which always points to the earth, nature has furnished a permanent
meridian, to which the different spots on her surface have been
referred, and their positions determined with as much accuracy as those
of many of the most remarkable places on the surface of our globe.
The rotation of the earth which determines the length of the day may be
regarded as one of the most important elements in the system of the
world. It serves as a measure of time, and forms the standard of
comparison for the revolutions of the celestial bodies, which by their
proportional increase or decrease would soon disclose any changes it
might sustain. Theory and observation concur in proving, that among the
innumerable vicissitudes that prevail throughout creation, the period of
the earth's diurnal rotation is immutable. A fluid, as Mr. Babbage
observes, in falling from a higher to a lower level, carries with it the
velocity due to its revolution with the earth at a greater distance from
its centre. It will therefore accelerate, although to an almost
infinitesimal extent, the earth's daily rotation. The sum of all these
increments of velocity, arising from the descent of all the rivers on
the earth's surface, would in time become perceptible, did not nature,
by the process of evaporation, raise the waters back to their sources;
and thus again by removing matter to a greater distance from the centre,
destroy the velocity generated by its previous approach; so that the
descent of the rivers does not affect the earth's rotation. Enormous
masses projected by volcanoes from the equator to the poles, and the
contrary, would indeed affect it, but there is no evidence of such
convulsions. The disturbing action of the moon and planets, which has so
powerful an effect on the revolution of the earth, in no way influences
its rotation: the constant friction of the trade winds on the mountains
and continents between the tropics does not impede its velocity, which
theory even proves to be the same, as if the sea together with the earth
formed one solid mass. But although these circumstances be inefficient,
a variation in the mean temperature would certainly occasion a
corresponding change in the velocity of rotation: for in the science of
dynamics, it is a principle in a system of bodies, or of particles
revolving about a fixed centre, that the momentum, or sum of the
products of the mass of each into its angular velocity and distance from
the centre is a constant quantity, if the system be not deranged by an
external cause. Now since the number of particles in the system is the
same whatever its temperature may be, when their distances from the
centre are diminished, their angular velocity must be increased in order
that the preceding quantity may still remain constant. It follows then,
that as the primitive momentum of rotation with which the earth was
projected into space must necessarily remain the same, the smallest
decrease in heat, by contracting the terrestrial spheroid, would
accelerate its rotation, and consequently diminish the length of the
day. Notwithstanding the constant accession of heat from the sun's rays,
geologists have been induced to believe from the nature of fossil
remains, that the mean temperature of the globe is decreasing.
The high temperature of mines, hot springs, and above all, the internal
fires that have produced, and do still occasion such devastation on our
planet, indicate an augmentation of heat towards its centre the increase
of density in the strata corresponding to the depth and the form of the
spheroid, being what theory assigns to a fluid mass in rotation, concur
to induce the idea that the temperature of the earth was originally so
high as to reduce all the substances of which it is composed to a state
of fusion, and that in the course of ages it has cooled down to its
present state; that it is still becoming colder, and that it will
continue to do so, till the whole mass arrives at the temperature of the
medium in which it is placed, or rather at a state of equilibrium
between this temperature, the cooling power of its own radiation, and
the heating effect of the sun's rays. But even if this cause be
sufficient to produce the observed effects, it must be extremely slow in
its operation; for in consequence of the rotation of the earth being a
measure of the periods of the celestial motions, it has been proved,
that if the length of the day had decreased by the three hundredth part
of a second since the observations of Hipparchus two thousand years ago,
it would have diminished the secular equation of the moon by 4"·4. It
is therefore beyond a doubt, that the mean temperature of the earth
cannot have sensibly varied during that time; if then the appearances
exhibited by the strata really owing to a decrease of internal
temperature, it either shows the immense periods requisite to produce
geological changes to which two thousand years are as nothing, or that
the mean temperature of the earth had arrived at a state of equilibrium
before these observations. However strong the indication of the
primitive fluidity of the earth, as there is no direct proof, it can
only be regarded as a very probable hypothesis; but one of the most
profound philosophers and elegant writers of modern times has found, in
the secular variation of the eccentricity of the terrestrial orbit, an
evident cause of decreasing temperature. That accomplished author, in
pointing out the mutual dependences of phenomena, says--'It is evident
that the mean temperature of the whole surface of the globe, in so far
as it is maintained by the action of the sun at 8 higher degree than it
would have were the sun extinguished, must depend on the mean quantity
of the sun's rays which it receives, or, which comes to the same thing,
on the total quantity received in a given invariable time: and the
length of the year being unchangeable in all the fluctuations of the
planetary system, it follows, that the total amount of solar radiation
will determine, _cœteris paribus_, the general climate of the earth. Now
it is not difficult to show, that this amount is inversely proportional
to the minor axis of the ellipse described by the earth about the sun,
regarded as slowly variable; and that, therefore, the major axis
remaining, as we know it to be, constant, and the orbit being actually
in a state of approach to a circle, and consequently the minor axis
being on the increase, the mean annual amount of solar radiation
received by the whole earth must be actually on the decrease. We have,
therefore, an evident real cause to account for the phenomenon.' The
limits of the variation in the eccentricity of the earth's orbit are
unknown; but if its ellipticity has ever been as great as that of the
orbit of Mercury or Pallas, the mean temperature of the earth must have
been sensibly higher than it is at present; whether it was great enough
to render our northern climates fit for the production of tropical
plants, and for the residence of the elephant, and the other inhabitants
of the torrid zone, it is impossible to say.
The relative quantity of heat received by the earth at different moments
during a single revolution, varies with the position of the perigee of
its orbit, which accomplishes a tropical revolution in 20935 years. In
the year 1250 of our era, and 29653 years before it, the perigee
coincided with the summer solstice; at both these periods the earth was
nearer the sun during the summer, and farther from him in the winter
than in any other position of the apsides: the extremes of temperature
must therefore have been greater than at present; but as the terrestrial
orbit was probably more elliptical at the distant epoch, the heat of the
summers must have been very great though possibly compensated by the
rigour of the winters; at all events, none of these changes affect the
length of the day.
It appears from the marine shells found on the tops of the highest
mountains, and in almost every part of the globe, that immense
continents have been elevated above the ocean, which must have which
must have engulphed others. Such a catastrophe would be occasioned by a
variation in the position of the axis of rotation on the surface of the
earth; for the seas ending to the new equator would leave some portions
of the globe, and overwhelm others.
But theory proves that neither nutation, precession, nor any of the
disturbing forces that affect the system, have the smallest influence on
the axis of rotation, which maintains a permanent position on the
surface, if the earth be not disturbed in its rotation by some foreign
cause, as the collision of a comet which may have happened in the
immensity of time. Then indeed, the equilibrium could only have been
restored by the rushing of the seas to the new equator, which they would
continue to do, till the surface was every where perpendicular to the
direction of gravity. But it is probable that such an accumulation of
the waters would not be sufficient to restore equilibrium if the
derangement had been great; for the mean density of the sea is only
about a fifth part of the mean density of the earth, and the mean depth
even of the Pacific ocean is not more than four miles, whereas the
equatorial radius of the earth exceeds the polar radius by twenty-five
or thirty miles; consequently the influence of the sea on the direction
of gravity is very small; and as it appears that a great change in the
position of the axes is incompatible with the law of equilibrium, the
geological phenomena must be ascribed to an internal cause. Thus amidst
the mighty revolutions which have swept innumerable races of organized
beings from the earth, which have elevated plains, and buried mountains
in the ocean, the rotation of the earth, and the position of the axis on
its surface, have undergone but slight variations.
It is beyond a doubt that the strata increase in density from the
surface of the earth to its centre, which is even proved by the lunar
inequalities; and it is manifest from the mensuration of arcs of the
meridian and the lengths of the seconds pendulum that the strata are
elliptical and concentric. This certainly would have happened if the
earth had originally been fluid, for the denser parts must have subsided
towards the centre, as it approached a state of equilibrium; but the
enormous pressure of the superincumbent mass is a sufficient cause for
these phenomena. Professor Leslie observes, that air compressed into the
fiftieth part of its volume has its elasticity fifty times augmented; if
it continue to contract at that rate, it would, from its own incumbent
weight, acquire the density of water at the depth of thirty-four miles.
But water itself would have its density doubled at the depth of
ninety-three miles, and would even attain the density of quicksilver at
a depth of 362 miles. In descending therefore towards the centre through
4000 miles, the condensation of ordinary materials would surpass the
utmost powers of conception. But a density so extreme is not borne out
by astronomical observation. It might seem therefore to follow, that our
planet must have a widely cavernous structure, and that we tread on a
crust or shell, whose thickness bears a very small proportion to the
diameter of its sphere. Possibly too this great condensation at the
central regions may be counterbalanced by the increased elasticity due
to a very elevated temperature. Dr. Young says that steel would be
compressed into one-fourth, and stone into one-eighth of its bulk at the
earth's centre. However we are yet ignorant of the laws of compression
of solid bodies beyond a certain limit; but, from the experiments of Mr.
Perkins, they appear to be capable of a greater degree of compression
than has generally been imagined.
It appears then, that the axis of rotation is invariable on the surface
of the earth, and observation shows, that were it not for the action of
the sun and moon on the matter at the equator, it would remain parallel
to itself in every point of its orbit.
The attraction of an exterior body not only draws a spheroid towards it;
but, as the force varies inversely as the square of the distance, it
gives it a motion about its centre of gravity, unless when the
attracting body is situated in the prolongation of one of the axes of
the spheroid.
The plane of the equator is inclined to the plane of the ecliptic at an
angle of about 23° 28', and the inclination of the lunar orbit on the
same is nearly 5°; consequently, from the oblate figure of the earth,
the sun and moon acting obliquely and unequally on the different parts
of the terrestrial spheroid, urge the plane of the equator from its
direction, and force it to move from east to west, so that the
equinoctial points have a slow retrograde motion on the plane of the
ecliptic of about 50"·412 annually. The direct tendency of this action
would be to make the planes of the equator and ecliptic coincide; but in
consequence of the rotation of the earth, the inclination of the two
planes remains constant, as a top in spinning preserves the same
inclination to the plane of the horizon. Were the earth spherical this
effect would not be produced, and the equinoxes would always correspond
to the same points of the ecliptic, at least as far as this kind of
action is concerned. But another and totally different cause operates on
this motion, which has already been mentioned. The action of the planets
on one another and on the sun, occasions a very slow variation in the
position of the plane of the ecliptic, which affects its inclination on
the plane of the equator, and gives the equinoctial points a slow but
direct motion on the ecliptic of 0"·312 annually, which is entirely
independent of the figure of the earth, and would be the same if it were
a sphere. Thus the sun and moon, by moving the plane of the equator,
cause the equinoctial points to retrograde on the ecliptic; and the
planets, by moving the plane of the ecliptic, give them a direct motion,
but much less than the former; consequently the difference of the two is
the mean precession, which is proved, both by theory and observation, to
be about 50"·1 annually. As the longitudes of all the fixed stars are
increased by this quantity, the effects of precession are soon detected;
it was accordingly discovered by Hipparchus, in the year 128 before
Christ, from a comparison of his own observations with those of
Timocharis, 155 years before. In the time of Hipparchus the entrance of
the sun into the constellation Aries was the beginning of spring, but
since then the equinoctial points have receded 30°; so that the
constellations called the signs of the zodiac are now at a considerable
distance from those divisions of the ecliptic which bear their names.
Moving at the rate of 50"·1 annually, the equinoctial points will
accomplish a revolution in 25868 years; but as the precession varies in
different centuries, the extent of this period will be slightly
modified. Since the motion of the sun is direct, and that of the
equinoctial points retrograde, he takes a shorter time to return to the
equator than to arrive at the same stars; so that the tropical year of
365.242264 days must be increased by the time he takes to move through
an arc of 50"·1, in order to have the length of the sidereal year. By
simple proportion it is the 0.014119th part of a day, so that the
sidereal year is 365.256383.
The mean annual precession is subject to a secular variation; for
although the change in the plane of the ecliptic which is the orbit of
the sun, be independent of the form of the earth, yet by bringing the
sun, moon and earth into different relative positions from age to age,
it alters the direct action of the two first on the prominent matter at
the equator; on this account the motion of the equinox is greater by
0"·455 now than it was in the lime of Hipparchus; consequently the
actual length of the tropical year is about 4"·154 shorter than it was
at that time. The utmost change that it can experience from this cause
amounts to 43".
Such is the secular motion of the equinoxes, but it is sometimes
increased and sometimes diminished by periodic variations, whose periods
depend on the relative positions of the sun and moon with regard to the
earth, and occasioned by the direct action of these bodies on the
equator. Dr. Bradley discovered that by this action the moon causes the
pole of the equator to describe a small ellipse in the heavens, the
diameters of which are 16" and 20". The period of this inequality is
nineteen years, the time employed by the nodes of the lunar orbit to
accomplish a revolution. The sun causes a small variation in the
description of this ellipse; it runs through its period in half a year.
This nutation in the earth's axis affects both the precession and
obliquity with small periodic variations; but in consequence of the
secular variation in the position of the terrestrial orbit, which is
chiefly owing to the disturbing energy of Jupiter on the earth, the
oblique of the ecliptic is annually diminished by 0"·52109. With
regard to the fixed stars, this variation in the course of ages may
amount to tea or eleven degrees; but the obliquity of the ecliptic to
the equator can never vary more than two or three degrees, since the
equator will follow in some measure the motion of the ecliptic.
It is evident that the places of all the celestial bodies are affected
by precession and nutation, and therefore all observations of them must
be corrected for these inequalities.
The densities of bodies are proportional to their masses divided by
their volumes; hence if the sun and planets be assumed to be spheres,
their volumes will be as the cubes of their diameters. Now the apparent
diameters of the sun and earth at their mean distance, are 1922" and
17"·08, and the mass of the earth is the 1/354936th part of that of the
sun taken as the unit; it follows therefore, that the earth is nearly
four times as dense as the sun; but the sun is so large that his
attractive force would cause bodies to fall through about 450 feet
in a second; consequently if he were even habitable by human beings,
they would be unable to move, since their weight would be thirty
times as great as it is here. A moderate sized man would weigh about
two tons at the surface of the sun. On the contrary, at the surface
of the four new planets we should be so light, that it would be
impossible to stand from the excess of our muscular force, for a man
would only weigh a few pounds. All the planets and satellites appear
to be of less density than the earth. The motions of Jupiter's
satellites show that his density increases towards his centre; and
the singular irregularities in the form of Saturn, and the great
compression of Mars, prove the internal structure of these two planets
to be very far from uniform.
Astronomy has been of immediate and essential use in affording
invariable standards for measuring duration, distance, magnitude, and
velocity. The sidereal day, measured by the time elapsed between two
consecutive transits of any star at the same meridian, and the sidereal
year, are immutable units with which to compare all great periods of
time; the oscillations of the isochronous pendulum measure its smaller
portions. By these invariable standards alone we can judge of the slow
changes that other elements of the system may have undergone in the
lapse of ages.
The returns of the sun to the same meridian, and to the same equinox or
solstice, have been universally adopted as the measure of our civil days
and years. The solar or astronomical day is the time that elapses
between two consecutive noons or midnights; it is consequently longer
than the sidereal day, on account of the proper motion of the sun during
a revolution of the celestial sphere; but as the sun moves with greater
rapidity at the winter than at the summer solstice, the astronomical day
is more nearly equal to the sidereal day in summer than in winter. The
obliquity of the ecliptic also affects its duration, for in the
equinoxes the arc of the equator is less than the corresponding arc of
the ecliptic, and in the solstices it is greater. The astronomical day
is therefore diminished in the first case, and increased in the second.
If the sun moved uniformly in the equator at the rate of 59' 8"·3
every day, the solar days would be all equal; the time therefore, which
is reckoned by the arrival of an imaginary sun at the meridian, or of
one which is supposed to move in the equator, is denominated mean solar
time, such as is given by clocks and watches in common life: when it is
reckoned by the arrival of the real sun at the meridian, it is apparent
time, such as is given by dials. The difference between the time shown
by a clock and a dial is the equation of time given in the Nautical
Almanac, and sometimes amounts to as much as sixteen minutes. The
apparent and mean time coincide four times in the year.
Astronomers begin the day at noon, but in common reckoning the day
begins at midnight. In England it is divided into twenty-four hours,
which are counted by twelve and twelve; but in France, astronomers
adopting decimal division, divide the day into ten hours, the hour into
one hundred minutes, and the minute into a hundred seconds, because of
the facility in computation, and in conformity with their system of
weights and measures. This subdivision is not used in common life, nor
has it been adopted in any other country, though their scientific
writers still employ that division of time. The mean length of the day,
though accurately determined, is not sufficient for the purposes either
of astronomy or civil life. The length of the year is pointed out by
nature as a measure of long periods; but the incommensurability that
exists between the lengths of the day, and the revolutions of the sun,
renders it difficult to adjust the estimation of both in whole numbers.
If the revolution of the sun were accomplished in 365 days, all the
years would be of precisely the same number of days, and would begin and
end with the sun at the same point of the ecliptic; but as the sun's
revolution includes the fraction of a day, a civil year and a revolution
of the sun have not the same duration. Since the fraction is nearly the
fourth of a day, four years are nearly equal to four revolutions of the
sun, so that the addition of a supernumerary day every fourth year
nearly compensates the difference; but in process of time further
correction will be necessary, because the fraction is less than the
fourth of a day. The period of seven days, by far the most permanent
division of time, and the most ancient monument of astronomical
knowledge, was used by the Brahmins in India with the same denominations
employed by us, and was alike found in the Calendars of the Jews,
Egyptians, Arabs, and Assyrians; it has survived the fall of empires,
and has existed among all successive generations, a proof of their
common origin.
The new moon immediately following the winter solstice in the 707th year
of Rome was made the 1st of January of the first year of Cæsar; the
25th of December in his 45th year, is considered as the date of Christ's
nativity; and Cæsar's 46th year is assumed to be the first of our era.
The preceding year is called the first year before Christ by
chronologists, but by astronomers it is called the year 0. The
astronomical year begins on the 31st of December at noon; and the date
of an observation expresses the days and hours which actually elapsed
since that time.