different portions of her illuminated side being turned towards the
earth at different times. When the moon is first seen after the setting
sun, her form is that of a bright crescent, on the side of the disk next
to the sun, while the other portions of the disk shine with a feeble
light, reflected to the moon from the earth. Every night, we observe the
moon to be further and further eastward of the sun, until, when she has
reached an elongation from the sun of ninety degrees, half her visible
disk is enlightened, and she is said to be in her _first quarter_. The
terminator, or line which separates the illuminated from the dark part
of the moon, is convex towards the sun from the new to the first
quarter, and the moon is said to be _horned_. The extremities of the
crescent are called _cusps_. At the first quarter, the terminator
becomes a straight line, coinciding with the diameter of the disk; but
after passing this point, the terminator becomes concave towards the
sun, bounding that side of the moon by an elliptical curve, when the
moon is said to be _gibbous_. When the moon arrives at the distance of
one hundred and eighty degrees from the sun, the entire circle is
illuminated, and the moon is _full_. She is then _in opposition_ to the
sun, rising about the time the sun sets. For a week after the full, the
moon appears gibbous again, until, having arrived within ninety degrees
of the sun, she resumes the same form as at the first quarter, being
then at her _third quarter_. From this time until new moon, she exhibits
again the form of a crescent before the rising sun, until, approaching
her _conjunction_ with the sun, her narrow thread of light is lost in
the solar blaze; and finally, at the moment of passing the sun, the dark
side is wholly turned towards us, and for some time we lose sight of the
moon.
By inspecting Fig. 38, (where T represents the earth, A, B, C, &c., the
moon in her orbit, and _a_, _b_, _c_, &c., her phases, as seen in the
heavens,) we shall easily see how all these changes occur.
[Illustration Fig. 38.]
You have doubtless observed, that the moon appears much further in the
south at one time than at another, when of the same age. This is owing
to the fact that the ecliptic, and of course the moon's path, which is
always very near it, is differently situated with respect to the
_horizon_, at a given time of night, at different seasons of the year.
This you will see at once, by turning to an artificial globe, and
observing how the ecliptic stands with respect to the horizon, at
different periods of the revolution. Thus, if we place the two
equinoctial points in the eastern and western horizon, Libra being in
the west, it will represent the position of the ecliptic at sunset in
the month of September, when the sun is crossing the equator; and at
that season of the year, the moon's path through our evening sky, one
evening after another, from new to full, will be nearly along the same
route, crossing the meridian nearly at right angles. But if we place the
Winter solstice, or first degree of Capricorn, in the western horizon,
and the first degree of Cancer in the eastern, then the position of the
ecliptic will be very oblique to the meridian, the Winter solstice being
very far in the southwest, and the Summer solstice very far in the
northeast; and the course of the moon from new to full will be nearly
along this track. Keeping these things in mind, we may easily see why
the moon runs sometimes high and sometimes low. Recollect, also, that
the new moon is always in the same part of the heavens with the sun, and
that the full moon is in the opposite part of the heavens from the sun.
Now, when the sun is at the Winter solstice, it sets far in the
southwest, and accordingly the new moon runs very low; but the full
moon, being in the opposite tropic, which rises far in the northeast,
runs very high, as is known to be the case in mid-winter. But now take
the position of the ecliptic in mid-summer. Then, at sunset, the tropic
of Cancer is in the northwest, and the tropic of Capricorn in the
southeast; consequently, the new moons run high and the full moons low.
It is a natural consequence of this arrangement, to render the moon's
light the most beneficial to us, by giving it to us in greatest
abundance, when we have least of the sun's light, and giving it to us
most sparingly, when the sun's light is greatest. Thus, during the long
nights of Winter, the full moon runs high, and continues a very long
time above the horizon; while in mid-summer, the full moon runs low, and
is above the horizon for a much shorter period. This arrangement
operates very favorably to the inhabitants of the polar regions. At the
season when the sun is absent, and they have constant night, then the
moon, during the second and third quarters, embracing the season of full
moon, is continually above the horizon, compensating in no small degree
for the absence of the sun; while, during the Summer months, when the
sun is constantly above the horizon, and the light of the moon is not
needed, then she is above the horizon during the first and last
quarters, when her light is least, affording at that time her greatest
light to the inhabitants of the other hemisphere, from whom the sun is
withdrawn.
About the time of the Autumnal equinox, the moon, when near her full,
rises about sunset a number of nights in succession. This occasions a
remarkable number of brilliant moonlight evenings; and as this is, in
England, the period of harvest, the phenomenon is called the _harvest
moon_. Its return is celebrated, particularly among the peasantry, by
festive dances, and kept as a festival, called the _harvest home_,--an
occasion often alluded to by the British poets. Thus Henry Kirke White:
"Moon of harvest, herald mild
Of plenty, rustic labor's child,
Hail, O hail! I greet thy beam,
As soft it trembles o'er the stream,
And gilds the straw-thatch'd hamlet wide,
Where innocence and peace reside;
'Tis thou that glad'st with joy the rustic throng,
Promptest the tripping dance, th' exhilarating song."
To understand the reason of the harvest moon, we will, as before,
consider the moon's orbit as coinciding with the ecliptic, because we
may then take the ecliptic, as it is drawn on the artificial globe, to
represent that orbit. We will also bear in mind, (what has been fully
illustrated under the last head,) that, since the ecliptic cuts the
meridian obliquely, while all the circles of diurnal revolution cut it
perpendicularly, different portions of the ecliptic will cut the horizon
at different angles. Thus, when the equinoxes are in the horizon, the
ecliptic makes a very small angle with the horizon; whereas, when the
solstitial points are in the horizon, the same angle is far greater. In
the former case, a body moving eastward in the ecliptic, and being at
the eastern horizon at sunset, would descend but a little way below the
horizon in moving over many degrees of the ecliptic. Now, this is just
the case of the moon at the time of the harvest home, about the time of
the Autumnal equinox. The sun being then in Libra, and the moon, when
full, being of course opposite to the sun, or in Aries; and moving
eastward, in or near the ecliptic, at the rate of about thirteen degrees
per day, would descend but a small distance below the horizon for five
or six days in succession; that is for two or three days before, and the
same number of days after, the full; and would consequently rise during
all these evenings nearly at the same time, namely, a little before, or
a little after, sunset, so as to afford a remarkable succession of fine
moonlight evenings.
The moon _turns on her axis_ in the same time in which she revolves
around the earth. This is known by the moon's always keeping nearly the
same face towards us, as is indicated by the telescope, which could not
happen unless her revolution on her axis kept pace with her motion in
her orbit. Take an apple, to represent the moon; stick a knittingneedle
through it, in the direction of the stem, to represent the axis, in
which case the two eyes of the apple will aptly represent the poles.
Through the poles cut a line around the apple, dividing it into two
hemispheres, and mark them, so as to be readily distinguished from each
other. Now place a candle on the table, to represent the earth, and
holding the apple by the knittingneedle, carry it round the candle, and
you will see that, unless you make the apple turn round on the axis as
you carry it about the candle, it will present different sides towards
the candle; and that, in order to make it always present the same side,
it will be necessary to make it revolve exactly once on its axis, while
it is going round the circle,--the revolution on its axis always keeping
exact pace with the motion in its orbit. The same thing will be
observed, if you walk around a tree, always keeping your face towards
the tree. If you have your face towards the tree when you set out, and
walk round without turning, when you have reached the opposite side of
the tree, your back will be towards it, and you will find that, in order
to keep your face constantly towards the tree, it will be necessary to
turn yourself round on your heel at the same rate as you go forward.
Since, however, the motion of the moon on its axis is uniform, while the
motion in its orbit is unequal, the moon does in fact reveal to us a
little sometimes of one side and sometimes of the other. Thus if, while
carrying the apple round the candle, you carry it forward a little
faster than the rate at which it turns on its axis, a portion of the
hemisphere usually out of sight is brought into view on one side; or if
the apple is moved forward slower than it is turned on its axis, a
portion of the same hemisphere comes into view on the other side. These
appearances are called the moon's _librations in longitude_. The moon
has also a _libration in latitude_;--so called, because in one part of
her revolution more of the region around one of the poles comes into
view, and, in another part of the revolution, more of the region around
the other pole, which gives the appearance of a tilting motion to the
moon's axis. This is owing to the fact, that the moon's axis is inclined
to the plane of her orbit. If, in the experiment with the apple, you
hold the knittingneedle parallel to the candle, (in which case the axis
will be perpendicular to the plane of revolution,) the candle will shine
upon both poles during the whole circuit, and an eye situated where the
candle is would constantly see both poles; but now incline the needle
towards the plane of revolution, and carry it round, always keeping it
parallel to itself, and you will observe that the two poles will be
alternately in and out of sight.
The moon exhibits another appearance of this kind, called her _diurnal
libration_, depending on the daily rotation of the spectator. She turns
the same face towards the _centre_ of the earth only, whereas we view
her from the surface. When she is on the meridian, we view her disk
nearly as though we viewed it from the centre of the earth, and hence,
in this situation, it is subject to little change; but when she is near
the horizon, our circle of vision takes in more of the upper limb than
would be presented to a spectator at the centre of the earth. Hence,
from this cause, we see a portion of one limb while the moon is rising,
which is gradually lost sight of, and we see a portion of the opposite
limb, as the moon declines to the west. You will remark that neither of
the foregoing changes implies any actual motion in the moon, but that
each arises from a change of position in the spectator. Since the
succession of day and night depends on the revolution of a planet on its
own axis, and it takes the moon twenty-nine and a half days to perform
this revolution, so that the sun shall go from the meridian of any place
and return to the same meridian again, of course the lunar day occupies
this long period. So protracted an exposure to the sun's rays,
especially in the equatorial regions of the moon, must occasion an
excessive accumulation of heat; and so long an absence of the sun must
occasion a corresponding degree of cold. A spectator on the side of the
moon which is opposite to us would never see the earth, but one on the
side next to us would see the earth constantly in his firmament,
undergoing a gradual succession of changes, corresponding to those which
the moon exhibits to the earth, but in the reverse order. Thus, when it
is full moon to us, the earth, as seen from the moon, is then in
conjunction with the sun, and of course presents her dark side to the
moon.
Soon after this, an inhabitant of the moon would see a crescent,
resembling our new moon, which would in like manner increase and go
through all the changes, from new to full, and from full to new, as we
see them in the moon. There are, however, in the two cases, several
striking points of difference. In the first place, instead of
twenty-nine and a half days, all these changes occur in one lunar day
and night. During the first and last quarters, the changes would occur
in the day-time; but during the second and third quarters, during the
night. By this arrangement, the lunarians would enjoy the greatest
possible benefit from the light afforded by the earth, since in the half
of her revolution where she appears to them as full, she would be
present while the sun was absent, and would afford her least light while
the sun was present. In the second place, the earth would appear
thirteen times as large to a spectator on the moon as the moon appears
to us, and would afford nearly the same proportion of light, so that
their long nights must be continually cheered by an extraordinary degree
of light derived from this source; and if the full moon is hailed by our
poets as "refulgent lamp of night,"[10] with how much more reason might
a lunarian exult thus, in view of the splendid orb that adorns his
nocturnal sky! In the third place, the earth, as viewed from any
particular place on the moon, would occupy invariably the same part of
the heavens. For while the rotation of the moon on her axis from west to
east would appear to make the earth (as the moon does to us) revolve
from east to west, the corresponding progress of the moon in her orbit
would make the earth appear to revolve from west to east; and as these
two motions are equal, their united effect would be to keep the moon
apparently stationary in the sky. Thus, a spectator at E, Fig. 38, page
175, in the middle of the disk that is turned towards the earth, would
have the earth constantly on his meridian, and at E, the conjunction of
the earth and sun would occur at mid-day; but when the moon arrived at
G, the same place would be on the margin of the circle of illumination,
and will have the sun in the horizon; but the earth would still be on
his meridian and in quadrature. In like manner, a place situated on the
margin of the circle of illumination, when the moon is at E, would have
the earth in the horizon; and the same place would always see the earth
in the horizon, except the slight variations that would occur from the
librations of the moon. In the fourth place, the earth would present to
a spectator on the moon none of that uniformity of aspect which the moon
presents to us, but would exhibit an appearance exceedingly diversified.
The comparatively rapid rotation of the earth, repeated fifteen times
during a lunar night, would present, in rapid succession, a view of our
seas, oceans, continents, and mountains, all diversified by our clouds,
storms, and volcanoes.
FOOTNOTES:
[9] Dick's 'Celestial Scenery.'
[10]
"As when the moon, refulgent lamp of night,
O'er heaven's clear azure sheds her sacred light,
When not a breath disturbs the deep serene,
And not a cloud o'ercasts the solemn scene,
Around her throne the vivid planets roll,
And stars unnumbered gild the glowing pole;
O'er the dark trees a yellower verdure shed,
And tip with silver every mountain's head;
Then shine the vales, the rocks in prospect rise,
A flood of glory bursts from all the skies;
The conscious swains, rejoicing in the sight,
Eye the blue vault, and bless the useful light."
_Pope's Homer._
LETTER XVII.
MOON'S ORBIT.--HER IRREGULARITIES.
"Some say the zodiac constellations
Have long since left their antique stations,
Above a sign, and prove the same
In Taurus now, once in the Ram;
That in twelve hundred years and odd,
The sun has left his ancient road,
And nearer to the earth is come,
'Bove fifty thousand miles from home."--_Hudibras._
WE have thus far contemplated the revolution of the moon around the
earth as though the earth were at rest. But in order to have just ideas
respecting the moon's motions, we must recollect that the moon likewise
revolves along with the earth around the sun. It is sometimes said that
the earth _carries_ the moon along with her, in her annual revolution.
This language may convey an erroneous idea; for the moon, as well as the
earth, revolves around the sun under the influence of two forces, which
are independent of the earth, and would continue her motion around the
sun, were the earth removed out of the way. Indeed, the moon is
attracted towards the sun two and one fifth times more than towards the
earth, and would abandon the earth, were not the latter also carried
along with her by the same forces. So far as the sun acts equally on
both bodies, the motion with respect to each other would not be
disturbed. Because the gravity of the moon towards the sun is found to
be greater, at the conjunction, than her gravity towards the earth, some
have apprehended that, if the doctrine of universal gravitation is true,
the moon ought necessarily to abandon the earth. In order to understand
the reason why it does not do thus, we must reflect, that, when a body
is revolving in its orbit under the influence of the projectile force
and gravity, whatever diminishes the force of gravity, while that of
projection remains the same, causes the body to approach nearer to the
tangent of her orbit, and of course to recede from the centre; and
whatever increases the amount of gravity, carries the body towards the
centre. Thus, in Fig. 33, page 152, if, with a certain force of
projection acting in the direction A B, and of attraction, in the
direction A C, the attraction which caused a body to move in the line A
D were diminished, it would move nearer to the tangent, as in A E, or A
F. Now, when the moon is in conjunction, her gravity towards the earth
acts in opposition to that towards the sun, (see Fig. 38, page 175,)
while her velocity remains too great to carry her with what force
remains, in a circle about the sun, and she therefore recedes from the
sun, and commences her revolution around the earth. On arriving at the
opposition, the gravity of the earth conspires with that of the sun, and
the moon's projectile force being less than that required to make her
revolve in a circular orbit, when attracted towards the sun by the sum
of these forces, she accordingly begins to approach the sun, and
descends again to the conjunction.
The attraction of the sun, however, being every where greater than that
of the earth, the actual path of the moon around the sun is every where
concave towards the latter. Still, the elliptical path of the moon
around the earth is to be conceived of, in the same way as though both
bodies were at rest with respect to the sun. Thus, while a steam-boat is
passing _swiftly_ around an island, and a man is walking _slowly_ around
a post in the cabin, the line which he describes in space between the
forward motion of the boat and his circular motion around the post, may
be every where concave towards the island, while his path around the
post will still be the same as though both were at rest. A nail in the
rim of a coach-wheel will turn around the axis of the wheel, when the
coach has a forward motion, in the same manner as when the coach is at
rest, although the line actually described by the nail will be the
resultant of both motions, and very different from either.
We have hitherto regarded the moon as describing a great circle on the
face of the sky, such being the visible orbit, as seen by projection.
But, on a more exact investigation, it is found that her orbit is not a
circle, and that her motions are subject to very numerous
irregularities. These will be best understood in connexion with the
causes on which they depend. The law of universal gravitation has been
applied with wonderful success to their developement, and its results
have conspired with those of long-continued observation, to furnish the
means of ascertaining with great exactness the place of the moon in the
heavens, at any given instant of time, past or future, and thus to
enable astronomers to determine longitudes, to calculate eclipses, and
to solve other problems of the highest interest. The whole number of
irregularities to which the moon is subject is not less than sixty, but
the greater part are so small as to be hardly deserving of attention;
but as many as thirty require to be estimated and allowed for, before we
can ascertain the exact place of the moon at any given time. You will be
able to understand something of the cause of these irregularities, if
you first gain a distinct idea of the mutual actions of the sun, the
moon, and the earth. The irregularities in the moon's motions are due
chiefly to the disturbing influence of the sun, which operates in two
ways; first, by acting unequally on the earth and moon; and secondly, by
acting obliquely on the moon, on account of the inclination of her orbit
to the ecliptic. If the sun acted equally on the earth and moon, and
always in parallel lines, this action would serve only to restrain them
in their annual motions around the sun, and would not affect their
actions on each other, or their motions about their common centre of
gravity. In that case, if they were allowed to fall towards the sun,
they would fall equally, and their respective situations would not be
affected by their descending equally towards it. But, because the moon
is nearer the sun in one half of her orbit than the earth is, and in the
other half of her orbit is at a greater distance than the earth from the
sun, while the power of gravity is always greater at a less distance; it
follows, that in one half of her orbit the moon is more attracted than
the earth towards the sun, and, in the other half, less attracted than
the earth.
To see the effects of this process, let us suppose that the projectile
motions of the earth and moon were destroyed, and that they were allowed
to fall freely towards the sun. (See Fig. 38, page 175.) If the moon was
in conjunction with the sun, or in that part of her orbit which is
nearest to him, the moon would be more attracted than the earth, and
fall with greater velocity towards the sun; so that the distance of the
moon from the earth would be increased by the fall. If the moon was in
opposition, or in the part of her orbit which is furthest from the sun,
she would be less attracted than the earth by the sun, and would fall
with a less velocity, and be left behind; so that the distance of the
moon from the earth would be increased in this case, also. If the moon
was in one of the quarters, then the earth and the moon being both
attracted towards the centre of the sun, they would both descend
directly towards that centre, and, by approaching it, they would
necessarily at the same time approach each other, and in this case their
distance from each other would be diminished. Now, whenever the action
of the sun would increase their distance, if they were allowed to fall
towards the sun, then the sun's action, by endeavoring to separate them,
diminishes their gravity to each other; whenever the sun's action would
diminish the distance, then it increases their mutual gravitation.
Hence, in the conjunction and opposition, their gravity towards each
other is diminished by the action of the sun, while in the quadratures
it is increased. But it must be remembered, that it is not the total
action of the sun on them that disturbs their motions, but only that
part of it which tends at one time to separate them, and at another time
to bring them nearer together. The other and far greater part has no
other effect than to retain them in their annual course around the sun.
The cause of the lunar irregularities was first investigated by Sir
Isaac Newton, in conformity with his doctrine of universal gravitation,
and the explanation was first published in the 'Principia;' but, as it
was given in a mathematical dress, there were at that age very few
persons capable of reading or understanding it. Several eminent
individuals, therefore, undertook to give a popular explanation of these
difficult points. Among Newton's contemporaries, the best commentator
was M'Laurin, a Scottish astronomer, who published a large work entitled
'M'Laurin's Account of Sir Isaac Newton's Discoveries.' No writer of his
own day, and, in my opinion, no later commentator, has equalled
M'Laurin, in reducing to common apprehension the leading principles of
the doctrine of gravitation, and the explanation it affords of the
motions of the heavenly bodies. To this writer I am indebted for the
preceding easy explanation of the irregularities of the moon's motions,
as well as for several other illustrations of the same sublime doctrine.