_MOONLIGHT._
The light of the moon and the changes of the moon were probably the
first phenomena which led men to study the motions of the heavenly
bodies. In our times, when most men live where artificial illumination
is used at night, we can scarcely appreciate the full value of moonlight
to men who cannot obtain artificial light. Especially must moonlight
have been valuable to the class of men among whom, according to all
traditions, the first astronomers appeared. The tiller of the soil might
fare tolerably well without nocturnal light, though even he,--as indeed
the familiar designation of the harvest-moon shows us,--finds special
value, sometimes, in moonlight. But to the shepherd moonlight and its
changes must have been of extreme importance as he watched his herds and
flocks by night. We can understand how carefully he would note the
change from the new moon to the time when throughout the whole night, or
at least of the darkest hours, the full moon illuminated the hills and
valleys over which his watch extended, and thence to the time when the
sickle of the fast waning moon shone but for a short time before the
rising of the sun. To him, naturally, the lunar month, and its
subdivision, the week, would be the chief measure of time. He would
observe--or rather he could not help observing--the passage of the moon
around the zodiacal band, some twenty moon-breadths wide, which is the
lunar roadway among the stars. These would be the first purely
astronomical observations made by man; so that we learn without surprise
that before the present division of the zodiac was adopted the old
Chaldean astronomers (as well as the Indian, Persian, Egyptian, and
Chinese astronomers, who still follow the practice) divided the zodiac
into 28 lunar mansions, each mansion corresponding nearly to one day's
motion of the moon among the stars.
It is easy to understand how the first rough observations of moonlight
and its changes taught men the true nature of the moon, as an opaque
globe circling round the earth, and borrowing her light from the sun.
They perceived, first, that the moon was only full when she was opposite
the sun, shining at her highest in the south at midnight when the sun
was at his lowest beneath the northern horizon. Before the time of full
moon, they saw that more or less of the moon's disc was illuminated as
he was nearer or farther from the position opposite the sun, the
illuminated side being towards the west--that is, towards the sun; while
after full moon the same law was perceived in the amount of light, the
illuminated side being still towards the sun, that is, towards the east.
They could not fail to observe the horned moon sometimes in the daytime,
with her horns turned directly from the sun, and showing as plainly, by
her aspect, whence her light was derived, as does any terrestrial ball
lit up either by a lamp or by the sun.
The explanation they gave was the explanation still given by
astronomers. Let us briefly consider it. In doing so I propose to modify
the ordinary text-book illustration which has always seemed to me
ingeniously calculated (with its double set of diversely illuminated
moons around the earth) to make a simple subject obscure.
In fig. 12, let E represent the earth one half in darkness, the other
half illuminated by the rays of the sun S, which should be supposed
placed at a much greater distance to the left,--in fact, about five
yards away from E. To preserve the right proportions, also, the sun
ought to be much smaller and the earth a mere point. I mention this to
prevent the reader from adopting erroneous ideas as to the size of these
bodies. In reality it is quite impossible to show in such figures the
true proportions of the heavenly bodies and of their distances. Next let
M_{1}, M_{2}, M_{3}, etc., represent the moon in different positions
along her circuit around the earth at E.
[Illustration: Fig. 12.--Explaining the Moon's changes.]
[Illustration: Fig. 13.--Illustrating the Moon's changes.]
Now, it is clear that when the moon is at M_{1}, her illuminated face is
turned from the earth, E. She therefore cannot be seen; and accordingly,
in fig. 12, she is presented as a black disc at 1 to correspond with her
invisibility when she is as at M_{1}. She passes on to M_{2}; and now
from E a part of her illuminated half can be seen towards the sun, which
would be towards the right, if we imagine an eye at E looking towards
M_{2}. Her appearance then is as shown at 2, fig. 13. In any
intermediate portion between M_{1} and M_{2}, the sickle of light is
visible but narrower. We see also that all this time the moon's place on
the sky cannot be far from the sun's place, for the line from E to M_{2}
is not greatly inclined to the line from E to S. When the moon has got
round to M_{3}, the observer on the earth sees as much of the dark half
as of the bright half of the moon, the bright half being seen, of
course, towards the sun. Thus the moon appears as at 3, fig. 13, Again
as to position, the moon is now a quarter of a circuit of the heavens
from the sun, for the line from E to M_{3} is square to the line from E
to S. We see similarly that when at M_{4} the moon appears as shown at
4, fig. 13, for now the observer at E sees as small a part of the moon's
dark side as he had seen of her bright side when she was at M_{2}. When
she is at M_{5} the observer at E sees her bright face only, the dark
face being turned directly from him. She, therefore, appears as at 5,
fig. 13. Also being now exactly opposite the sun, as we see from fig.
12, she is at her highest when the sun is at his lowest, or at midnight;
and at this time she rules the night as the sun rules the day.[10] As
the moon passes on to M_{6}, a portion of her dark half comes into view,
the bright side being now towards the left, as we look at M_{5} from E,
fig. 12. Her appearance, therefore, is as shown at 5. When at M_{7} she
is seen as at 7, half-bright and half-dark, as when she was at M_{3},
but the halves interchanged. At M_{8} she appears as at 8, and, lastly,
at M_{1} she is again undiscernible.
The ancient Chaldean astronomers could have little doubt as to the
validity of this explanation. In fact, while it is the explanation
obviously suggested by observed facts, one cannot see how any other
could have occurred to them.
But if they had had any doubts for a while, the occurrence of eclipses
would soon have removed those doubts. They must early have noticed that
at times the full moon became first partly obscured, then either wholly
disappeared or changed in colour to a deep coppery red, and after a
while reappeared. Sometimes the darkening was less complete, so that at
the time of greatest darkness a portion of the moon seemed eaten out,
though not by a well defined or black shadow. These phenomena, they
would find, occurred only at the time of full moon. And if they were
closely observant, they would find that these eclipses of the moon only
occurred when the full moon was on or near the great circle round the
stellar heavens, which they had learned to be the sun's track. They
could hardly fail to infer that these darkenings of the moon were caused
by the earth's shadow, near which the moon must always pass when she is
full, and through which she must sometimes pass more or less fully; in
fact, whenever, at the time of full, she is on or near the plane in
which the earth travels round the sun. Solar eclipses would probably be
observed later. For though a total eclipse of the sun is a much more
striking phenomenon than a total eclipse of the moon, yet the latter
are far more common. A partial eclipse of the sun may readily pass
unnoticed, unless the sun's rays are so mitigated by haze or mist that
it is possible to look at his disc without pain. Whenever solar eclipses
came to be noted, and we know from the Chaldean discovery of the great
eclipse period, called the _Saros_, that they were observed at least two
thousand years before the Christian era, the fact that the moon is an
opaque body circling round the earth, and much nearer to the earth than
the sun is, must be regarded as demonstrated. Not only would eclipses of
the sun be observed to occur only when the moon was passing between the
earth and the sun, but in an eclipse of the sun, whether total or
partial, the round black body cutting off the sun's light wholly or
partially would be seen to have the familiar dimensions of the lunar
orb.
Leaving solar and lunar eclipses for description on another occasion, I
will now proceed to consider a peculiarity of moonlight which must very
early have attracted attention,--I mean the phenomenon called the
harvest-moon.
The moon circuits the heavens in a path but slightly inclined to that of
the sun, called the ecliptic, and for our present purpose we may speak
of the moon as travelling in the ecliptic. Now we know that during the
winter half of the year the sun is south of the equator, the circle of
the heavenly sphere which passes through the east and west points of the
horizon, and has its plane square to the polar axis of the heavens.
During the other or summer half of the year he is north of the equator.
In the former case the sun is above the horizon less than half the
twenty-four hours, day being so much shorter as the sun is farther south
of the equator; whereas in the latter case the sun is above the horizon
more than twelve hours, day being so much the longer as the sun is
farther north of the equator. Precisely similar changes affect the moon,
only, instead of taking place in a year (the time in which the sun
circuits the stellar heavens), they occur in what is called a sidereal
month, the time in which the moon completes her circuit of the stellar
heavens. For about a fortnight the moon is above the horizon longer than
she is below the horizon, while during the next fortnight she is below
the horizon longer than she is above the horizon. Now clearly when the
length of what we may call the moon's diurnal path (meaning her path
above the horizon) is lengthening most, the time of her rising on
successive nights must change least. She comes to the south later and
later each successive night by about 50½ minutes, because she is always
travelling towards the east at such a rate as to complete one circuit in
about four weeks; and losing thus one day in 28, she losses about 50½
minutes per day. If the interval between her rising and her arriving to
the south were always the same, she would rise 50½ minutes later night
after night. But if the interval is lengthening, say by 10 minutes per
night, she would of course rise only 40½ minutes later: if the interval
_is_ lengthening 20 minutes per night, she would rise only 30½ minutes
later, and so forth. But the lunar diurnal arc is lengthening all the
time she is passing from her position farthest south of the equator to
her position farthest north, just in the same way as the solar day is
lengthening from mid-winter to midsummer, only to a much greater degree.
And as the solar day lengthens fastest at spring when the sun crosses
the equator from south to north, so the time the moon is above the
horizon lengthens most, day by day, when the moon is crossing the
equator from south to north. It lengthens, _then_, from an hour to an
hour and 20 minutes in one day, that is, the interval between moon-rise
and moon-setting increases from 30 to 40 minutes. At this time, then,
whenever it happens in each lunar month, the moon's time of rising
changes least: instead of the moon rising night after night 50½ minutes
later, the actual difference varies only from 10 to 20 minutes.
Now if this happens at a time when the moon is not nearly full, it is
not specially noticed, because the moon's light is not then specially
useful. But if it happens when the moon is nearly full, it is noticed,
because her light is then so useful. A moon nearly full, afterwards
quite full, and then for a day or two still nearly full, rising night
after night at nearly the same time, remaining also night after night
longer above the horizon, manifestly serves man for the time being in
the most convenient way possible. But it is clear that as the full moon
is opposite the sun, and as to fulfil the condition described we have
seen that she must be crossing the equator from south to north, the sun,
opposite to her, must be at the part of his path where he crosses the
equator from north to south. In other words, the time of year must be
the autumnal equinox. Thus the moon which comes to "full" nearest to
September 22 or 23 will behave in the convenient way described. At this
time, moreover, when she rises night after night nearly at the same
time, the nights are lengthening fastest while the time the moon is
above the horizon is lengthening still more, and therefore, in all
respects, the moon is then doing her best, so to speak, to illuminate
the nights. At this season the moon is called the harvest-moon, from the
assistance she sometimes renders to harvesters.
The moon which is full nearest to September 22-23 may precede or follow
that date. In the former case only can it properly be called a
harvest-moon. In the latter it is sometimes called the hunter's moon.
The full moon occurring nearest to harvest time will always partake more
or less of the qualities of a full moon occurring at the autumnal
equinox: and similarly of a full moon following the autumnal equinox. So
that, in almost every year, there may be said to be a harvest-moon and a
hunter's moon. But, of course, it will very often happen that in any
particular agricultural district the harvest has to be gathered in
during the wrong half of the lunar month, that is, during the last and
first, instead of the second and third quarters.
The reader must not fall into the mistake of supposing, as I have seen
sometimes stated in text-books of astronomy, that we are more favoured
in this respect than the inhabitants of the southern hemisphere. It is
quite true that the same full moon shines on us as on our friends in New
Zealand, Australia, and Cape Colony, and also that our autumn is their
spring, and their spring our autumn. But the full moon we have in autumn
behaves in the southern hemisphere not as with us, but as our spring
full moon behaves; and the full moon of our spring, which is their
autumn, behaves with them as our autumn moon behaves with us. It is,
therefore, for them a harvest-moon if it occur before the equinox, and a
hunter's moon if it occur after the equinox. A very little consideration
will show why this is. In fact if, in the explanation given above, the
words north and south be interchanged, and March 21-22 written for
September 22-23, the explanation will be precisely that which I should
have given respecting the harvest (or March) moon of the southern
hemisphere, if I had been writing for southern readers.
* * * * *
Having thus considered the moon as a light-giver, both in respect of her
monthly changes and of that yearly change which causes her services to
be most useful in harvest time, let us consider what science tells us of
the orb which thus usefully reflects to us the solar rays.
The moon is a globe about 2159½ miles in diameter, travelling round the
earth at a mean distance of 238,818 miles. Her path round the earth is
not, however, a circle, but an ellipse, which itself is constantly
varying in shape. The average eccentricity of the moon's path is such
that her greatest and least distances, as she circuits round it, are
251,953 miles and 225,683 miles respectively; but when it is most
eccentric, her greatest and least distances are 252,948 miles and
221,593 miles respectively; while, when it is least eccentric, they are
respectively 250,324 miles and 227,312 miles. The earth's surface
exceeds the moon's nearly 13½ times, the actual number of square miles
in the moon's surface amounting to 14,600,000. This is nearly equal to
Europe and Africa together, or, more nearly still, to North and South
America together, without their islands. In volume our earth exceeds the
moon rather more than 49¼ times: or, more nearly, if the earth's volume
be represented by 10,000, the moon's will be represented by 209. The
materials of the moon's globe are either lighter or (more probably) they
are less closely compacted than those forming our earth,--for, according
to the best modern estimates, the earth exceeds the moon in mass nearly
81½ times. Assuming as the most probable value of the earth's mean
density about 5-7/10 times the density of water, the moon's mean density
is equal to 3-46/100 times that of water. Gravity at her surface is
accordingly much less than at the surface of the earth; a quantity of
matter weighing six pounds at the surface of the earth would weigh
almost exactly one pound at the surface of the moon.
The moon circuits once round the earth in 27d. 7h. 43m. 11.5s. This is
the time in which, viewed from the earth, she seems to complete one
circuit round the stellar heavens, and is therefore called a sidereal
month. But as the earth is all the time travelling the same way round
the sun, the lunar month is longer. Thus, suppose S (fig. 14) to be the
sun, E the earth at the beginning of a lunar month, M_{1} M_{2} M_{3}
M_{4} the moon's path, and M_{1} the moon's place on the line joining E
and S. If the earth remained at rest while the moon went round the path
M_{1} M_{3}, then after completing one circuit the moon would again be
at M_{1} on the line joining E and S, or it would be new moon again. But
the earth is moving onwards along the arc EE´ of her circuit round the
sun. So that when the moon has completed one circuit she is at M_{4}
(E´m_{1} drawn parallel to EM_{1}) and has still to travel some distance
before she gets round to M´ on the line joining S and E´. The lunation,
or interval between successive new moons, has an average duration of
29d. 12h. 44m. 38s., exceeding a sidereal month by 2d. 5h.
[Illustration: Fig. 14.--Explaining the difference between a sidereal
lunar month and a common lunar month or lunation.]
It would not, however, be correct to regard the earth as the true
centre of the moon's motion. The moon is in reality a planet circling
round the sun, but largely perturbed by the attraction of its companion
planet the earth. If the moon's path in the course of a year were
carefully drawn to scale, or, better, were modelled by means of a fine
wire, it would scarcely be distinguishable from a similar picture or
model of the earth's path round the sun. Or thus, the entire width of
the moon's track is about 477,636 miles, while the diameter of the orbit
along which she and the earth both travel is nearly 104,000,000 miles,
or 385 times as great. If we draw then a circle 3-85/100 inches in
diameter to represent the earth's path round the sun, somewhat
eccentrically placed, and the circular line is 1-100th of an inch wide,
the moon's track would be fairly represented by a curve touching
alternately the inside and the outside edge of this circular line, at
equidistant points dividing the circle into about 24¾ parts.
Regarding the moon as a planet, she may be said to have a year, and
seasons, and day and night, as the earth has, but very unlike our
seasons and days. Her axis is inclined only 1½ degrees from uprightness
to her path, whereas our earth's axis is inclined 23½ degrees. The sun's
range of mid-day altitude is in fact not quite equal to the range of our
sun in mid-day height, from four days before to four days after either
spring or autumn. The lunar day lasts a lunar month, daytime and
night-time each lasting rather more than a fortnight. The lunar year of
seasons is not, as is commonly stated, the same in length as ours. She
goes round the sun in the same time, so that her sidereal year is the
same as ours; but owing to the swaying round of her axis her year of
seasons or tropical year is shorter. Our tropical year is also shorter
than the sidereal year, but very little shorter, because the earth's
axis sways round once only in 25,868 years. The moon's axis sways round
once in 18⅗ years, and accordingly the year of seasons is much more
effectively shortened. It lasts, in fact, only 346d. 14h. 34m. of our
time; and contains only 11¾ lunar days. So that I cannot altogether
agree with Sir W. Herschel's statement, that "the moon's situation with
respect to the sun is much like that of our earth, and by a rotation on
its axis it enjoys an agreeable variety of seasons, and of day and
night."
When the moon is examined with a telescope her surface is seen to be
marked by many irregularities. There are large dark regions which were
formerly thought to be seas, but are now known to be land-surfaces. Some
of these regions are singularly level, and have been thought to be old
sea-bottoms. Mountains and mountain ranges are another important
feature of the moon's surface. Some, like our Rocky Mountains and
Andes, form long continuous chains; others form elevated plateaus whence
ridges extend in various directions. A very striking form is that of
narrow ridges little raised above the general level, but reaching over
enormous areas of the moon's globe. It is a system of this kind,
radiating from a great lunar crater called Tycho, which gives to small
photographs of the moon the appearance of a peeled orange. They are
supposed to indicate the action of tremendous forces of upheaval, in
past ages, bursting open portions of the moon's crust.
But the most characteristic of all the lunar features are the crater
mountains, which exist on a scale not only much larger relatively to the
moon's globe than the scale on which terrestrial craters are formed, but
much larger absolutely. They are also far more numerous. Some parts of
the moon's surface, especially in the bright south-western quarter of
her face, are literally crowded with craters of various dimensions.
There are few signs of the former emission of lava from the lunar
craters. Within some of them recent changes have been suspected. A
remarkable instance is that of the crater Linné, marked in Mädler's map
as a deep, well-walled crater, some four miles in diameter. At present
only a small crater can be seen in its place. The surrounding region is
rather conspicuously bright. It is not necessary to infer that there
has been any volcanic disturbance, however. Far more probably the walls
have been thrown down through the long-continued action of that
alternate expansion and contraction, which must affect the moon's crust
as the long fortnightly day proceeds, and then the equally long lunar
night.
There are many well-marked valleys on the moon, besides clefts and
ravines. The features called _rilles_ are among the most perplexing
objects on the moon's surface. Webb, in his charming and most useful
little book, "Celestial Objects for Common Telescopes," thus describes
them: "These most singular furrows pass chiefly through levels,
intersect craters (proving a more recent date), reappear beyond
obstructing mountains, as though carried through by a tunnel, and
commence and terminate with little reference to any conspicuous feature
of the neighbourhood. The idea of artificial formation is negatived by
their magnitude; they have been more probably referred to cracks in a
shrinking surface." Some observations would seem to show that they have
been formed from rows of closely-adjacent small craters. _Faults_, also,
or closed cracks where the surface is higher on one side than on the
other, have been recognised from the careful study of the shadows on the
moon's disc.
From measurements of the shadows of lunar mountains, it appears that
their average height is about five miles. In comparing this elevation
with that assigned to terrestrial mountains, it must be remembered that
these are measured from the sea-level; if the average height of
terrestrial mountains were determined with reference to the sea-bottom
it would be far greater. Still, even taking this circumstance into
account, the average height of the lunar mountains bears a far greater
ratio to the diameter of the globe on which they stand than the average
height of our mountains to the earth's diameter.
Several circumstances agree in showing that the moon's atmosphere must
be exceedingly rare. The shadows of lunar mountains are either actually
black or nearly so. When the moon hides the sun in total eclipse, no
sign can be seen of any refractive effort exerted on the sun's rays.
When a star is hidden (or _occulted_) by the moon, the star vanishes in
an instant and reappears with equal suddenness. It is certain from these
phenomena that the moon has either no air, or air exceedingly tenuous.
It is equally clear that she has no water, for if she had we should
undoubtedly be able to recognise the occasional formation or dissipation
of mist and vapour over parts of the moon's surface. No signs of such
phenomena have ever been observed. The moon is certainly at present a
waterless globe, so far at least as her surface is concerned.
It has been thought that though there is no water and very little air
on the side of the moon turned towards the earth, there may be both
water and air on the farther unseen side. The theory has been long since
given up, but the reasoning on which it depends is worth noting. Owing
to the strange circumstance that the moon rotates on her axis in the
same time in which she revolves round the earth, she always presents the
same face towards the earth, or very nearly so. If her axis were exactly
square to the path in which she circuits the earth, and if she revolved
at a uniform rate, we should have exactly the same side constantly
turned towards us. But as the axis is inclined about 6⅔° from
uprightness to the path round the _earth_ (which, be it remembered, is
not in the same plane as the path round the sun, but inclined 5° 8´ to
it), the northern and southern parts of the moon are alternately swayed
over by about 6⅔° into view. This apparent swaying is called a
libration, and the libration just described is called the libration in
latitude. Again, as the moon does not travel at a uniform rate round the
earth, but faster than her mean rate when nearer to us, and slower when
farther from us, she alternately gains and loses in her motion of
revolution as compared with her motion of rotation, by a quantity
varying between 5° and 7¾°, to which varying extent the parts east and
west of her mean disc are alternately swayed into view. This is called
the libration in longitude. Thus we see, beyond the edge of the _mean_
half turned towards us, a considerable fringe of the other half. If a
globe, as PAP´B, fig. 15, were divided into two halves to represent the
farther and nearer halves of the moon, and held so that that dividing
circle were seen as PEP´ in the figure, then Ppep´P´ would represent the
part brought into view at different times by the apparent swaying
described above; while P_pep´_P´ would represent the parts swayed out of
view. The regions thus alternately in view and out of view have their
greatest breadth, not at the poles or east and west, but at mMm and
m´M´m´, where the two librations act together. The narrow fringe
bordering these regions is that brought into or out of view by changes
in the place of the observer on earth, due to the earth's rotation. It
is called the parallactic fringe, any change in the apparent position of
a heavenly body, or part of one, on account of the earth's rotation,
being termed _parallax_.
[Illustration: Fig. 15.--Illustrating lunar libration.]
Lastly, let us return to the consideration of moonlight, as depending on
the condition of the moon's surface, To one who observes the moon as
seen on the sky, her light appears white; but it must not be supposed
that she is a white body. Careful estimates of the quantity of light she
reflects show that she is more nearly black than white, though in
reality she is neither one nor the other. It has been said, and truly,
that if the surface of the moon were covered with black velvet she would
still appear white; for even black velvet reflects some light, and
whatever light the moon reflected would show her by contrast with the
blackness of the sky, as a luminous body or white. It follows from the
observations made by Zöllner that if the moon's surface were covered
with white snow she could give us about 4½ times as much light as she
actually does. If she were covered with white paper she would give more
than 4 times as much light as she does. If she had a surface of white
sandstone her light would be nearly half as great again as it is. She
gives rather more light than she would if her surface consisted entirely
of weathered grey sandstone, or of clay marl, and more than twice as
much light as she would give if her surface were of moist earth, or dark
grey syenite. As some parts of her surface are obviously much brighter
than others, we must infer that some parts shine with much more, and
others with much less, brightness than weathered grey sandstone.
Probably some parts are much brighter than white sandstone, and some
much darker than dark grey syenite. From the degree in which her lustre
changes with her changing aspect, Zöllner infers that her mountains have
an average slope of about fifty-two degrees.