Mean and Apparent Sidereal Time—Mean and Apparent Solar Time—Equation of
Time—English and French Subdivisions of Time—Leap Year—Christian
Era—Equinoctial Time—Remarkable Eras depending upon the Position of
the Solar Perigee—Inequality of the Lengths of the Seasons in the two
Hemispheres—Application of Astronomy to Chronology—English and French
Standards of Weights and Measures.
ASTRONOMY has been of immediate and essential use in affording
invariable standards for measuring duration, distance, magnitude, and
velocity. The mean sidereal day measured by the time elapsed between two
consecutive transits of any star at the same meridian (N. 148), and the
mean sidereal year which is the time included between two consecutive
returns of the sun to the same star, are immutable units with which all
great periods of time are compared; 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. Apparent sidereal time, which is measured by the
transit of the equinoctial point at the meridian of any place, is a
variable quantity, from the effects of precession and nutation. Clocks
showing apparent sidereal time are employed for observation, and are so
regulated that they indicate 0^h 0^m 0^s at the instant the
equinoctial point passes the meridian of the observatory. And as time is
a measure of angular motion, the clock gives the distances of the
heavenly bodies from the equinox by observing the instant at which each
passes the meridian, and converting the interval into arcs at the rate
of 15° to an hour.
The returns of the sun to the 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 near the
equinoxes the arc of the equator is less than the corresponding arc of
the ecliptic, and in the solstices it is greater (N. 149). 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 59ʹ 8ʺ·33 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 uniformly in the
equator, is denominated mean solar time, and 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 true or apparent time, and 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, sometimes amounting to
as much as sixteen minutes. The apparent and mean time coincide four
times in the year; when the sun’s daily motion in right ascension is
equal to 59ʹ 8ʺ·33 in a mean solar day, which happens about the 16th of
April, the 16th of June, the 1st of September, and the 25th of December.
The astronomical day begins 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 the 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 decimal
system of weights and measures. This subdivision is not now used in
common life, nor has it been adopted in any other country; and although
some scientific writers in France still employ that division of time,
the custom is beginning to wear out. At one period during the French
Revolution, the clock in the gardens of the Tuileries was regulated to
show decimal time. The mean length of the day, though accurately
determined, is not sufficient for the purposes either of astronomy or
civil life. The tropical or civil year of 365^d 5^h 48^m 49^s·7,
which is the time elapsed between the consecutive returns of the sun to
the mean equinoxes or solstices, including all the changes of the
seasons, is a natural cycle peculiarly suited for a measure of duration.
It is estimated from the winter solstice, the middle of the long annual
night under the north pole. But although the length of the civil year is
pointed out by nature as a measure of long periods, the
incommensurability that exists between the length of the day and the
revolution 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, in four years it is nearly equal
to a revolution 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. In fact, if a bissextile be suppressed at the
end of three out of four centuries, the year so determined will only
exceed the true year by an extremely small fraction of a day; and if in
addition to this a bissextile be suppressed every 4000 years, the length
of the year will be nearly equal to that given by observation. Were the
fraction neglected, the beginning of the year would precede that of the
tropical year, so that it would retrograde through the different seasons
in a period of about 1507 years. The Egyptian year began with the
heliacal rising of Sirius (N. 150), and contained only 365 days, by
which they lost one year in every 1461 years, their Sothaic period, or
that cycle in which the heliacal rising of Sirius passes through the
whole year and takes place again on the same day. The division of the
year into months is very old and almost universal. But 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 day of 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
Julius Cæsar. The 25th of December of his forty-fifth year is considered
as the date of Christ’s nativity; and the forty-sixth year of the Julian
Calendar 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 have actually elapsed since that time.
Since solar and sidereal time are estimated from the passage of the sun
and the equinoctial point across the meridian of each place, the hours
are different at different places: while it is one o’clock at one place,
it is two at another, three at another, &c.; for it is obvious that it
is noon at one part of the globe at the same moment that it is midnight
at another diametrically opposite to it: consequently an event which
happens at one and the same instant of absolute time is recorded at
different places as having happened at different times. Therefore, when
observations made at different places are to be compared, they must be
reduced by computation to what they would have been had they been made
under the same meridian. To obviate this it was proposed by Sir John
Herschel to employ mean equinoctial time, which is the same for all the
world, and independent alike of local circumstances and inequalities in
the sun’s motion. It is the time elapsed from the instant the mean sun
enters the mean vernal equinox, and is reckoned in mean solar days and
parts of a day.
Some remarkable astronomical eras are determined by the position of the
major axis of the solar ellipse, which depends upon the direct motion of
the perigee (N. 102) and the precession of the equinoxes conjointly, the
annual motion of the one being 11ʺ·8, and that of the other 50ʺ·1. Hence
the axis, moving at the rate of 61ʺ·9 annually, accomplishes a tropical
revolution in 209·84 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 6483 the major axis
will again coincide with the line of the equinoxes; but then the solar
perigee will coincide with the equinox of autumn, whereas at the
creation of man it coincided with the vernal equinox. In the year 1246
the major axis was perpendicular to the line of the equinoxes; then the
solar perigee coincided with the solstice of summer, and the apogee with
the solstice of winter. According to La Place, who computed these
periods from different data, the last coincidence happened in the year
1250 of our era, which induced him to propose that year as a universal
epoch, the vernal equinox of the year 1250 to be the first day of the
first year. These eras can only be regarded as approximate, since
ancient observations are too inaccurate, and modern observations too
recent, to afford data for their precise determination.
The variation in the position of the solar ellipse occasions
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 between seven and eight days. The intervals
will be equal towards the year 6483, when the perigee will coincide with
the equinox of spring; but, when it passes that point, the spring and
summer taken together will be shorter than the period including the
autumn and winter (N. 151). These changes will be accomplished in a
tropical revolution of the major axis of the earth’s orbit, which
includes an interval of 20,984 years. Were the orbit circular, the
seasons would be equal; their difference arises from the excentricity of
the orbit, small as it is; but the changes are so trifling as to be
imperceptible in the short span 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 languages, arts, and
sciences, leaving but confused masses of ruins 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 time, 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
calculation 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 will show to how many
centuries they may be extended without the fear of error. A few examples
will show the importance of the 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 (N. 152), which was formerly determined from the meridian
length of the shadow of the stile of a dial on the day of a solstice.
The lengths of the meridian shadow at the summer and winter solstices
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 (N. 153) 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 of the obliquity is known,
both the time and place of the observations have been verified by
computations from modern tables. Thus the Chinese had made some advances
in the science of astronomy at that early period. Their whole chronology
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 years 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, who lived in the second
century after it. The great inequality of Jupiter and Saturn, whose
cycle embraces 918 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 mean
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 it appears from
computation that χ Draconis was not very far from that place about 3000
years ago; but, as it is only about 2150 years since Eudoxus lived, he
must have described an anterior state of the heavens, supposed to be the
same that was mentioned by Chiron about the time of the siege of Troy.
Thus every circumstance concurs in showing that astronomy was cultivated
in the highest ages of antiquity.
It is possible that a knowledge of astronomy may lead to the
interpretation of hieroglyphical characters. Astronomical signs are
often found on the ancient Egyptian monuments, probably employed by the
priests to record dates. The author had occasion to witness an instance
of this most interesting application of astronomy, in ascertaining the
date 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 to his country, and 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 date 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 of mean solar time, in the latitude of London, forms
the standard of the British measure of extension. Its approximate length
oscillating in vacuo at the temperature of 62° of Fahrenheit, and
reduced to the level of the sea (N. 154), was determined by Captain
Kater to be 39·1393 inches. The weight of a cubic inch of water at the
temperature of 62° of Fahrenheit, barometer 30 inches, was also
determined in parts of the imperial troy pound, whence a standard both
of weight and capacity was deduced. The French have adopted the mètre,
equal to 3·2808992 English feet, for their unit of linear measure, which
is the ten-millionth part of the arc of the meridian which extends from
the equator to the pole, as deduced from the measures of the separate
arc extending from Formentera, the most southern of the Balearic
Islands, to Dunkirk. Should the national standards of the two countries
ever be lost, both may be recovered, since they are derived from natural
and invariable ones. The length of the measure deduced from that of the
pendulum would be found again with more facility than the mètre. 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 (N. 155) is rendered totally insensible by subdivision in
taking its ten-millionth part. The French have adopted the decimal
division, not only in time, but also in their degrees, weights, and
measures, on account of the very great facility it affords in
computation. It has not been adopted by any other country, though
nothing is more desirable than that all nations should concur in using
the same standards, not only on account of convenience, but as affording
a more definite idea of quantity. It is singular that the decimal
division of the day, of space, weights, and measures, was employed in
China 4000 years ago; and that at the time Ibn Junis made his
observations at Cairo, about the year 1000 of the Christian era, the
Arabs were in the habit of employing the vibrations of the pendulum in
their astronomical observations as a measure of time.