the moon also revolved around the earth in this plane, we should have a
solar eclipse at every new moon, and a lunar eclipse at every full moon;
for, in the former case, the moon would come directly between us and
the sun, and in the latter case, the earth would come directly between
the sun and the moon. But the moon is inclined to the ecliptic about
five degrees, and the centre of the moon may be all this distance from
the centre of the sun at new moon, and the same distance from the centre
of the earth's shadow at full moon. It is true, the moon extends across
her path, one half her breadth lying on each side of it, and the sun
likewise reaches from the ecliptic a distance equal to half his breadth.
But these luminaries together make but little more than a degree, and
consequently, their two semidiameters would occupy only about half a
degree of the five degrees from one orbit to the other where they are
furthest apart. Also, the earth's shadow, where the moon crosses it,
extends from the ecliptic less than three fourths of a degree, so that
the semidiameter of the moon and of the earth's shadow would together
reach but little way across the space that may, in certain cases,
separate the two luminaries from each other when they are in opposition.
Thus, suppose we could take hold of the circle in the figure that
represents the moon's orbit, (Fig. 42, page 197,) and lift the moon up
five degrees above the plane of the paper, it is evident that the moon,
as seen from the earth, would appear in the heavens five degrees above
the sun, and of course would cut off none of his light; and it is also
plain that the moon, at the full, would pass the shadow of the earth
five degrees below it, and would suffer no eclipse. But in the course of
the sun's apparent revolution round the earth once a year he is
successively in every part of the ecliptic; consequently, the
conjunctions and oppositions of the sun and moon may occur at any part
of the ecliptic, and of course at the two points where the moon's orbit
crosses the ecliptic,--that is, at the nodes; for the sun must
necessarily come to each of these nodes once a year. If, then, the moon
overtakes the sun just as she is crossing his path, she will hide more
or less of his disk from us. Since, also, the earth's shadow is always
directly opposite to the sun, if the sun is at one of the nodes, the
shadow must extend in the direction of the other node, so as to lie
directly across the moon's path; and if the moon overtakes it there, she
will pass through it, and be eclipsed. Thus, in Fig. 43, let BN
represent the sun's path, and AN, the moon's,--N being the place of the
node; then it is evident, that if the two luminaries at new moon be so
far from the node, that the distances between their centres is greater
than their semidiameters, no eclipse can happen; but if that distance is
less than this sum, as at E, F, then an eclipse will take place; but if
the position be as at C, D, the two bodies will just touch one another.
If A denotes the earth's shadow, instead of the sun, the same
illustration will apply to an eclipse of the moon.
[Illustration Fig. 43.]
Since bodies are defined to be in conjunction when they are in the
_same_ part of the heavens, and to be in opposition when they are in
_opposite_ parts of the heavens, it may not appear how the sun and moon
can be in conjunction, as at A and B, when they are still at some
distance from each other. But it must be recollected that bodies are in
conjunction when they have the same longitude, in which case they are
situated in the same great circle perpendicular to the ecliptic,--that
is, in the same secondary to the ecliptic. One of these bodies may be
much further from the ecliptic than the other; still, if the same
secondary to the ecliptic passes through them both, they will be in
conjunction or opposition.
In a total eclipse of the moon, its disk is still visible, shining with
a dull, red light. This light cannot be derived directly from the sun,
since the view of the sun is completely hidden from the moon; nor by
reflection from the earth, since the illuminated side of the earth is
wholly turned from the moon; but it is owing to refraction from the
earth's atmosphere, by which a few scattered rays of the sun are bent
round into the earth's shadow and conveyed to the moon, sufficient in
number to afford the feeble light in question.
It is impossible fully to understand the _method of calculating
eclipses_, without a knowledge of trigonometry; still it is not
difficult to form some general notion of the process. It may be readily
conceived that, by long-continued observations on the sun and moon, the
laws of their revolution may be so well understood, that the exact
places which they will occupy in the heavens at any future times may be
foreseen and laid down in tables of the sun and moon's motions; that we
may thus ascertain, by inspecting the tables, the instant when these two
bodies will be together in the heavens, or be in conjunction, and when
they will be one hundred and eighty degrees apart, or in opposition.
Moreover, since the exact place of the moon's node among the stars at
any particular time is known to astronomers, it cannot be difficult to
determine when the new or full moon occurs in the same part of the
heavens as that where the node is projected, as seen from the earth. In
short, as astronomers can easily determine what will be the relative
position of the sun, the moon, and the moon's nodes, for any given time,
they can tell when these luminaries will meet so near the node as to
produce an eclipse of the sun, or when they will be in opposition so
near the node as to produce an eclipse of the moon.
A little reflection will enable you to form a clear idea of the
situation of the sun, the moon, and the earth, at the time of a solar
eclipse. First, suppose the conjunction to take place at the node; that
is, imagine the moon to come _directly_ between the earth and the sun,
as she will of course do, if she comes between the earth and the sun the
moment she is crossing the ecliptic; for then the three bodies will all
lie in one and the same straight line. But when the moon is in the
ecliptic, her shadow, or at least the axis, or central line, of the
shadow, must coincide with the line that joins the centres of the sun
and earth, and reach along the plane of the ecliptic towards the earth.
The moon's shadow, at her average distance from the earth, is just about
long enough to reach the surface of the earth; but when the moon, at the
new, is in her apogee, or at her greatest distance from the earth, the
shadow is not long enough to reach the earth. On the contrary, when the
moon is nearer to us than her average distance, her shadow is long
enough to reach beyond the earth, extending, when the moon is in her
perigee, more than fourteen thousand miles beyond the centre of the
earth. Now, as during the eclipse the moon moves nearly in the plane of
the ecliptic, her shadow which accompanies her must also move nearly in
the same plane, and must therefore traverse the earth across its central
regions, along the terrestrial ecliptic, since this is nothing more than
the intersection of the plane of the celestial ecliptic with the earth's
surface. The motion of the earth, too, on its axis, in the same
direction, will carry a place along with the shadow, though with a less
velocity by more than one half; so that the actual velocity of the
shadow, in respect to places over which it passes on the earth, will
only equal the difference between its own rate and that of the places,
as they are carried forward in the diurnal revolution.
We have thus far supposed that the moon comes to her conjunction
precisely at the node, or at the moment when she is crossing the
ecliptic. But, secondly, suppose she is on the north side of the
ecliptic at the time of conjunction, and moving towards her descending
node, and that the conjunction takes place as far from the node as an
eclipse can happen. The shadow will not fall in the plane of the
ecliptic, but a little northward of it, so as just to graze the earth
near the pole of the ecliptic. The nearer the conjunction comes to the
node, the further the shadow will fall from the polar towards the
equatorial regions.
In a solar eclipse, the shadow of the moon travels over a portion of the
earth, as the shadow of a small cloud, seen from an eminence in a clear
day, rides along over hills and plains. Let us imagine ourselves
standing on the moon; then we shall see the earth partially eclipsed by
the moon's shadow, in the same manner as we now see the moon eclipsed by
the shadow of the earth; and we might calculate the various
circumstances of the eclipse,--its commencement, duration, and
quantity,--in the same manner as we calculate these elements in an
eclipse of the moon, as seen from the earth. But although the general
characters of a solar eclipse might be investigated on these principles,
so far as respects the earth at large, yet, as the appearances of the
same eclipse of the sun are very different at different places on the
earth's surface, it is necessary to calculate its peculiar aspects for
each place separately, a circumstance which makes the calculation of a
solar eclipse much more complicated and tedious than that of an eclipse
of the moon. The moon, when she enters the shadow of the earth, is
deprived of the light of the part immersed, and the effect upon its
appearance is the same as though that part were painted black, in which
case it would be black alike to all places where the moon was above the
horizon. But it not so with a solar eclipse. We do not see this by the
shadow cast on the earth, as we should do, if we stood on the moon, but
by the interposition of the moon between us and the sun; and the sun may
be hidden from one observer, while he is in full view of another only a
few miles distant. Thus, a small insulated cloud sailing in a clear sky
will, for a few moments, hide the sun from us, and from a certain space
near us, while all the region around is illuminated. But although the
analogy between the motions of the shadow of a small cloud and of the
moon in a solar eclipse holds good in many particulars, yet the velocity
of the lunar shadow is far greater than that of the cloud, being no less
than two thousand two hundred and eighty miles per hour.
The moon's shadow can never cover a space on the earth more than one
hundred and seventy miles broad, and the space actually covered commonly
falls much short of that. The portion of the earth's surface ever
covered by the moon's penumbra is about four thousand three hundred and
ninety-three miles.
The apparent diameter of the moon varies materially at different times,
being greatest when the moon is nearest to us, and least when she is
furthest off; while the sun's apparent dimensions remain nearly the
same. When the moon is at her average distance from the earth, she is
just about large enough to cover the sun's disk; consequently, if, in a
central eclipse of the sun, the moon is at her mean distance, she covers
the sun but for an instant, producing only a momentary eclipse. If she
is nearer than her average distance, then the eclipse may continue total
some time, though never more than eight minutes, and seldom so long as
that; but if she is further off than usual, or towards her apogee, then
she is not large enough to cover the whole solar disk, but we see a ring
of the sun encircling the moon, constituting an _annular eclipse_, as
seen in Fig. 44. Even the elevation of the moon above the horizon will
sometimes sensibly affect the dimensions of the eclipse. You will
recollect that the moon is nearer to us when on the meridian than when
in the horizon by nearly four thousand miles, or by nearly the radius of
the earth; and consequently, her apparent diameter is largest when on
the meridian. The difference is so considerable, that the same eclipse
will appear total to a spectator who views it near his meridian, while,
at the same moment, it appears annular to one who has the moon near his
horizon. An annular eclipse may last, at most, twelve minutes and
twenty-four seconds.
[Illustration Fig. 44.]
Eclipses of the sun are more frequent than those of the moon. Yet lunar
eclipses being visible to every part of the terrestrial hemisphere
opposite to the sun, while those of the sun are visible only to a small
portion of the hemisphere on which the moon's shadow falls, it happens
that, for any particular place on the earth, lunar eclipses are more
frequently visible than solar. In any year, the number of eclipses of
both luminaries cannot be less than two nor more than seven: the most
usual number is four, and it is very rare to have more than six. A total
eclipse of the moon frequently happens at the next full moon after an
eclipse of the sun. For since, in a solar eclipse, the sun is at or near
one of the moon's nodes,--that is, is projected to the place in the sky
where the moon crosses the ecliptic,--the earth's shadow, which is of
course directly opposite to the sun, must be at or near the other node,
and may not have passed too far from the node before the moon comes
round to the opposition and overtakes it. In total eclipses of the sun,
there has sometimes been observed a remarkable radiation of light from
the margin of the sun, which is thought to be owing to the zodiacal
light, which is of such dimensions as to extend far beyond the solar
orb. A striking appearance of this kind was exhibited in the total
eclipse of the sun which occurred in June, 1806.
A total eclipse of the sun is one of the most sublime and impressive
phenomena of Nature. Among barbarous tribes it is ever contemplated with
fear and astonishment, and as strongly indicative of the displeasure of
the gods. Two ancient nations, the Lydians and Medes, alluded to before,
who were engaged in a bloody war, about six hundred years before Christ,
were smitten with such awe, on the appearance of a total eclipse of the
sun, just on the eve of a battle, that they threw down their arms, and
made peace. When Columbus first discovered America, and was in danger of
hostility from the Natives, he awed them into submission by telling them
that the sun would be darkened on a certain day, in token of the anger
of the gods at them, for their treatment of him.
Among cultivated nations, a total eclipse of the sun is recognised, from
the exactness with which the time of occurrence and the various
appearances answer to the prediction, as affording one of the proudest
triumphs of astronomy. By astronomers themselves, it is of course viewed
with the highest interest, not only as verifying their calculations, but
as contributing to establish, beyond all doubt, the certainty of those
grand laws, the truth of which is involved in the result. I had the good
fortune to witness the total eclipse of the sun of June, 1806, which was
one of the most remarkable on record. To the wondering gaze of childhood
it presented a spectacle that can never be forgotten. A bright and
beautiful morning inspired universal joy, for the sky was entirely
cloudless. Every one was busily occupied in preparing smoked glass, in
readiness for the great sight, which was to be first seen about ten
o'clock. A thrill of mingled wonder and delight struck every mind when,
at the appointed moment, a little black indentation appeared on the limb
of the sun. This gradually expanded, covering more and more of the solar
disk, until an increasing gloom was spread over the face of Nature; and
when the sun was wholly lost, near mid-day, a feeling of horror pervaded
almost every beholder. The darkness was wholly unlike that of twilight
or night. A thick curtain, very different from clouds, hung upon the
face of the sky, producing a strange and indescribably gloomy
appearance, which was reflected from all things on the earth, in hues
equally strange and unnatural. Some of the planets, and the largest of
the fixed stars, shone out through the gloom, yet with their usual
brightness. The temperature of the air rapidly declined, and so sudden a
chill came over the earth, that many persons caught severe colds from
their exposure. Even the animal tribes exhibited tokens of fear and
agitation. Birds, especially, fluttered and flew swiftly about, and
domestic fowls went to rest.
Indeed, the word _eclipse_ is derived from a Greek word, (= ekleipsis=,
_ekleipsis_,) which signifies to fail, to faint or swoon away; since the
moon, at the period of her greatest brightness, falling into the shadow
of the earth, was imagined by the ancients to sicken and swoon, as if
she were going to die. By some very ancient nations she was supposed, at
such times, to be in pain; and, in order to relieve her fancied
distress, they lifted torches high in the atmosphere, blew horns and
trumpets, beat upon brazen vessels, and even, after the eclipse was
over, they offered sacrifices to the moon. The opinion also extensively
prevailed, that it was in the power of witches, by their spells and
charms, not only to darken the moon, but to bring her down from her
orbit, and to compel her to shed her baleful influences upon the earth.
In solar eclipses, also, especially when total, the sun was supposed to
turn away his face in abhorrence of some atrocious crime, that either
had been perpetrated or was about to be perpetrated, and to threaten
mankind with everlasting night, and the destruction of the world. To
such superstitions Milton alludes, in the passage which I have taken for
the motto of this Letter.
The Chinese, who, from a very high period of antiquity, have been great
observers of eclipses, although they did not take much notice of those
of the moon, regarded eclipses of the sun in general as unfortunate, but
especially such as occurred on the first day of the year. These were
thought to forebode the greatest calamities to the emperor, who on such
occasions did not receive the usual compliments of the season. When,
from the predictions of their astronomers, an eclipse of the sun was
expected, they made great preparation at court for observing it; and as
soon as it commenced, a blind man beat a drum, a great concourse
assembled, and the mandarins, or nobility, appeared in state.
LETTER XIX.
LONGITUDE.--TIDES.
"First in his east, the glorious lamp was seen,
Regent of day, and all the horizon round
Invested with bright rays, jocund to run
His _longitude_ through heaven's high road; the gray
Dawn and the Pleiades before him danced,
Shedding sweet influence."--_Milton._
THE ancients studied astronomy chiefly as subsidiary to astrology, with
the vain hope of thus penetrating the veil of futurity, and reading
their destinies among the stars. The moderns, on the other hand, have in
view, as the great practical object of this study, the perfecting of the
art of navigation. When we reflect on the vast interests embarked on the
ocean, both of property and life, and upon the immense benefits that
accrue to society from a safe and speedy intercourse between the
different nations of the earth, we cannot but see that whatever tends to
enable the mariner to find his way on the pathless ocean, and to secure
him against its multiplied dangers, must confer a signal benefit on
society.
In ancient times, to venture out of sight of land was deemed an act of
extreme audacity; and Horace, the Roman poet, pronounces him who first
ventured to trust his frail bark to the stormy ocean, endued with a
heart of oak, and girt with triple folds of brass. But now, the
navigator who fully avails himself of all the resources of science, and
especially of astronomy, may launch fearlessly on the deep, and almost
bid defiance to rocks and tempests. By enabling the navigator to find
his place on the ocean with almost absolute precision, however he may
have been driven about by the winds, and however long he may have been
out of sight of land, astronomers must be held as great benefactors to
all who commit either their lives or their fortunes to the sea. Nor
have they secured to the art of navigation such benefits without
incredible study and toil, in watching the motions of the heavenly
bodies, in investigating the laws by which their movements are governed,
and in reducing all their discoveries to a form easily available to the
navigator, so that, by some simple observation on one or two of the
heavenly bodies, with instruments which the astronomer has invented, and
prepared for his use, and by looking out a few numbers in tables which
have been compiled for him, with immense labor, he may ascertain the
exact place he occupies on the surface of the globe, thousands of miles
from land.
The situation of any place is known by its latitude and longitude. As
charts of every ocean and sea are furnished to the sailor, in which are
laid down the latitudes and longitudes of every point of land, whether
on the shores of islands or the main, he has, therefore, only to
ascertain his latitude and longitude at any particular place on the
ocean, in order to find where he is, with respect to the nearest point
of land, although this may be, and may always have been, entirely out of
sight to him.
To determine the _latitude_ of a place is comparatively an easy matter,
whenever we can see either the sun or the stars. The distance of the sun
from the zenith, when on the meridian, on a given day of the year,
(which distance we may easily take with the sextant,) enables us, with
the aid of the tables, to find the latitude of the place; or, by taking
the altitude of the north star, we at once obtain the latitude.
The _longitude_ of a place may be found by any method, by which we may
ascertain how much its time of day differs from that of Greenwich at the
same moment. A place that lies eastward of another comes to the meridian
an hour earlier for every fifteen degrees of longitude, and of course
has the hour of the day so much in advance of the other, so that it
counts one o'clock when the other place counts twelve. On the other
hand, a place lying westward of another comes to the meridian later by
one hour for every fifteen degrees, so that it counts only eleven
o'clock when the other place counts twelve. Keeping these principles in
view, it is easy to see that a comparison of the difference of time
between two places at the same moment, allowing fifteen degrees for an
hour, sixty minutes for every four minutes of time, and sixty seconds
for every four seconds of time, affords us an accurate mode of finding
the difference of longitude between the two places. This comparison may
be made by means of a chronometer, or from solar or lunar eclipses, or
by what is called the lunar method of finding the longitude.
_Chronometers_ are distinguished from clocks, by being regulated by
means of a balance-wheel instead of a pendulum. A watch, therefore,
comes under the general definition of a chronometer; but the name is
more commonly applied to larger timepieces, too large to be carried
about the person, and constructed with the greatest possible accuracy,
with special reference to finding the longitude. Suppose, then, we are
furnished with a chronometer set to Greenwich time. We arrive at New
York, for example, and compare it with the time there. We find it is
five hours in advance of the New-York time, indicating five o'clock,
P.M., when it is noon at New York. Hence we find that the longitude of
New York is 5×15=75 degrees.[11] The time at New York, or any individual
place, can be known by observations with the transit-instrument, which
gives us the precise moment when the sun is on the meridian.
It would not be necessary to resort to Greenwich, for the purpose of
setting our chronometer to Greenwich time, as it might be set at any
place whose longitude is known, having been previously determined. Thus,
if we know that the longitude of a certain place is exactly sixty
degrees east of Greenwich, we have only to set our chronometer four
hours behind the time at that place, and it will be regulated to
Greenwich time. Hence it is a matter of the greatest importance to
navigation, that the longitude of numerous ports, in different parts of
the earth, should be accurately determined, so that when a ship arrives
at any such port, it may have the means of setting or verifying its
chronometer.