major axis of the solar ellipse. Moving at the rate of 61"·906
annually, it accomplishes a tropical revolution in 20935 years. It
coincided with the line of the equinoxes 4000 or 4089 years before the
Christian era, much about the time chronologists assign for the creation
of man. In 6485 the major axis will again coincide with the line of the
equinoxes, but then the solar perigee will coincide with the equinox of
spring; whereas at the creation of man it coincided with the autumnal
equinox. In the year 1250 the major axis was perpendicular to the line
of the equinoxes, and then the solar perigee coincided with the solstice
of winter, and the apogee with the solstice of summer. On that account
La Place proposed the year 1250 as a universal epoch, and that the
vernal equinox of that year should be the first day of the first year.
The variations in the positions of the solar ellipse occasion
corresponding changes in the length of the seasons. In its present
position spring is shorter than summer, and autumn longer than winter;
and while the solar perigee continues as it now is, between the solstice
of winter and the equinox of spring, the period including spring and
summer will be longer than that including autumn and winter: in this
century the difference is about seven days. These intervals will be
equal towards the year 6485, when the perigee comes to the equinox of
spring. Were the earth's orbit circular, the seasons would be equal;
their differences arise from the eccentricity of the earth's orbit,
small as it is; but the changes are so gradual as to be imperceptible in
the short space of human life.
No circumstance in the whole science of astronomy excites a deeper
interest than its application to chronology. 'Whole nations,' says La
Place, 'have been swept from the earth, with their language, arts and
sciences, leaving but confused masses of ruin to mark the place where
mighty cities stood; their history, with the exception of a few doubtful
traditions, has perished; but the perfection of their astronomical
observations marks their high antiquity, fixes the periods of their
existence, and proves that even at that early period they must have made
considerable progress in science.'
The ancient state of the heavens may now be computed with great
accuracy; and by comparing the results of computation with ancient
observations, the exact period at which they were made may be verified
if true, or if false, their error may be detected. If the date be
accurate, and the observation good, it will verify the accuracy of
modern tables, and show to how many centuries they may be extended,
without the fear of error. A few examples will show the importance of
this subject.
At the solstices the sun is at his greatest distance from the equator,
consequently his declination at these times is equal to the obliquity of
the ecliptic, which in former times was determined from the meridian
length of the shadow of the style of a dial on the day of the solstice.
The lengths of the meridian shadow at the summer and winter solstice are
recorded to have been observed at the city of Layang, in China, 1100
years before the Christian era. From these, the distances of the sun
from the zenith of the city of Layang are known. Half the sum of these
zenith distances determines the latitude, and half their difference
gives the obliquity of the ecliptic at the period of the observation;
and as the law of the variation in the obliquity is known, both the time
and place of the observations have been verified by computation from
modern tables. Thus the Chinese had made some advances in the science of
astronomy at that early period; the whole chronology of the Chinese is
founded on the observations of eclipses, which prove the existence of
that empire for more than 4700 years. The epoch of the lunar tables of
the Indians, supposed by Bailly to be 3000 before the Christian era, was
proved by La Place from the acceleration of the moon, not to be more
ancient than the time of Ptolemy. The great inequality of Jupiter and
Saturn whose cycle embraces 929 years, is peculiarly fitted for marking
the civilization of a people. The Indians had determined the mean
motions of these two planets in that part of their periods when the
apparent menu motion of Saturn was at the slowest, and that of Jupiter
the most rapid. The periods in which that happened were 3102 years
before the Christian era, and the year 1491 after it.
The returns of comets to their perihelia may possibly mark the present
state of astronomy to future ages.
The places of the fixed stars are affected by the precession of the
equinoxes; and as the law of that variation is known, their positions at
any time may be computed. Now Eudoxus, a contemporary of Plato, mentions
a star situate in the pole of the equator, and from computation it
appears that _χ_ Draconis was not very far from that place about 3000
years ago; but as Eudoxus lived only about 2150 years ago, he must have
described an anterior state of the heavens, supposed to be the same that
was determined by Chiron, about the time of the siege of Troy. Every
circumstance concurs in showing that astronomy was cultivated in the
highest ages of antiquity.
A knowledge of astronomy leads to the interpretation of hieroglyphical
characters, since astronomical signs are often found on the ancient
Egyptian monuments, which were probably employed by the priests to
record dates. On the ceiling of the portico of a temple among the ruins
of Tentyris, there is a long row of figures of men and animals,
following each other in the some direction among these are the twelve
signs of the zodiac, placed according to the motion of the sun: it is
probable that the first figure in the procession represents the
beginning of the year. Now the first is the Lion as if coming out of the
temple; and as it is well known that the agricultural year of the
Egyptians commenced at the solstice of summer, the epoch of the
inundations of the Nile, if the preceding hypothesis be true, the
solstice at the time the temple was built must have happened in the
constellation of the lion; but as the solstice now happens 21° 6' north
of the constellation of the Twins, it is easy to compute that the zodiac
of Tentyris must have been made 4000 years ago.
The author had occasion to witness an instance of this most interesting
application of astronomy, in ascertaining the dale of a papyrus sent
from Egypt by Mr. Salt, in the hieroglyphical researches of the late Dr.
Thomas Young, whose profound and varied acquirements do honour not only
to his country, but to the age in which he lived. The manuscript was
found in a mummy case; it proved to be a horoscope of the age of
Ptolemy, and its antiquity was determined from the configuration of the
heavens at the time of its construction.
The form of the earth furnishes a standard of weights and measures for
the ordinary purposes of life, as well as for the determination of the
masses and distances of the heavenly bodies. The length of the pendulum
vibrating seconds in the latitude of London forms the standard of the
British measure of extension. Its length oscillating in vacuo at the
temperature of 62° of Fahrenheit, and reduced to the level of the sea,
was determined by Captain Kater, in parts of the imperial standard yard,
to be 39.1387 inches. The weight of a cubic inch of water at the
temperature of 62° Fahrenheit, barometer 30, was also determined in
parts of the imperial troy pound, whence a standard both of weight and
capacity is deduced. The French have adopted the metre for their unit of
linear measure, which is the ten millionth part of that quadrant of the
meridian passing through Formentera and Greenwich, the middle of which
is nearly in the forty-fifth degree of latitude. Should the national
standards of the two countries be lost in the vicissitudes of human
affairs, both may be recovered, since they are derived from natural
standards presumed to be invariable. The length of the pendulum would be
found again with more facility than the metre; but as no measure is
mathematically exact, an error in the original standard may at length
become sensible in measuring a great extent, whereas the error that must
necessarily arise in measuring the quadrant of the meridian is rendered
totally insensible by subdivision in taking its ten millionth part. The
French have adopted the decimal division not only in time, but in their
degrees, weights, and measures, which affords very great facility in
computation. It has not been adopted by any other people; though nothing
is more desirable than that all nations should concur in using the same
division and standards, not only on account of the convenience, but as
affording a more definite idea of quantity. It is singular that the
decimal division of the day, of degrees, weights and measures, was
employed in China 4000 years ago; and that, at the time Ibn Yunus made
his observations at Cairo, about the year 1000, the Arabians were in the
habit of employing the vibrations of the pendulum in their astronomical
observations.
One of the most immediate and striking effects of a gravitating force
external to the earth is the alternate rise and fall of the surface of
the sea twice in the course of a lunar day, or 24^h 50^m 48^s of mean solar
time. As it depends on the action of the sun and moon, it is classed
among astronomical problems, of which it is by far the most difficult
and the least satisfactory. The form of the surface of the ocean in
equilibrio, when revolving with the earth round its axis, is an
ellipsoid flattened at the poles; but the action of the sun and moon,
especially of the moon, disturbs the equilibrium of the ocean.
If the moon attracted the centre of gravity of the earth and all its
particles with equal and parallel forces, the whole system of the earth
and the waters that cover it, would yield to these forces with a common
motion, and the equilibrium of the seas would remain undisturbed. The
difference of the forces, and the inequality of their directions, alone
trouble the equilibrium.
It is proved by daily experience, as well as by strict mechanical
reasoning, that if a number of waves or oscillations be excited in a
fluid by different forces, each pursues its course, and has its effect
independently of the rest. Now in the tides there are three distinct
kinds of oscillations, depending on different causes, producing their
effects independently of each other, which may therefore be estimated
separately.
The oscillations of the first kind which are very small, are independent
of the rotation of the earth; and as they depend on the motion of the
disturbing body in its orbit, they are of long periods. The second kind
of oscillations depends on the rotation of the earth, therefore their
period is nearly a day: and the oscillations of the third kind depend on
an angle equal to twice the angular rotation of the earth; and
consequently happen twice in twenty-four hours. The first afford no
particular interest, and are extremely small; but the difference of two
consecutive tides depends on the second. At the time of the solstices,
this difference which, according to Newton's theory, ought to be very
great, is hardly sensible on our shores. La Place has shown that this
discrepancy arises from the depth of the sea, and that if the depth were
uniform, there would be no difference in the consecutive tides, were it
not for local circumstances: it follows therefore, that as this
difference is extremely small, the sea, considered in a large extent,
must be nearly of uniform depth, that is to say, there is a certain mean
depth from which the deviation is not great. The mean depth of the
Pacific Ocean is supposed to be about four miles, that of the Atlantic
only three. From the formulæ which determine the difference of the
consecutive tides it is also proved that the precession of the
equinoxes, and the nutation in the earth's axis, are the same as if the
sea formed one solid mass with the earth.
The third kind of oscillations are the semidiurnal tides, so remarkable
on our coasts; they are occasioned by the combined action of the sun and
moon, but as the effect of each is independent of the other, they may be
considered separately.
The particles of water under the moon are more attracted than the centre
of gravity of the earth, in the inverse ratio of the square of the
distances; hence they have a tendency to leave the earth, but are
retained by their gravitation, which this tendency diminishes. On the
contrary, the moon attracts the centre of the earth more powerfully than
she attracts the particles of water in the hemisphere opposite to her;
so that the earth has a tendency to leave the waters but is retained by
gravitation, which this tendency again diminishes. Thus the waters
immediately under the moon are drawn from the earth at the same time
that the earth is drawn from those which are diametrically opposite to
her; in both instances producing an elevation of the ocean above the
surface of equilibrium of nearly the same height; for the diminution of
the gravitation of the particles in each position is almost the same, on
account of the distance of the moon being great in comparison of the
radius of the earth. Were the earth entirely covered by the sea, the
water thus attracted by the moon would assume the form of an oblong
spheroid, whose greater axis would point towards the moon, since the
columns of water under the moon and in the direction diametrically
opposite to her are rendered lighter, in consequence of the diminution
of their gravitation in order to preserve the equilibrium, the axes 90°
distant would be shortened. The elevation, on account of the smaller
space to which it is confined, is twice as great as the depression,
because the contents of the spheroid always remain the same. The effects
of the sun's attraction are in all respects similar to those of the
moon's, though really less in degree, on account of his distance; he
therefore only modifies the form of this spheroid a little. If the
waters were capable of instantly assuming the form of equilibrium, that
is, the form of the spheroid, its summit would always point to the moon,
notwithstanding the earth's rotation; but on account of their
resistance, the rapid motion produced in them by rotation prevents them
from assuming at every instant the form which the equilibrium of the
forces acting on them requires. Hence, on account of the inertia of the
waters, if the tides be considered relatively to the whole earth and
open sea, there is a meridian about 30° eastward of the moon, where it
is always high water both in the hemisphere where the moon is, and in
that which is opposite. On the west side of this circle the tide is
flowing, on the east it is ebbing, and on the meridian at 90° distant,
it is everywhere low water. It is evident that these tides must happen
twice in a day, since in that time the rotation of the earth brings the
same point twice under the meridian of the moon, once under the superior
and once under the inferior meridian.
In the semidiurnal tides there are two phenomena particularly to be
distinguished, one that happens twice in a month, and the other twice in
a year.
The first phenomenon is, that the tides are much increased in the
syzigies, or at the time of new and full moon. In both cases the sun and
moon are in the same meridian, for when the moon is new they are in
conjunction, and when she is full they are in opposition. In each of
these positions their action is combined to produce the highest or
spring tides under that meridian, and the lowest in those points that
are 90° distant. It is observed that the higher the sea rises in the
full tide, the lower it is in the ebb. The neap tides lake place when
the moon is in quadrature, they neither rise so high nor sink so low as
the spring tides. The spring tides are much increased when the moon is
in perigee. It is evident that the spring tides must happen twice a
month, since in that time the moon is once new and once full.
The second phenomenon in the tides is the augmentation which occurs at
the time of the equinoxes when the sun's declination is zero, which
happens twice every year. The greatest tides take place when a new or
full moon happens, near the equinoxes while the moon is in perigee. The
inclination of the moon's orbit on the ecliptic is 5° 9'; hence in
the equinoxes the action of the moon would be increased if her node were
to coincide with her perigee. The equinoctial gales often raise these
tides to a great height. Beside these remarkable variations, there are
others arising from the declination of the moon, which has a great
influence on the ebb and flow of the waters.
Both the height and time of high water are thus perpetually changing;
therefore, in solving the problem, it is required to determine the
heights to which they rise, the times at which they happen, and the
daily variations.
The periodic motions of the waters of the ocean on the hypothesis of an
ellipsoid of revolution entirely covered by the sea, are very far from
according with observation; this arises from the very great
irregularities in the surface of the earth, which is but partially
covered by the sea, the variety in the depths of the ocean, the manner
in which it is spread out on the earth, the position and inclination of
the shores, the currents, the resistance the waters meet with, all of
them causes which it is impossible to estimate, but which modify the
oscillations of the great mass of the ocean. However, amidst all these
irregularities, the ebb and flow of the sea maintain a ratio to the
forces producing them sufficient to indicate their nature, and to verify
the law of the attraction of the sun and moon on the sea. La Place
observes, that the investigation of such relations between cause and
effect is no less useful in natural philosophy than the direct solution
of problems, either to prove the existence of the causes, or trace the
laws of their effects. Like the theory of probabilities, it is a happy
supplement to the ignorance and weakness of the human mind. Thus the
problem of the tides does not admit of a general solution; it is
certainly necessary to analyse the funeral phenomena which ought to
result from the attraction of the sun and moon, but these must be
corrected in each particular case by those local observations which are
modified by the extent and depth of the sea, and the peculiar
circumstances of the port.
Since the disturbing action of the sun and moon can only become sensible
in a very great extent of water, it is evident that the Pacific ocean is
one of the principal sources of our tides; but in consequence of the
rotation of the earth, and the inertia of the ocean, high water does not
happen till some time after the moon's southing. The tide raised in that
world of waters is transmitted to the Atlantic, and from that sea it
moves in a northerly direction along the coasts of Africa and Europe,
arriving later and later at each place. This great wave however is
modified by the tide raised in the Atlantic, which sometimes combines
with that from the Pacific in raising the sea, and sometimes is in
opposition to it, so that the tides only rise in proportion to their
difference. This great combined wave, reflected by the shores of the
Atlantic, extending nearly from pole to pole, still coming northward,
occurs through the Irish and British channels into the North sea, so
that the tides in our ports are modified by those of another hemisphere.
Thus the theory of the tides in each port, both as to their height and
the times at which they take place, is really a matter of experiment,
and can only be perfectly determined by the mean of a very great number
of observations including several revolutions of the moon's nodes.
The height to which the tides rise is much greater in narrow channels
than in the open sea, on account of the obstructions they meet with. In
high latitudes where the ocean is less directly under the influence of
the luminaries, the rise and fall of the sea is inconsiderable, so that,
in all probability, there is no tide at the poles, or only a small
annual and monthly one. The ebb and flow of the sea are perceptible in
rivers to a very great distance from their estuaries. In the straits of
Pauxis, in the river of the Amazons, more than five hundred miles from
the sea, the tides are evident. It requires so many days for the tide to
ascend this mighty stream, that the returning tides meet a succession of
those which are coming up; so that every possible variety occurs in some
part or other of its shores, both as to magnitude and time. It requires
a very wide expanse of water to accumulate the impulse of the sun and
moon, so as to render their influence sensible; on that account the
tides in the Mediterranean and Black Sea are scarcely perceptible.
These perpetual commotions in the waters of the ocean are occasioned by
forces that bear a very small proportion to terrestrial gravitation: the
sun's action in raising the ocean is only the 1/38448000 of gravitation
at the earth's surface, and the action of the moon is little more than
twice as much these forces being in the ratio of 1 to 2.35333. From this
ratio the mass of the moon is found to be only 1/15 part of that of the
earth. The initial state of the ocean has no influence on the tides;
for whatever its primitive conditions may have been, they must soon have
vanished by the friction and mobility of the fluid. One of the most
remarkable circumstances in the theory of the tides is the assurance
that in consequence of the density of the sea being only one-fifth of
the mean density of the earth, the stability of the equilibrium of the
ocean never can be subverted by any physical cause whatever. A general
inundation arising from the mere instability of the ocean is therefore
impossible.
The atmosphere when in equilibrio is an ellipsoid flattened at the poles
from its rotation with the earth: in that state its strata are of
uniform density at equal heights above the level of the sea, and it is
sensibly of finite extent, whether it consists of particles infinitely
divisible or not. On the latter hypothesis it must really be finite; and
even if the particles of matter be infinitely divisible, it is known by
experience to be of extreme tenuity at very small heights. The barometer
rises in proportion to the superincumbent pressure. Now at the
temperature of melting ice, the density of mercury is to that of air as
10320 to 1; and as the mean height of the barometer is 29.528 inches,
the height of the atmosphere by simple proportion is 30407 feet, at the
mean temperature of 62°, or 34153 feet, which is extremely small, when
compared with the radius of the earth. The action of the sun and moon
disturbs the equilibrium of the atmosphere, producing oscillations
similar to those in the ocean, which occasion periodic variations in the
heights of the barometer. These, however, are so extremely small, that
their existence in latitudes so far removed from the equator is
doubtful; a series of observations within the tropics can alone decide
this delicate point. La Place seems to think that the flux and reflux
distinguishable at Paris may be occasioned by the rise and fall of the
ocean, which forms a variable base to so great a portion of the
atmosphere.
The attraction of the sun and moon has no sensible effect on the trade
winds; the heat of the sun occasions these aerial currents, by rarefying
the air at the equator, which causes the cooler and more dense part of
the atmosphere to rush along the surface of the earth to the equator,
while that which is heated is carried along the higher strata to the
poles, forming two currents in the direction of the meridian. But the
rotatory velocity of the air corresponding to its geographical situation
decreases towards the poles; in approaching the equator it must
therefore revolve more slowly than the corresponding parts of the earth,
and the bodies on the surface of the earth must strike against it with
the excess of their velocity, and by its reaction they will meet with a
resistance contrary to their motion of rotation; so that the wind will
appear, to a person supposing himself to be at rest, to blow in a
contrary direction to the earth's rotation, or from east to west, which
is the direction of the trade winds. The atmosphere scatters the sun's
rays, and gives all the beautiful tints and cheerfulness of day. It
transmits the blue light in greatest abundance; the higher we ascend,
the sky assumes a deeper hue, but in the expanse of space the sun and
stars must appear like brilliant specks in profound blackness.