THE MOON
91. RESULTS OF OBSERVATION WITH THE UNAIDED EYE.--The student who has
made the observations of the moon which are indicated in Chapter III has
in hand data from which much may be learned about the earth's satellite.
Perhaps the most striking feature brought out by them is the motion of
the moon among the stars, always from west toward east, accompanied by
that endless series of changes in shape and brightness--new moon, first
quarter, full moon, etc.--whose successive stages we represent by the
words, the phase of the moon. From his own observation the student
should be able to verify, at least approximately, the following
statements, although the degree of numerical precision contained in some
of them can be reached only by more elaborate apparatus and longer study
than he has given to the subject:
A. The phase of the moon depends upon the distance apart of sun and moon
in the sky, new moon coming when they are together, and full moon when
they are as far apart as possible.
[Illustration: THE MOON, ONE DAY AFTER FIRST QUARTER. From a photograph
made at the Paris Observatory.]
B. The moon is essentially a round, dark body, giving off no light of
its own, but shining solely by reflected sunlight. The proof of this is
that whenever we see a part of the moon which is turned away from the
sun it looks dark--e. g., at new moon, sun and moon are in nearly the
same direction from us and we see little or nothing of the moon, since
the side upon which the sun shines is turned away from us. At full moon
the earth is in line between sun and moon, and we see, round and
bright, the face upon which the sun shines. At other phases, such as the
quarters, the moon turns toward the earth a part of its night hemisphere
and a part of its day hemisphere, but in general only that part which
belongs to the day side of the moon is visible and the peculiar curved
line which forms the boundary--the "ragged edge," or _terminator_, as it
is called, is the dividing line between day and night upon the moon.
A partial exception to what precedes is found for a few days after new
moon when the moon and sun are not very far apart in the sky, for then
the whole round disk of the moon may often be seen, a small part of it
brightly illuminated by the sun and the larger part feebly illuminated
by sunlight which fell first upon the earth and was by it reflected back
to the moon, giving the pleasing effect which is sometimes called the
old moon in the new moon's arms. The new moon--i. e., the part illumined
by the sun--usually appears to belong to a sphere of larger radius than
the old moon, but this is purely a trick played by the eyes of the
observer, and the effect disappears altogether in a telescope. Is there
any similar effect in the few days before new moon?
C. The moon makes the circuit of the sky from a given star around to the
same star again in a little more than 27 days (27.32166), but the
interval between successive new moons--i. e., from the sun around to the
sun again--is more than 29 days (29.53059). This last interval, which is
called a lunar month or _synodical_ month, indicates what we have
learned before--that the sun has changed its place among the stars
during the month, so that it takes the moon an extra two days to
overtake him after having made the circuit of the sky, just as it takes
the minute hand of a clock an extra 5 minutes to catch up with the hour
hand after having made a complete circuit of the dial.
D. Wherever the moon may be in the sky, it turns always the same face
toward the earth, as is shown by the fact that the dark markings which
appear on its surface stand always upon (nearly) the same part of its
disk. It does not always turn the same face toward the sun, for the
boundary line between the illumined and unillumined parts of the moon
shifts from one side to the other as the phase changes, dividing at each
moment day from night upon the moon and illustrating by its slow
progress that upon the moon the day and the month are of equal length
(29.5 terrestrial days), instead of being time units of different
lengths as with us.
[Illustration: FIG. 53.--Motion of moon and earth relative to the sun.]
92. THE MOON'S MOTION.--The student should compare the results of his
own observations, as well as the preceding section, with Fig. 53, in
which the lines with dates printed on them are all supposed to radiate
from the sun and to represent the direction from the sun of earth and
moon upon the given dates which are arbitrarily assumed for the sake of
illustration, any other set would do equally well. The black dots, small
and large, represent the moon revolving about the earth, but having the
circular path shown in Fig. 34 (ellipse) transformed by the earth's
forward motion into the peculiar sinuous line here shown. With respect
to both earth and sun, the moon's orbit deviates but little from a
circle, since the sinuous curve of Fig. 53 follows very closely the
earth's orbit around the sun and is almost identical with it. For
clearness of representation the distance between earth and moon in the
figure has been made ten times too great, and to get a proper idea of
the moon's orbit with reference to the sun, we must suppose the moon
moved up toward the earth until its distance from the line of the
earth's orbit is only a tenth part of what it is in the figure. When
this is done, the moon's path becomes almost indistinguishable from that
of the earth, as may be seen in the figure, where the attempt has been
made to show both lines, and it is to be especially noted that this
real orbit of the moon is everywhere concave toward the sun.
The phase presented by the moon at different parts of its path is
indicated by the row of circles at the right, and the student should
show why a new moon is associated with June 30th and a full moon with
July 15th, etc. What was the date of first quarter? Third quarter?
We may find in Fig. 53 another effect of the same kind as that noted
above in C. Between noon, June 30th, and noon, July 3d, the earth makes
upon its axis three complete revolutions with respect to the sun, but
the meridian which points toward the moon at noon on June 30th will not
point toward it at noon on July 3d, since the moon has moved into a new
position and is now 37° away from the meridian. Verify this statement by
measuring, in Fig. 53, with the protractor, the moon's angular distance
from the meridian at noon on July 3d. When will the meridian overtake
the moon?
93. HARVEST MOON.--The interval between two successive transits of the
meridian past the moon is called a lunar day, and the student should
show from the figure that on the average a lunar day is 51 minutes
longer than a solar day--i. e., upon the average each day the moon comes
to the meridian 51 minutes of solar time later than on the day before.
It is also true that on the average the moon rises and sets 51 minutes
later each day than on the day before. But there is a good deal of
irregularity in the retardation of the time of moonrise and moonset,
since the time of rising depends largely upon the particular point of
the horizon at which the moon appears, and between two days this point
may change so much on account of the moon's orbital motion as to make
the retardation considerably greater or less than its average value. In
northern latitudes this effect is particularly marked in the month of
September, when the eastern horizon is nearly parallel with the moon's
apparent path in the sky, and near the time of full moon in that month
the moon rises on several successive nights at nearly the same hour, and
in less degree the same is true for October. This highly convenient
arrangement of moonlight has caused the full moons of these two months
to be christened respectively the Harvest Moon and the Hunter's Moon.
94. SIZE AND MASS OF THE MOON.--It has been shown in Chapter I how the
distance of the moon from the earth may be measured and its diameter
determined by means of angles, and without enlarging upon the details of
these observations, we note as their result that the moon is a globe
2,163 miles in diameter, and distant from the earth on the average about
240,000 miles. But, as we have seen in Chapter VII, this distance
changes to the extent of a few thousand miles, sometimes less, sometimes
greater, mainly on account of the elliptic shape of the moon's orbit
about the earth, but also in part from the disturbing influence of other
bodies, such as the sun, which pull the moon to and fro, backward and
forward, to quite an appreciable extent.
From the known diameter of the moon it is a matter of elementary
geometry to derive in miles the area of its surface and its volume or
solid contents. Leaving this as an exercise for the student, we adopt
the earth as the standard of comparison and find that the diameter of
the moon is rather more than a quarter, 4/15, that of the earth, the
area of its surface is a trifle more than 1/14 that of the earth, and
its volume a little more than 1/49 of the earth's. So much is pure
geometry, but we may combine with it some mechanical principles which
enable us to go a step farther and to "weigh" the moon--i. e., determine
its mass and the average density of the material of which it is made.
We have seen that the moon moves around the sun in a path differing but
little from the smooth curve shown in Fig. 53, with arrows indicating
the direction of motion, and it would follow absolutely such a smooth
path were it not for the attraction of the earth, and in less degree of
some of the other planets, which swing it about first to one side then
to the other. But action and reaction are equal; the moon pulls as
strongly upon the earth as does the earth upon the moon, and if earth
and moon were of equal mass, the deviation of the earth from the smooth
curve in the figure would be just as large as that of the moon. It is
shown in the figure that the moon does displace the earth from this
curve, and we have only to measure the amount of this displacement of
the earth and compare it with the displacement suffered by the moon to
find how much the mass of the one exceeds that of the other. It may be
seen from the figure that at first quarter, about July 7th, the earth is
thrust ahead in the direction of its orbital motion, while at the third
quarter, July 22d, it is pulled back by the action of the moon, and at
all times it is more or less displaced by this action, so that, in order
to be strictly correct, we must amend our former statement about the
moon moving around the earth and make it read, Both earth and moon
revolve around a point on line between their centers. This point is
called their _center of gravity_, and the earth and the moon both move
in ellipses having this center of gravity at their common focus. Compare
this with Kepler's First Law. These ellipses are similarly shaped, but
of very different size, corresponding to Newton's third law of motion
(Chapter IV), so that the action of the earth in causing the small moon
to move around a large orbit is just equal to the reaction of the moon
in causing the larger earth to move in the smaller orbit. This is
equivalent to saying that the dimensions of the two orbits are inversely
proportional to the masses of the earth and the moon.
By observing throughout the month the direction from the earth to the
sun or to a near planet, such as Mars or Venus, astronomers have
determined that the diameter of the ellipse in which the earth moves is
about 5,850 miles, so that the distance of the earth from the center of
gravity is 2,925 miles, and the distance of the moon from it is
240,000-2,925 = 237,075. We may now write in the form of a proportion--
Mass of earth : Mass of moon :: 237,075 : 2,925,
and find from it that the mass of the earth is 81 times as great as the
mass of the moon--i. e., leaving kind and quality out of account, there
is enough material in the earth to make 81 moons. We may note in this
connection that the diameter of the earth, 7,926 miles, is greater than
the diameter of the monthly orbit in which the moon causes it to move,
and therefore the center of gravity of earth and moon always lies inside
the body of the earth, about 1,000 miles below the surface.
95. DENSITY OF THE MOON.--It is believed that in a general way the moon
is made of much the same kind of material which goes to make up the
earth--metals, minerals, rocks, etc.--and a part of the evidence upon
which this belief is based lies in the density of the moon. By density
of a substance we mean the amount of it which is contained in a given
volume--i. e., the weight of a bushel or a cubic centimeter of the
stuff. The density of chalk is twice as great as the density of water,
because a cubic centimeter of chalk weighs twice as much as an equal
volume of water, and similarly in other cases the density is found by
dividing the mass or weight of the body by the mass or weight of an
equal volume of water.
We know the mass of the earth (§ 45), and knowing the mass of a cubic
foot of water, it is easy, although a trifle tedious, to compute what
would be the mass of a volume of water equal in size to the earth. The
quotient obtained by dividing one of these masses by the other (mass of
earth ÷ mass of water) is the average density of the material composing
the earth, and we find numerically that this is 5.6--i. e., it would
take 5.6 water earths to attract as strongly as does the real one. From
direct experiment we know that the average density of the principal
rocks which make up the crust of the earth is only about half of this,
showing that the deep-lying central parts of the earth are denser than
the surface parts, as we should expect them to be, because they have to
bear the weight of all that lies above them and are compressed by it.
Turning now to the moon, we find in the same way as for the earth that
its average density is 3.4 as great as that of water.
96. FORCE OF GRAVITY UPON THE MOON.--This number, 3.4, compared with the
5.6 which we found for the earth, shows that on the whole the moon is
made of lighter stuff than is the body of the earth, and this again is
much what we should expect to find, for weight, the force which tends to
compress the substance of the moon, is less there than here. The weight
of a cubic yard of rock at the surface of either earth or moon is the
force with which the earth or moon attracts it, and this by the law of
gravitation is for the earth--
W = k × (m m´) / (3963)^{2};
and for the moon--
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 mass 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 masses
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.
[Illustration: FIG. 54.--Illustrating 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 orbit. 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 orbit the head on this small
coin will be successively directed toward every point of the compass,
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
orbit. In no other way can it be made to face always away from the
figure at the center of its orbit 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 orbit 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 orbital 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
orbit; 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
anchored 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 constitutes 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.
[Illustration: 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 illustrated 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 glass.
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 analogous to the cañons 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 principal 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.
[Illustration: 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.
[Illustration: 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.
[Illustration: 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.
[Illustration: FIG. 59.--Illustrating 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 circumstances 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.
[Illustration: 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.
[Illustration: FIG. 61.--Occultations and the moon's atmosphere.]
[Illustration: 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 altitude 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 principal 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 altitude of
18,000 feet, and the Leibnitz and Doerfel Mountains, near the south pole
of the moon, reach an altitude 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.
[Illustration: 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.
D. Whatever may have been the mode of their formation, the craters can
not have been produced by scooping out material from the center and
piling it up to make the wall, for in three cases out of four the volume
of the excavation is greater than the volume of material contained in
the wall.
106. MOON AND EARTH.--We have gone far enough now to appreciate both the
likeness and the unlikeness of the moon and earth. They may fairly
enough be likened to offspring of the same parent who have followed very
different careers, and in the fullness of time find themselves in very
different circumstances. The most serious point of difference in these
circumstances is the atmosphere, which gives to the earth a wealth of
phenomena altogether lacking in the moon. Clouds, wind, rain, snow,
dew, frost, and hail are all dependent upon the atmosphere and can not
be found where it is not. There can be nothing upon the moon at all like
that great group of changes which we call weather, and the unruffled
aspect of the moon's face contrasts sharply with the succession of cloud
and sunshine which the earth would present if seen from the moon.
The atmosphere is the chief agent in the propagation of sound, and
without it the moon must be wrapped in silence more absolute than can be
found upon the surface of the earth. So, too, the absence of an
atmosphere shows that there can be no water or other liquid upon the
moon, for if so it would immediately evaporate and produce a gaseous
envelope which we have seen does not exist. With air and water absent
there can be of course no vegetation or life of any kind upon the moon,
and we are compelled to regard it as an arid desert, utterly waste.
107. TEMPERATURE OF THE MOON.--A characteristic feature of terrestrial
deserts, which is possessed in exaggerated degree by the moon, is the
great extremes of temperature to which they and it are subject. Owing to
its slow rotation about its axis, a point on the moon receives the solar
radiation uninterruptedly for more than a fortnight, and that too
unmitigated by any cloud or vaporous covering. Then for a like period it
is turned away from the sun and allowed to cool off, radiating into
interplanetary space without hindrance its accumulated store of heat. It
is easy to see that the range of temperature between day and night must
be much greater under these circumstances than it is with us where
shorter days and clouded skies render day and night more nearly alike,
to say nothing of the ocean whose waters serve as a great balance wheel
for equalizing temperatures. Just how hot or how cold the moon becomes
is hard to determine, and very different estimates are to be found in
the books. Perhaps the most reliable of these are furnished by the
recent researches of Professor Very, whose experiments lead him to
conclude that "its rocky surface at midday, in latitudes where the sun
is high, is probably hotter than boiling water and only the most
terrible of earth's deserts, where the burning sands blister the skin,
and men, beasts, and birds drop dead, can approach a noontide on the
cloudless surface of our satellite. Only the extreme polar latitudes of
the moon can have an endurable temperature by day, to say nothing of the
night, when we should have to become troglodytes to preserve ourselves
from such intense cold."
While the night temperature of the moon, even very soon after sunset,
sinks to something like 200° below zero on the centigrade scale, or 320°
below zero on the Fahrenheit scale, the lowest known temperature upon
the earth, according to General Greely, is 90° Fahr. below zero,
recorded in Siberia in January, 1885.
Winter and summer are not markedly different upon the moon, since its
rotation axis is nearly perpendicular to the plane of the earth's orbit
about the sun, and the sun never goes far north or south of the moon's
equator. The month is the one cycle within which all seasonal changes in
its physical condition appear to run their complete course.
108. CHANGES IN THE MOON.--It is evidently idle to look for any such
changes in the condition of the moon's surface as with us mark the
progress of the seasons or the spread of civilization over the
wilderness. But minor changes there may be, and it would seem that the
violent oscillations of temperature from day to night ought to have some
effect in breaking down and crumbling the sharp peaks and crags which
are there so common and so pronounced. For a century past astronomers
have searched carefully for changes of this kind--the filling up of some
crater or the fall of a mountain peak; but while some things of this
kind have been reported from time to time, the evidence in their behalf
has not been altogether conclusive. At the present time it is an open
question whether changes of this sort large enough to be seen from the
earth are in progress. A crater much less than a mile wide can be seen
in the telescope, but it is not easy to tell whether so minute an object
has changed in size or shape during a year or a decade, and even if
changes are seen they may be apparent rather than real. Fig. 64 contains
two views of the crater Archimedes, taken under a morning and an
afternoon sun respectively, and shows a very pronounced difference
between the two which proceeds solely from a difference of illumination.
In the presence of such large fictitious changes astronomers are slow to
accept smaller ones as real.
[Illustration: FIG. 64.--Archimedes in the lunar morning and
afternoon.--WEINEK.]
It is this absence of change that is responsible for the rugged and
sharp-cut features of the moon which continue substantially as they were
made, while upon the earth rain and frost are continually wearing down
the mountains and spreading their substance upon the lowland in an
unending process of smoothing off the roughnesses of its surface. Upon
the moon this process is almost if not wholly wanting, and the moon
abides to-day much more like its primitive condition than is the earth.
109. THE MOON'S INFLUENCE UPON THE EARTH.--There is a widespread popular
belief that in many ways the moon exercises a considerable influence
upon terrestrial affairs: that it affects the weather for good or ill,
that crops must be planted and harvested, pigs must be killed, and
timber cut at the right time of the moon, etc. Our common word lunatic
means moonstruck--i. e., one upon whom the moon has shone while
sleeping. There is not the slightest scientific basis for any of these
beliefs, and astronomers everywhere class them with tales of witchcraft,
magic, and popular delusion. For the most part the moon's influence upon
the earth is limited to the light which it sends and the effect of its
gravitation, chiefly exhibited in the ocean tides. We receive from the
moon a very small amount of second-hand solar heat and there is also a
trifling magnetic influence, but neither of these last effects comes
within the range of ordinary observation, and we shall not go far wrong
in saying that, save the moonlight and the tides, every supposed lunar
influence upon the earth is either fictitious or too small to be readily
detected.