sun, a spectator on either would project the other body upon the concave
sphere of the heavens, always seeing it on the opposite side of a great
circle one hundred and eighty degrees from himself.
Recollect that the path in which the earth moves round the sun is
called the ecliptic. We are not to conceive of this, or of any other
celestial circle, as having any real, palpable existence, any more than
the path of a bird through the sky. You will perhaps think it quite
superfluous for me to remind you of this; but, from the habit of seeing
the orbits of the heavenly bodies represented in diagrams and orreries,
by palpable lines and circles, we are apt inadvertently to acquire the
notion, that the orbits of the planets, and other representations of the
artificial sphere, have a real, palpable existence in Nature; whereas,
they denote the places where mere geometrical or imaginary lines run.
You might have expected to see an orrery, exhibiting a view of the sun
and planets, with their various motions, particularly described in my
Letter on astronomical instruments and apparatus. I must acknowledge,
that I entertain a very low opinion of the utility of even the best
orreries, and I cannot recommend them as auxiliaries in the study of
astronomy. The numerous appendages usually connected with them, some to
support them in a proper position, and some to communicate to them the
requisite motions, enter into the ideas which the learner forms
respecting the machinery of the heavens; and it costs much labor
afterwards to divest the mind of such erroneous impressions. Astronomy
can be exhibited much more clearly and beautifully to the mental eye
than to the visual organ. It is much easier to conceive of the sun
existing in boundless space, and of the earth as moving around him at a
great distance, the mind having nothing in view but simply these two
bodies, than it is, in an orrery, to contemplate the motion of a ball
representing the earth, carried by a complicated apparatus of wheels
around another ball, supported by a cylinder or wire, to represent the
sun. I would advise you, whenever it is practicable, to think how things
are in Nature, rather than how they are represented by art. The
machinery of the heavens is much simpler than that of an orrery.
In endeavoring to obtain a clear idea of the revolution of the earth
around the sun, imagine to yourself a plane (a geometrical plane, having
merely length and breadth, but no thickness) passing through the centres
of the sun and the earth, and extended far beyond the earth till it
reaches the firmament of stars. Although, indeed, no such dome actually
exists as that under which we figure to ourselves the vault of the sky,
yet, as the fixed stars appear to be set in such a dome, we may imagine
that the circles of the sphere, when indefinitely enlarged, finally
reach such an imaginary vault. All that is essential is, that we should
imagine this to exist far beyond the bounds of the solar system, the
various bodies that compose the latter being situated close around the
sun, at the centre.
Along the line where this great circle meets the starry vault, are
situated a series of constellations,--Aries, Taurus, Gemini, &c.,--which
occupy successively this portion of the heavens. When bodies are at such
a distance from each other as the sun and the earth, I have said that a
spectator on either would project the other body upon the concave sphere
of the heavens, always seeing it on the opposite side of a great circle
one hundred and eighty degrees from himself. The place of a body, when
viewed from any point, is denoted by the position it occupies among the
stars. Thus, in the diagram, Fig. 25, page 114, when the earth arrives
at E, it is said to be in Aries, because, if viewed from the sun, it
would be projected on that part of the heavens; and, for the same
reason, to a spectator at E, the sun would be in Libra. When the earth
shifts its position from Aries to Taurus, as we are unconscious of our
own motion, the sun it is that appears to move from Libra to Scorpio, in
the opposite part of the heavens. Hence, as we go forward, in the order
of the signs, on one side of the ecliptic, the sun seems to be moving
forward at the same rate on the opposite side of the same great circle;
and therefore, although we are unconscious of our own motion, we can
read it, from day to day, in the motions of the sun. If we could see
the stars at the same time with the sun, we could actually observe, from
day to day, the sun's progress through them, as we observe the progress
of the moon at night; only the sun's rate of motion would be nearly
fourteen times slower than that of the moon. Although we do not see the
stars when the sun is present, we can observe that it makes daily
progress eastward, as is apparent from the constellations of the zodiac
occupying, successively, the western sky immediately after sunset,
proving that either all the stars have a common motion westward,
independent of their diurnal motion, or that the sun has a motion past
them from west to east. We shall see, hereafter, abundant evidence to
prove, that this change in the relative position of the sun and stars,
is owing to a change in the apparent place of the sun, and not to any
change in the stars.
[Illustration Fig. 25.]
To form a clear idea of the two motions of the earth, imagine yourself
standing on a circular platform which turns slowly round its centre.
While you are carried slowly round the entire of the circuit of the
heavens, along with the platform, you may turn round upon your heel the
same way three hundred and sixty-five times. The former is analogous to
our annual motion with the earth around the sun; the latter, to our
diurnal revolution in common with the earth around its own axis.
Although the apparent revolution of the sun is in a direction opposite
to the real motion of the earth, as regards absolute space, yet both are
nevertheless from west to east, since these terms do not refer to any
directions in absolute space, but to the order in which certain
constellations (the constellations of the Zodiac) succeed one another.
The earth itself, on opposite sides of its orbit, does in fact move
towards directly opposite points of space; but it is all the while
pursuing its course in the order of the signs. In the same manner,
although the earth turns on its axis from west to east, yet any place on
the surface of the earth is moving in a direction in space exactly
opposite to its direction twelve hours before. If the sun left a visible
trace on the face of the sky, the ecliptic would of course be distinctly
marked on the celestial sphere, as it is on an artificial globe; and
were the equator delineated in a similar manner, we should then see, at
a glance, the relative position of these two circles,--the points where
they intersect one another, constituting the equinoxes; the points where
they are at the greatest distance asunder, that is, the solstices; and
various other particulars, which, for want of such visible traces, we
are now obliged to search for by indirect and circuitous methods. It
will aid you, to have constantly before your mental vision an imaginary
delineation of these two important circles on the face of the sky.
The equator makes an angle with the ecliptic of twenty-three degrees and
twenty-eight minutes. This is called the obliquity of the ecliptic. As
the sun and earth are both always in the ecliptic, and as the motion of
the earth in one part of it makes the sun appear to move in the
opposite part, at the same rate, the sun apparently descends, in Winter,
twenty-three degrees and twenty-eight minutes to the south of the
equator, and ascends, in Summer, the same number of degrees north of it.
We must keep in mind, that the celestial equator and celestial ecliptic
are here understood, and we may imagine them to be two great circles
delineated on the face of the sky. On comparing observations made at
different periods, for more than two thousand years, it is found, that
the obliquity of the ecliptic is not constant, but that it undergoes a
slight diminution, from age to age, amounting to fifty-two seconds in a
century, or about half a second annually. We might apprehend that, by
successive approaches to each other, the equator and ecliptic would
finally coincide; but astronomers have discovered, by a most profound
investigation, based on the principles of universal gravitation, that
this irregularity is confined within certain narrow limits; and that the
obliquity, after diminishing for some thousands of years, will then
increase for a similar period, and will thus vibrate forever about a
mean value.
As the earth traverses every part of her orbit in the course of a year,
she will be once at each solstice, and once at each equinox. The best
way of obtaining a correct idea of her two motions is, to conceive of
her as standing still for a single day, at some point in her orbit,
until she has turned once on her axis, then moving about a degree, and
halting again, until another diurnal revolution is completed. Let us
suppose the earth at the Autumnal equinox, the sun, of course, being at
the Vernal equinox,--for we must always think of these two bodies as
diametrically opposite to each other. Suppose the earth to stand still
in its orbit for twenty-four hours. The revolution of the earth on its
axis, from west to east, will make the sun appear to describe a great
circle of the heavens from east to west, coinciding with the equator. At
the end of this period, suppose the sun to move northward one degree,
and to remain there for twenty-four hours; in which time, the
revolution of the earth, will make the sun appear to describe another
circle, from east to west, parallel to the equator, but one degree north
of it. Thus, we may conceive of the sun as moving one degree north,
every day, for about three months, when it will reach the point of the
ecliptic furthest from the equator, which point is called the _tropic_,
from a Greek word, signifying _to turn_; because, after the sun has
passed this point, his motion in his orbit carries him continually
towards the equator, and therefore he seems to turn about. The same
point is also called the _solstice_, from a Latin word, signifying to
_stand still_; since, when the sun has reached its greatest northern or
southern limit, while its declination is at the point where it ceases to
increase, but begins to decrease, there the sun seems for a short time
stationary, with regard to the equator, appearing for several days to
describe the same parallel of latitude.
When the sun is at the northern tropic, which happens about the
twenty-first of June, his elevation above the southern horizon at noon
is the greatest in the year; and when he is at the southern tropic,
about the twenty-first of December, his elevation at noon is the least
in the year. The difference between these two meridian altitudes will
give the whole distance from one tropic to the other, and consequently,
twice the distance from each tropic to the equator. By this means, we
find how far the tropic is from the equator, and that gives us the angle
which the equator and ecliptic make with each other; for the greatest
distance between any two great circles on the sphere is always equal to
the angle which they make with each other. Thus, the ancient astronomers
were able to determine the obliquity of the ecliptic with a great degree
of accuracy. It was easy to find the situation of the zenith, because
the direction of a plumb-line shows us where that is; and it was easy to
find the distances from the zenith where the sun was at the greatest and
least distances; respectively. The difference of these two arcs is the
angular distance from one tropic to the other; and half this arc is the
distance of either tropic from the equator, and of course, equal to the
obliquity of the ecliptic. All this will be very easily understood from
the annexed diagram, Fig. 26. Let Z be the zenith of a spectator
situated at C; Z _n_ the least, and Z _s_ the greatest distance of the
sun from the zenith. From Z _s_ subtract Z _n_, and then _s n_, the
difference, divided by two, will give the obliquity of the ecliptic.
[Illustration Fig. 26.]
The motion of the earth in its orbit is nearly seventy times as great as
its greatest motion around its axis. In its revolution around the sun,
the earth moves no less than one million six hundred and forty thousand
miles per day, sixty-eight thousand miles per hour, eleven hundred miles
per minute, and nearly nineteen miles every second; a velocity nearly
sixty times as great as the greatest velocity of a cannon ball. Places
on the earth turn with very different degrees of velocity in different
latitudes. Those near the equator are carried round on the circumference
of a large circle; those towards the poles, on the circumference of a
small circle; while one standing on the pole itself would not turn at
all. Those who live on the equator are carried about one thousand miles
an hour. In our latitude, (forty-one degrees and eighteen minutes,) the
diurnal velocity is about seven hundred and fifty miles per hour. It
would seem, at first view, quite incredible, that we should be whirled
round at so rapid a rate, and yet be entirely insensible of any motion;
and much more, that we could be going so swiftly through space, in our
circuit around the sun, while all things, when unaffected by local
causes, appear to be in such a state of quiescence. Yet we have the most
unquestionable evidence of the fact; nor is it difficult to account for
it, in consistency with the general state of repose among bodies on the
earth, when we reflect that their relative motions, with respect to each
other, are not in the least disturbed by any motions which they may have
in common. When we are on board a steam-boat, we move about in the same
manner when the boat is in rapid motion, as when it is lying still; and
such would be the case, if it moved steadily a hundred times faster than
it does. Were the earth, however, suddenly to stop its diurnal
revolution, all movable bodies on its surface would be thrown off in
tangents to the surface with velocities proportional to that of their
diurnal motion; and were the earth suddenly to halt in its orbit, we
should be hurled forward into space with inconceivable rapidity.
I will next endeavor to explain to you the phenomena of the _Seasons_.
These depend on two causes; first, the inclination of the earth's axis
to the plane of its orbit; and, secondly, to the circumstance, that the
axis always remains parallel to itself. Imagine to yourself a candle
placed in the centre of a ring, to represent the sun in the centre of
the earth's orbit, and an apple with a knittingneedle running through it
in the direction of the stem. Run a knife around the central part of the
apple, to mark the situation of the equator. The circumference of the
ring represents the earth's orbit in the plane of the ecliptic. Place
the apple so that the equator shall coincide with the wire; then the
axis will lie directly across the plane of the ecliptic; that is, at
right angles to it. Let the apple be carried quite round the ring,
constantly preserving the axis parallel to itself, and the equator all
the while coinciding with the wire that represents the orbit. Now, since
the sun enlightens half the globe at once, so the candle, which here
represents the sun, will shine on the half of the apple that is turned
towards it; and the circle which divides the enlightened from the
unenlightened side of the apple, called the _terminator_, will pass
through both the poles. If the apple be turned slowly round on its axis,
the terminator will successively pass over all places on the earth,
giving the appearance of sunrise to places at which it arrives, and of
sunset to places from which it departs. If, therefore, the equator had
coincided with the ecliptic, as would have been the case, had the
earth's axis been perpendicular to the plane of its orbit, the diurnal
motion of the sun would always have been in the equator, and the days
and nights would have been equal all over the globe. To the inhabitants
of the equatorial parts of the earth, the sun would always have appeared
to move in the prime vertical, rising directly in the east, passing
through the zenith at noon, and setting in the west. In the polar
regions, the sun would always have appeared to revolve in the horizon;
while, at any place between the equator and the pole, the course of the
sun would have been oblique to the horizon, but always oblique in the
same degree. There would have been nothing of those agreeable
vicissitudes of the seasons which we now enjoy; but some regions of the
earth would have been crowned with perpetual spring, others would have
been scorched with the unremitting fervor of a vertical sun, while
extensive regions towards either pole would have been consigned to
everlasting frost and sterility.
To understand, then, clearly, the causes of the change of seasons, use
the same apparatus as before; but, instead of placing the axis of the
earth at right angles to the plane of its orbit, turn it out of a
perpendicular position a little, (twenty-three degrees and twenty-eight
minutes,) then the equator will be turned just the same number of
degrees out of a coincidence with the ecliptic. Let the apple be carried
around the ring, always holding the axis inclined at the same angle to
the plane of the ring, and always parallel to itself. You will find that
there will be two points in the circuit where the plane of the equator,
that you had marked around the centre of the apple, will pass through
the centre of the sun; these will be the points where the celestial
equator and the ecliptic cut one another, or the equinoxes. When the
earth is at either of these points, the sun shines on both poles alike;
and, if we conceive of the earth, while in this situation, as turning
once round on its axis, the apparent diurnal motion of the sun will be
the same as it would be, were the earth's axis perpendicular to the
plane of the equator. For that day, the sun would revolve in the
equator, and the days and nights would be equal all over the globe. If
the apple were carried round in the manner supposed, then, at the
distance of ninety degrees from the equinoxes, the same pole would be
turned from the sun on one side, just as much as it was turned towards
him on the other. In the former case, the sun's light would fall short
of the pole twenty-three and one half degrees, and in the other case, it
would reach beyond it the same number of degrees. I would recommend to
you to obtain as clear an idea as you can of the cause of the change of
seasons, by thinking over the foregoing illustration. You may then clear
up any remaining difficulties, by studying the diagram, Fig. 27, on page
122.
[Illustration Fig. 27.]
Let A B C D represent the earth's place in different parts of its orbit,
having the sun in the centre. Let A, C, be the positions of the earth at
the equinoxes, and B, D, its positions at the tropics,--the axis _n s_
being always parallel to itself. It is difficult to represent things of
this kind correctly, all on the same plane; but you will readily see,
that the figure of the earth, here, answers to the apple in the former
illustration; that the hemisphere towards _n_ is above, and that towards
_s_ is below, the plane of the paper. When the earth is at A and C, the
Vernal and Autumnal equinoxes, the sun, you will perceive, shines on
both the poles _n_ and _s_; and, if you conceive of the globe, while in
this position, as turned round on its axis, as it is in the diurnal
revolution, you will readily understand, that the sun would describe the
celestial equator. This may not at first appear so obvious, by
inspecting the figure; but if you consider the point _n_ as raised above
the plane of the paper, and the point _s_ as depressed below it, you
will readily see how the plane of the equator would pass through the
centre of the sun. Again, at B, when the earth is at the southern
tropic, the sun shines twenty-three and a half degrees beyond the north
pole, _n_, and falls the same distance short of the south pole, _s_. The
case is exactly reversed when the earth is at the northern tropic, and
the sun at the southern. While the earth is at one of the tropics, at B,
for example, let us conceive of it as turning on its axis, and we shall
readily see, that all that part of the earth which lies within the north
polar circle will enjoy continual day, while that within the south polar
circle will have continual night; and that all other places will have
their days longer as they are nearer to the enlightened pole, and
shorter as they are nearer to the unenlightened pole. This figure
likewise shows the successive positions of the earth, at different
periods of the year, with respect to the signs, and what months
correspond to particular signs. Thus, the earth enters Libra, and the
sun Aries, on the twenty-first of March, and on the twenty-first of
June, the earth is just entering Capricorn, and the sun, Cancer. You
will call to mind what is meant by this phraseology,--that by saying the
earth enters Libra, we mean that a spectator placed on the sun would see
the earth in that part of the celestial ecliptic, which is occupied by
the sign Libra; and that a spectator on the earth sees the sun at the
same time projected on the opposite part of the heavens, occupied by the
sign Cancer.
Had the axis of the earth been perpendicular to the plane of the
ecliptic, then the sun would always have appeared to move in the
equator, the days would every where have been equal to the nights, and
there could have been no change of seasons. On the other hand, had the
inclination of the ecliptic to the equator been much greater than it is,
the vicissitudes of the seasons would have been proportionally greater,
than at present. Suppose, for instance, the equator had been at right
angles to the ecliptic, in which case, the poles of the earth would have
been situated in the ecliptic itself; then, in different parts of the
earth, the appearances would have been as follows: To a spectator on the
_equator_, (where all the circles of diurnal revolution are
perpendicular to the horizon,) the sun, as he left the vernal equinox,
would every day perform his diurnal revolution in a smaller and smaller
circle, until he reached the north pole, when he would halt for a
moment, and then wheel about and return to the equator, in a reverse
order. The progress of the sun through the southern signs, to the south
pole, would be similar to that already described. Such would be the
appearances to an inhabitant of the equatorial regions. To a spectator
living in an _oblique_ sphere, in our own latitude, for example, the
sun, while north of the equator, would advance continually northward,
making his diurnal circuit in parallels further and further distant from
the equator, until he reached the circle of perpetual apparition; after
which, he would climb, by a spiral course, to the north star, and then
as rapidly return to the equator. By a similar progress southward, the
sun would at length pass the circle of perpetual occultation, and for
some time (which would be longer or shorter, according to the latitude
of the place of observation) there would be continual night. To a
spectator on the _pole_ of the earth and under the pole of the heaven,
during the long day of six months, the sun would wind its way to a point
directly over head, pouring down upon the earth beneath not merely the
heat of the torrid zone, but the heat of a torrid noon, accumulating
without intermission.
The great vicissitudes of heat and cold, which would attend these
several movements of the sun, would be wholly incompatible with the
existence of either the animal or the vegetable kingdom, and all
terrestrial Nature would be doomed to perpetual sterility and
desolation. The happy provision which the Creator has made against such
extreme vicissitudes, by confining the changes of the seasons within
such narrow bounds, conspires with many other express arrangements in
the economy of Nature, to secure the safety and comfort of the human
race.