which
it would be seen from the centre. Horizontal parallax might be
defined as the difference in the directions in which a body on the
horizon would be seen from the surface and from the centre of the
earth. Thus, in Fig. 101, _C_ is the centre of the earth, _A_ a
point on the surface, and _B_ a body on the horizon of _A_. _AB_ is
the direction in which the body would be seen from _A_, and _CB_ the
direction in which it would be seen from _C_. The difference of
these directions, or the angle _ABC_, is the parallax of the body.

The triangle _BAC_ is right-angled at _A_; the side _AC_ is the
radius of the earth, and the hypothenuse is the distance of the body
from the centre of the earth. When the parallax _ABC_ is known, the
length of _CB_ can easily by found by trigonometrical computation.

We have seen (32) that the parallax of a heavenly body grows less
and less as the body passes from the horizon towards the zenith. The
parallax of a body and its altitude are, however, so related, that,
when we know the parallax at any altitude, we can readily compute
the horizontal parallax.

The usual method of finding the parallax of one of the nearer
heavenly bodies is first to find its parallax when on the meridian,
as seen from two places on the earth which differ considerably in
latitude: then to calculate what would be the parallax of the body
as seen from one of these places and the centre of the earth: and
then finally to calculate what would be the parallax were the body
on the horizon.

Thus, we should ascertain the parallax of the body _B_ (Fig. 102) as
seen from _A_ and _D_, or the angle _ABD_. We should then calculate
its parallax as seen from _A_ and _C_, or the angle _ABC_. Finally
we should calculate what its parallax would be were the body on the
horizon, or the angle _AB'C_.

The simplest method of finding the parallax of a body _B_ (Fig. 102)
as seen from the two points _A_ and _D_ is to compare its direction
at each point with that of the same fixed star near the body. The
star is so distant, that it will be seen in the same direction from
both points: hence, if the direction of the body differs from that
of the star 2° as seen from one point, and 2° 6' as seen from the
other point, the two lines _AB_ and _DB_ must differ in direction by
6'; in other words, the angle _ABD_ would be 6'.

The method just described is the usual method of finding the
parallax of the moon.

88. _The Apparent Size of the Moon._--The _apparent size_ of a body is the visual angle subtended by it; that is, the angle formed by two lines drawn from the eye to two opposite points on the outline of the body. The apparent size of a body depends upon both its _magnitude_ and its _distance_.

The apparent size, or _angular diameter_, of the moon is about thirty-one minutes. This is ascertained by means of the wire micrometer already described (19). The instrument is adjusted so that its longitudinal wire shall pass through the centre of the moon, and its transverse wires shall be tangent to the limbs of the moon on each side, at the point where they are cut by the longitudinal wire. The micrometer screw is then turned till the wires are brought together. The number of turns of the screw needed to accomplish this will indicate the arc between the wires, or the angular diameter of the moon.

In order to be certain that the longitudinal wire shall pass through the centre of the moon, it is best to take the moon when its disc is in the form of a crescent, and to place the longitudinal wire against the points, or _cusps_, of the crescent, as shown in Fig. 103.

89. _The Real Size of the Moon._--The real diameter of the moon is a little over one-fourth of that of the earth, or a little more than two thousand miles. The comparative sizes of the earth and moon are shown in Fig. 104.

The distance and apparent size of the moon being known, her real
diameter is found by means of a triangle formed as shown in Fig.
105. _C_ represents the centre of the moon, _CB_ the distance of the
moon from the earth, and _CA_ the radius of the moon. _BAC_ is a
triangle, right-angled at _A_. The angle _ABC_ is half the apparent
diameter of the moon. With the angles _A_ and _B_, and the side _CB_
known, it is easy to find the length of _AC_ by trigonometrical
computation. Twice _AC_ will be the diameter of the moon.

The volume of the moon is about one-fiftieth of that of the earth.

90. _Apparent Size of the Moon on the Horizon and in the Zenith._.--The moon is nearly four thousand miles farther from the observer when she is on the horizon than when she is in the zenith. This is evident from Fig. 106. _C_ is the centre of the earth, _M_ the moon on the horizon, _M'_ the moon in the zenith, and _O_ the point of observation. _OM_ is the distance of the moon when she is on the horizon, and _OM'_ the distance of the moon from the observer when she is in the zenith. _CM_ is equal to _CM'_, and _OM_ is about the length of _CM_; but _OM'_ is about four thousand miles shorter than _CM'_: hence _OM'_ is about four thousand miles shorter than _OM_.

Notwithstanding the moon is much nearer when at the zenith than at
the horizon, it seems to us much larger at the horizon.

This is a pure illusion, as we become convinced when we measure the
disc with accurate instruments, so as to make the result independent
of our ordinary way of judging. When the moon is near the horizon,
it seems placed beyond all the objects on the surface of the earth
in that direction, and therefore farther off than at the zenith,
where no intervening objects enable us to judge of its distance. In
any case, an object which keeps the same apparent magnitude seems to
us, through the instinctive habits of the eye, the larger in
proportion as we judge it to be more distant.

91. _The Apparent Size of the Moon increased by Irradiation._--In
the case of the moon, the word _apparent_ means much more than it
does in the case of other celestial bodies. Indeed, its brightness
causes our eyes to play us false. As is well known, the crescent of
the new moon seems part of a much larger sphere than that which it
has been said, time out of mind, to "hold in its arms." The bright
portion of the moon as seen with our measuring instruments, as well
as when seen with the naked eye, covers a larger space in the field
of the telescope than it would if it were not so bright. This effect
of _irradiation_, as it is called, must be allowed for in exact
measurements of the diameter of the moon.

92. _Apparent Size of the Moon in Different Parts of her Orbit._--Owing to the eccentricity of the moon's orbit, her distance from the earth varies somewhat from time to time. This variation causes a corresponding variation in her apparent size, which is illustrated in Fig. 107.

93. _The Mass of the Moon._--The moon is considerably less dense than the earth, its mass being only about one-eightieth of that of the earth; that is, while it would take only about fifty moons to make the bulk of the earth, it would take about eighty to make the mass of the earth.

One method of finding the mass of the moon is to compare her effect
in producing the _tides_ with that of the sun. We first calculate
what would be the moon's effect in producing the tides, were she as
far off as the sun. We then form the following proportion: as the
sun's effect in producing the tides is to the moon's effect at the
same distance, so is the mass of the sun to the mass of the moon.

The method of finding the mass of the sun will be given farther on.

94. _The Orbital Motion of the Moon._--If we watch the moon from night to night, we see that she moves eastward quite rapidly among the stars. When the new moon is first visible, it appears near the horizon in the west, just after sunset. A week later the moon will be on the meridian at the same hour, and about a week later still on the eastern horizon. The moon completes the circuit of the heavens in a period of about thirty days, moving eastward at the rate of about twelve degrees a day. This eastward motion of the moon is due to the fact that she is revolving around the earth from west to east.

95. _The Aspects of the Moon._--As the moon revolves around the earth, she comes into different positions with reference to the earth and sun. These different positions of the moon are called the _aspects_ of the moon. The four chief aspects of the moon are shown in Fig. 108. When the moon is at _M_, she appears in the opposite part of the heavens to the sun, and is said to be in _opposition_; when at _M'_ and at _M'''_, she appears ninety degrees away from the sun, and is said to be in _quadrature_; when at _M''_, she appears in the same part of the heavens as the sun, and is said to be in _conjunction_.

96. _The Sidereal and Synodical Periods of the Moon._--The _sidereal period_ of the moon is the time it takes her to pass around from a star to that star again, or the time it takes her to _make a complete revolution around the earth_. This is a period of about twenty-seven days and a third. It is sometimes called the _sidereal month_.

The _synodical period_ of the moon is the time that it takes the moon to _pass from one aspect around to the same aspect again_. This is a period of about twenty-nine days and a half, and it is sometimes called the _synodical month_.

The reason why the synodical period is longer than the sidereal period will appear from Fig. 109. _S_ represents the position of the sun, _E_ that of the earth, and the small circle the orbit of the moon around the earth. The arrow in the small circle represents the direction the moon is revolving around the earth, and the arrow in the arc between _E_ and _E'_ indicates the direction of the earth's motion in its orbit. When the moon is at _M_{1}_, she is in conjunction. As the moon revolves around the earth, the earth moves forward in its orbit. When the moon has come round to _m_{1}_, so that _m_{3}m_{1}_ is parallel with _M_{3}M_{1}_, she will have made a complete or _sidereal_ revolution around the earth; but she will not be in conjunction again till she has come round to _M_, so as again to be between the earth and sun. That is to say, the moon must make more than a complete revolution in a synodical period.

The greater length of the synodical period is also evident from Fig.
110. _T_ represents the earth, and _L_ the moon. The arrows indicate
the direction in which each is moving. When the earth is at _T_, and
the moon at _L_, the latter is in conjunction. When the earth has
reached _T'_, and the moon _L'_, the latter has made a sidereal
revolution; but she will not be in conjunction again till the earth
has reached _T''_, and the moon _L''_.

97. _The Phases of the Moon._--When the new moon appears in the west, it has the form of a _crescent_, with its convex side towards the sun, and its horns towards the east. As the moon advances towards quadrature, the crescent grows thicker and thicker, till it becomes a _half-circle_ at first quarter. When it passes quadrature, it begins to become convex also on the side away from the sun, or _gibbous_ in form. As it approaches opposition, it becomes more and more nearly circular, until at opposition it is a _full_ circle. From full moon to last quarter it is again gibbous, and at last quarter a half-circle. From last quarter to new moon it is again crescent; but the horns of the crescent are now turned towards the west. The successive phases of the moon are shown in Fig. 111.

98. _Cause of the Phases of the Moon._--Take a globe, half of which is colored white and the other half black in such a way that the line which separates the white and black portions shall be a great circle which passes through the poles of the globe, and rotate the globe slowly, so as to bring the white half gradually into view. When the white part first comes into view, the line of separation between it and the black part, which we may call the _terminator_, appears concave, and its projection on a plane perpendicular to the line of vision is a concave line. As more and more of the white portion comes into view, the projection of the terminator becomes less and less concave. When half of the white portion comes into view, the terminator is projected as a straight line. When more than half of the white portion comes into view, the terminator begins to appear as a convex line, and this line becomes more and more convex till the whole of the white half comes into view, when the terminator becomes circular.

The moon is of itself a dark, opaque globe; but the half that is towards the sun is always bright, as shown in Fig. 112. This bright half of the moon corresponds to the white half of the globe in the preceding illustration. As the moon revolves around the earth, different portions of this illumined half are turned towards the earth. At new moon, when the moon is in conjunction, the bright half is turned entirely away from the earth, and the disc of the moon is black and invisible. Between new moon and first quarter, less than half of the illumined side is turned towards the earth, and we see this illumined portion projected as a crescent. At first quarter, just half of the illumined side is turned towards the earth, and we see this half projected as a half-circle. Between first quarter and full, more than half of the illumined side is turned towards the earth, and we see it as gibbous. At full, the whole of the illumined side is turned towards us, and we see it as a full circle. From full to new moon again, the phases occur in the reverse order.

99. _The Form of the Moon's Orbit._--The orbit of the moon around the earth is an ellipse of slight eccentricity. The form of this ellipse is shown in Fig. 113. _C_ is the centre of the ellipse, and _E_ the position of the earth at one of its foci. The eccentricity of the ellipse is only about one-eighteenth. It is impossible for the eye to distinguish such an ellipse from a circle.

100. _The Inclination of the Moon's Orbit._--The plane of the moon's orbit is inclined to the ecliptic by an angle of about five degrees. The two points where the moon's orbit cuts the ecliptic are called her _nodes_. The moon's nodes have a westward motion corresponding to that of the equinoxes, but much more rapid. They complete the circuit of the ecliptic in about nineteen years.

The moon's latitude ranges from 5° north to 5° south; and since, owing to the motion of her nodes, the moon is, during a period of nineteen years, 5° north and 5° south of every part of the ecliptic, her declination will range from 23-1/2° + 5° = 28-1/2° north to 23-1/2° + 5° = 28-1/2° south.

101. _The Meridian Altitude of the Moon._--The _meridian altitude_ of any body is its altitude when on the meridian. In our latitude, the meridian altitude of any point on the equinoctial is forty-nine degrees. The meridian altitude of the summer solstice is 49° + 23-1/2° = 72-1/2°, and that of the winter solstice is 49° - 23-1/2° = 25-1/2°. The greatest meridian altitude of the moon is 72-1/2° + 5° = 77-1/2°, and its least meridian altitude, 25-1/2° - 5° = 20-1/2°.

When the moon's meridian altitude is greater than the elevation of the equinoctial, it is said to run _high_, and when less, to run _low_. The full moon runs high when the sun is south of the equinoctial, and low when the sun is north of the equinoctial. This is because the full moon is always in the opposite part of the heavens to the sun.

102. _Wet and Dry Moon._--At the time of new moon, the cusps of the
crescent sometimes lie in a line which is nearly perpendicular with
the horizon, and sometimes in a line which is nearly parallel with
the horizon. In the former case the moon is popularly described as a
_wet_ moon, and in the latter case as a _dry_ moon.

The great circle which passes through the centre of the sun and moon
will pass through the centre of the crescent, and be perpendicular
to the line joining the cusps. Now the ecliptic makes the least
angle with the horizon when the vernal equinox is on the eastern
horizon and the autumnal equinox is on the western. In our latitude,
as we have seen, this angle is 25-1/2°: hence in our latitude, if
the moon were at new on the ecliptic when the sun is at the autumnal
equinox, as shown at _M_{3}_ (Fig. 114), the great circle passing
through the centre of the sun and moon would be the ecliptic, and at
New York would be inclined to the horizon at an angle of 25-1/2°. If
the moon happened to be 5° south of the ecliptic at this time, as at
_M_{4}_, the great circle passing through the centre of the sun and
moon would make an angle of only 20-1/2° with the horizon. In either
of these cases the line joining the cusps would be nearly
perpendicular to the horizon.

If the moon were at new on the ecliptic when the sun is near the
vernal equinox, as shown at _M_{1}_ (Fig. 115), the great circle
passing through the centres of the sun and moon would make an angle
of 72-1/2° with the horizon at New York; and were the moon 5° north
of the ecliptic at that time, as shown at _M_{2}_, this great circle
would make an angle of 77-1/2° with the horizon. In either of these
cases, the line joining the cusps would be nearly parallel with the
horizon.

At different times, the line joining the cusps may have every
possible inclination to the horizon between the extreme cases shown
in Figs. 114 and 115.

103. _Daily Retardation of the Moon's Rising._--The moon rises, on the average, about fifty minutes later each day. This is owing to her eastward motion. As the moon makes a complete revolution around the earth in about twenty-seven days, she moves eastward at the rate of about thirteen degrees a day, or about twelve degrees a day faster than the sun. Were the moon, therefore, on the horizon at any hour to-day, she would be some twelve degrees below the horizon at the same hour to-morrow. Now, as the horizon moves at the rate of one degree in four minutes, it would take it some fifty minutes to come up to the moon so as to bring her upon the horizon. Hence the daily retardation of the moon's rising is about fifty minutes; but it varies considerably in different parts of her orbit.

There are two reasons for this variation in the daily retardation:--

(1) The moon moves at a _varying rate in her orbit_; her speed being
greatest at perigee, and least at apogee: hence, other things being
equal, the retardation is greatest when the moon is at perigee, and
least when she is at apogee.

(2) The moon moves at a _varying angle to the horizon_. The moon
moves nearly in the plane of the ecliptic, and of course she passes
both equinoxes every lunation. When she is near the autumnal
equinox, her path makes the greatest angle with the eastern horizon,
and when she is near the vernal equinox, the least angle: hence the
moon moves away from the horizon fastest when she is near the
autumnal equinox, and slowest when she is near the vernal equinox.
This will be evident from Figs. 116 and 117. In each figure, _SN_
represents a portion of the eastern horizon, and _Ec_, _E'c'_, a
portion of the ecliptic. _AE_, in Fig. 116, represents the autumnal
equinox, and _AEM_ the daily motion of the moon. _VE_, in Fig. 117,
represents the vernal equinox, and _VEM'_ the motion of the moon for
one day. In the first case this motion would carry the moon away
from the horizon the distance _AM_, and in the second case the
distance _A'M'_. Now, it is evident that _AM_ is greater than
_A'M'_: hence, other things being equal, the greatest retardation of
the moon's rising will be when the moon is near the autumnal
equinox, and the least retardation when the moon is near the vernal
equinox.

The least retardation at New York is twenty-three minutes, and the greatest an hour and seventeen minutes. The greatest and least retardations vary somewhat from month to month; since they depend not only upon the position of the moon in her orbit with reference to the equinoxes, but also upon the latitude of the moon, and upon her nearness to the earth.

The direction of the moon's motion with reference to the ecliptic is shown in Fig. 118, which shows the moon's motion for one day in July, 1876.

104. _The Harvest Moon_--The long and short retardations in the rising of the moon, though they occur every month, are not likely to attract attention unless they occur at the time of full moon. The long retardations for full moon occur when the moon is near the autumnal equinox at full. As the full moon is always opposite to the sun, the sun must in this case be near the vernal equinox: hence the long retardations for full moon occur in the spring, the greatest retardation being in March.

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.

116. _Lunar Craters._--The smaller saucer-shaped formations on the surface of the moon are called _craters_. They are of all sizes, from a mile to a hundred and fifty miles in diameter; and they are supposed to be of volcanic origin. A high telescopic power shows that these craters vary remarkably, not only in size, but also in structure and arrangement. Some are considerably elevated above the surrounding surface, others are basins hollowed out of that surface, and with low surrounding ramparts; some are like walled plains, while the majority have their lowest depression considerably below the surrounding surface; some are isolated upon the plains, others are thickly crowded together, overlapping and intruding upon each other; some have elevated peaks or cones in their centres, and some are without these central cones, while others, again, contain several minute craters instead; some have their ramparts whole and perfect, others have them broken or deformed, and many have them divided into terraces, especially on their inner sides.

A typical lunar crater is shown in Fig. 136.

It is not generally believed that any active volcanoes exist on the moon at the present time, though some observers have thought they discerned indications of such volcanoes.

117. _Copernicus._--This is one of the grandest of lunar craters (Fig. 137). Although its diameter (forty-six miles) is exceeded by others, yet, taken as a whole, it forms one of the most impressive and interesting objects of its class. Its situation, near the centre of the lunar disk, renders all its wonderful details conspicuous, as well as those of objects immediately surrounding it. Its vast rampart rises to upwards of twelve thousand feet above the level of the plateau, nearly in the centre of which stands a magnificent group of cones, three of which attain a height of more than twenty-four hundred feet.

Many ridges, or spurs, may be observed leading away from the outer banks of the great rampart. Around the crater, extending to a distance of more than a hundred miles on every side, there is a complex network of bright streaks, which diverge in all directions. These streaks do not appear in the figure, nor are they seen upon the moon, except at and near the full phase. They show conspicuously, however, by their united lustre on the full moon.

This crater is seen just to the south-west of the large dusky plain in the upper part of Fig. 132. This plain is _Mare Imbrium_, and the mountain-chain seen a little to the right of Copernicus is named the _Apennines_. Copernicus is also seen in Fig. 135, a little to the left of the same range.

Under circumstances specially favorable, myriads of comparatively minute but perfectly formed craters may be observed for more than seventy miles on all sides around Copernicus. The district on the south-east side is specially rich in these thickly scattered craters, which we have reason to suppose stand over or upon the bright streaks.

118. _Dark Chasms._--Dark cracks, or chasms, have been observed on various parts of the moon's surface. They sometimes occur singly, and sometimes in groups. They are often seen to radiate from some central cone, and they appear to be of volcanic origin. They have been called _canals_ and _rills_.

One of the most remarkable groups of these chasms is that to the west of the crater named _Triesneker_. The crater and the chasms are shown in Fig. 138. Several of these great cracks obviously diverge from a small crater near the west bank of the great one, and they subdivide as they extend from the apparent point of divergence, while they are crossed by others. These cracks, or chasms, are nearly a mile broad at the widest part, and, after extending full a hundred miles, taper away till they become invisible.

119. _Mountain-Ranges._--There are comparatively few mountain-ranges on the moon. The three most conspicuous are those which partially enclose Mare Imbrium; namely, the _Apennines_ on the south, and the _Caucasus_ and the _Alps_ on the east and north-east. The Apennines are the most extended of these, having a length of about four hundred and fifty miles. They rise gradually, from a comparatively level surface towards the south-west, in the form of innumerable small elevations, which increase in number and height towards the north-east, where they culminate in a range of peaks whose altitude and rugged aspect must form one of the most terribly grand and romantic scenes which imagination can conceive. The north-east face of the range terminates abruptly in an almost vertical precipice; while over the plain beneath, intensely black spire-like shadows are cast, some of which at sunrise extend full ninety miles, till they lose themselves in the general shading due to the curvature of the lunar surface. Many of the peaks rise to heights of from eighteen thousand to twenty thousand feet above the plain at their north-east base (Fig. 139).

Fig. 140 represents an ideal lunar landscape near the base of such a lunar range. Owing to the absence of an atmosphere, the stars will be visible in full daylight.

120. _The Valley of the Alps._--The range of the _Alps_ is shown in Fig. 141. The great crater at the north end of this range is named _Plato_. It is seventy miles in diameter.

The most remarkable feature of the Alps is the valley near the centre of the range. It is more than seventy-five miles long, and about six miles wide at the broadest part. When examined under favorable circumstances, with a high magnifying power, it is seen to be a vast flat-bottomed valley, bordered by gigantic mountains, some of which attain heights of ten thousand feet or more.

121. _Isolated Peaks._--There are comparatively few isolated peaks to be found on the surface of the moon. One of the most remarkable of these is that known as _Pico_, and shown in Fig. 142. Its height exceeds eight thousand feet, and it is about three times as long at the base as it is broad. The summit is cleft into three peaks, as is shown by the three-peaked shadow it casts on the plain.

122. _Bright Rays._--About the time of full moon, with a telescope of moderate power, a number of bright lines may be seen radiating from several of the lunar craters, extending often to the distance of hundreds of miles. These streaks do not arise from any perceptible difference of level of the surface, they have no very definite outline, and they do not present any sloping sides to catch more sunlight, and thus shine brighter, than the general surface. Indeed, one great peculiarity of them is, that they come out most forcibly when the sun is shining perpendicularly upon them: hence they are best seen when the moon is at full, and they are not visible at all at those regions upon which the sun is rising or setting. They are not diverted by elevations in their path, but traverse in their course craters, mountains, and plains alike, giving a slight additional brightness to all objects over which they pass, but producing no other effect upon them. "They look as if, after the whole surface of the moon had assumed its final configuration, a vast brush charged with a whitish pigment had been drawn over the globe in straight lines, radiating from a central point, leaving its trail upon every thing it touched, but obscuring nothing."

The three most conspicuous craters from which these lines radiate are _Tycho_, _Copernicus_, and _Kepler_. Tycho is seen at the bottom of Figs. 143 and 130. Kepler is a little to the left of Copernicus in the same figures.

It has been thought that these bright streaks are chasms which have been filled with molten lava, which, on cooling, would afford a smooth reflecting surface on the top.

123. _Tycho._--This crater is fifty-four miles in diameter, and about sixteen thousand feet deep, from the highest ridge of the rampart to the surface of the plateau, whence rises a central cone five thousand feet high. It is one of the most conspicuous of all the lunar craters; not so much on account of its dimensions as from its being the centre from whence diverge those remarkable bright streaks, many of which may be traced over a thousand miles of the moon's surface (Fig. 143). Tycho appears to be an instance of a vast disruptive action which rent the solid crust of the moon into radiating fissures, which were subsequently filled with molten matter, whose superior luminosity marks the course of the cracks in all directions from the crater as their common centre. So numerous are these bright streaks when examined by the aid of the telescope, and they give to this region of the moon's surface such increased luminosity, that, when viewed as a whole, the locality can be distinctly seen at full moon by the unassisted eye, as a bright patch of light on the southern portion of the disk.