called a sidereal day, and is determined by the revolution of a star in
the heavens. This interval is divided into twenty-four _sidereal_
hours. Observations taken on numerous stars, in different ages of the
world, show that they all perform their diurnal revolution in the same
time, and that their motion, during any part of the revolution, is
always uniform. Here, then, we have an exact measure of time, probably
more exact than any thing which can be devised by art. _Solar time_ is
reckoned by the apparent revolution of the sun from the meridian round
to the meridian again. Were the sun stationary in the heavens, like a
fixed star, the time of its apparent revolution would be equal to the
revolution of the earth on its axis, and the solar and the sidereal days
would be equal. But, since the sun passes from west to east, through
three hundred and sixty degrees, in three hundred and sixty-five and one
fourth days, it moves eastward nearly one degree a day. While,
therefore, the earth is turning round on its axis, the sun is moving in
the same direction, so that, when we have come round under the same
celestial meridian from which we started, we do not find the sun there,
but he has moved eastward nearly a degree, and the earth must perform so
much more than one complete revolution, before we come under the sun
again. Now, since we move, in the diurnal revolution, fifteen degrees in
sixty minutes, we must pass over one degree in four minutes. It takes,
therefore, four minutes for us to _catch up_ with the sun, after we have
made one complete revolution. Hence the solar day is about four minutes
longer than the sidereal; and if we were to reckon the sidereal day
twenty-four hours, we should reckon the solar day twenty-four hours four
minutes. To suit the purposes of society at large, however, it is found
more convenient to reckon the solar days twenty-four hours, and throw
the fraction into the sidereal day. Then,
24h. 4m. : 24h. :: 24h. : 23h. 56m. 4s.
That is, when we reduce twenty-four hours and four minutes to
twenty-four hours, the same proportion will require that we reduce the
sidereal day from twenty-four hours to twenty-three hours fifty-six
minutes four seconds; or, in other words, a sidereal day is such a part
of a solar day. The solar days, however, do not always differ from the
sidereal by precisely the same fraction, since they are not constantly
of the same length. Time, as measured by the sun, is called _apparent
time_, and a clock so regulated as always to keep exactly with the sun,
is said to keep apparent time. _Mean time_ is time reckoned by the
_average_ length of all the solar days throughout the year. This is the
period which constitutes the _civil_ day of twenty-four hours, beginning
when the sun is on the lower meridian, namely, at twelve o'clock at
night, and counted by twelve hours from the lower to the upper meridian,
and from the upper to the lower. The _astronomical_ day is the apparent
solar day counted through the whole twenty-four hours, (instead of by
periods of twelve hours each, as in the civil day,) and begins at noon.
Thus it is now the tenth of June, at nine o'clock, A.M., according to
civil time; but we have not yet reached the tenth of June by
astronomical time, nor shall we, until noon to-day; consequently, it is
now June ninth, twenty-first hour of astronomical time. Astronomers,
since so many of their observations are taken on the meridian, are
always supposed to look towards the south. Geographers, having formerly
been conversant only with the northern hemisphere, are always understood
to be looking towards the north. Hence, left and right, when applied to
the astronomer, mean east and west, respectively; but to the geographer
the right is east, and the left, west.
Clocks are usually regulated so as to indicate mean solar time; yet, as
this is an artificial period not marked off, like the sidereal day, by
any natural event, it is necessary to know how much is to be added to,
or subtracted from, the apparent solar time, in order to give the
corresponding mean time. The interval, by which apparent time differs
from mean time, is called the _equation of time_. If one clock is so
constructed as to keep exactly with the sun, going faster or slower,
according as the lengths of the solar days vary, and another clock is
regulated to mean time, then the difference of the two clocks, at any
period, would be the equation of time for that moment. If the apparent
clock were _faster_ than the mean, then the equation of time must be
subtracted; but if the apparent clock were slower than the mean, then
the equation of time must be added, to give the mean time. The two
clocks would differ most about the third of November, when the apparent
time is sixteen and one fourth minutes greater than the mean. But since
apparent time is sometimes greater and sometimes less than mean time,
the two must obviously be sometimes equal to each other. This is, in
fact, the case four times a year, namely, April fifteenth, June
fifteenth, September first, and December twenty-fourth.
Astronomical clocks are made of the best workmanship, with every
advantage that can promote their regularity. Although they are brought
to an astonishing degree of accuracy, yet they are not as regular in
their movements as the stars are, and their accuracy requires to be
frequently tested. The transit instrument itself, when once accurately
placed in the meridian, affords the means of testing the correctness of
the clock, since one revolution of a star, from the meridian to the
meridian again, ought to correspond exactly to twenty-four hours by the
clock, and to continue the same, from day to day; and the right
ascensions of various stars, as they cross the meridian, ought to be
such by the clock, as they are given in the tables, where they are
stated according to the accurate determinations of astronomers. Or, by
taking the difference of any two stars, on successive days, it will be
seen whether the going of the clock is uniform for that part of the day;
and by taking the right ascensions of different pairs of stars, we may
learn the rate of the clock at various parts of the day. We thus learn,
not only whether the clock accurately measures the length of the
sidereal day, but also whether it goes uniformly from hour to hour.
Although astronomical clocks have been brought to a great degree of
perfection, so as hardly to vary a second for many months, yet none are
absolutely perfect, and most are so far from it, as to require to be
corrected by means of the transit instrument, every few days. Indeed,
for the nicest observations, it is usual not to attempt to bring the
clock to a state of absolute correctness, but, after bringing it as near
to such a state as can conveniently be done, to ascertain how much it
gains or loses in a day; that is, to ascertain the _rate_ of its going,
and to make allowance accordingly.
Having considered the manner in which the smaller divisions of time are
measured, let us now take a hasty glance at the larger periods which
compose the calendar.
As a _day_ is the period of the revolution of the earth on its axis, so
a _year_ is the period of the revolution of the earth around the sun.
This time, which constitutes the _astronomical year_, has been
ascertained with great exactness, and found to be three hundred and
sixty-five days five hours forty-eight minutes and fifty-one seconds.
The most ancient nations determined the number of days in the year by
means of the _stylus_, a perpendicular rod which casts its shadow on a
smooth plane bearing a meridian line. The time when the shadow was
shortest, would indicate the day of the Summer solstice; and the number
of days which elapsed, until the shadow returned to the same length
again, would show the number of days in the year. This was found to be
three hundred and sixty-five whole days, and accordingly, this period
was adopted for the civil year. Such a difference, however, between the
civil and astronomical years, at length threw all dates into confusion.
For if, at first, the Summer solstice happened on the twenty-first of
June, at the end of four years, the sun would not have reached the
solstice until the twenty-second of June; that is, it would have been
behind its time. At the end of the next four years, the solstice would
fall on the twenty-third; and in process of time, it would fall
successively on every day of the year. The same would be true of any
other fixed date.
Julius Cæsar, who was distinguished alike for the variety and extent of
his knowledge, and his skill in arms, first attempted to make the
calendar conform to the motions of the sun.
"Amidst the hurry of tumultuous war,
The stars, the gods, the heavens, were still his care."
Aided by Sosigenes, an Egyptian astronomer, he made the first correction
of the calendar, by introducing an additional day every fourth year,
making February to consist of twenty-nine instead of twenty-eight days,
and of course the whole year to consist of three hundred and sixty-six
days. This fourth year was denominated _Bissextile_, because the sixth
day before the Kalends of March was reckoned twice. It is also called
Leap Year.
The Julian year was introduced into all the civilized nations that
submitted to the Roman power, and continued in general use until the
year 1582. But the true correction was not six hours, but five hours
forty-nine minutes; hence the addition was too great by eleven minutes.
This small fraction would amount in one hundred years to three fourths
of a day, and in one thousand years to more than seven days. From the
year 325 to the year 1582, it had, in fact, amounted to more than ten
days; for it was known that, in 325, the vernal equinox fell on the
twenty-first of March, whereas, in 1582, it fell on the eleventh. It was
ordered by the Council of Nice, a celebrated ecclesiastical council,
held in the year 325, that Easter should be celebrated upon the first
Sunday after the first full moon, next following the vernal equinox; and
as certain other festivals of the Romish Church were appointed at
particular seasons of the year, confusion would result from such a want
of constancy between any fixed date and a particular season of the year.
Suppose, for example, a festival accompanied by numerous religious
ceremonies, was decreed by the Church to be held at the time when the
sun crossed the equator in the Spring, (an event hailed with great joy,
as the harbinger of the return of Summer,) and that, in the year 325,
March twenty-first was designated as the time for holding the festival,
since, at that period, it was on the twenty-first of March when the sun
reached the equinox; the next year, the sun would reach the equinox a
little sooner than the twenty-first of March, only eleven minutes,
indeed, but still amounting in twelve hundred years to ten days; that
is, in 1582, the sun reached the equinox on the eleventh of March. If,
therefore, they should continue to observe the twenty-first as a
religious festival in honor of this event, they would commit the
absurdity of celebrating it ten days after it had passed by. Pope
Gregory the Thirteenth, who was then at the head of the Roman See, was a
man of science, and undertook to reform the calendar, so that fixed
dates would always correspond to the same seasons of the year. He first
decreed, that the year should be brought forward ten days, by reckoning
the fifth of October the fifteenth; and, in order to prevent the
calendar from falling into confusion afterwards, he prescribed the
following rule: _Every year whose number is not divisible by four,
without a remainder, consists of three hundred and sixty-five days;
every year which is so divisible, but is not divisible by one hundred,
of three hundred and sixty-six; every year divisible by one hundred, but
not by four hundred, again, of three hundred and sixty-five; and every
year divisible by four hundred, of three hundred and sixty-six._
Thus the year 1838, not being divisible by four, contains three hundred
and sixty-five days, while 1836 and 1840 are leap years. Yet, to make
every fourth year consist of three hundred and sixty-six days would
increase it too much, by about three fourths of a day in a century;
therefore every hundredth year has only three hundred and sixty-five
days. Thus 1800, although divisible by four, was not a leap year, but a
common year. But we have allowed a _whole_ day in a hundred years,
whereas we ought to have allowed only _three fourths_ of a day. Hence,
in four hundred years, we should allow a day too much, and therefore, we
let the four hundredth remain a leap year. This rule involves an error
of less than a day in four thousand two hundred and thirty-seven years.
The Pope, who, you will recollect, at that age assumed authority over
all secular princes, issued his decree to the reigning sovereigns of
Christendom, commanding the observance of the calendar as reformed by
him. The decree met with great opposition among the Protestant States,
as they recognised in it a new exercise of ecclesiastical tyranny; and
some of them, when they received it, made it expressly understood, that
their acquiescence should not be construed as a submission to the Papal
authority.
In 1752, the Gregorian year, or _New Style_, was established in Great
Britain by act of Parliament; and the dates of all deeds, and other
legal papers, were to be made according to it. As above a century had
then passed since the first introduction of the new style, eleven days
were suppressed, the third of September being called the fourteenth. By
the same act, the beginning of the year was changed from March
twenty-fifth to January first. A few persons born previously to 1752
have come down to our day, and we frequently see inscriptions on
tombstones of those whose time of birth is recorded in old style. In
order to make this correspond to our present mode of reckoning, we must
add eleven days to the date. Thus the same event would be June twelfth
of old style, or June twenty-third of new style; and if an event
occurred between January first and March twenty-fifth, the date of the
year would be advanced one, since February 1st, 1740, O.S. would be
February 1st, 1741, N.S. Thus, General Washington was born February
11th, 1731, O.S., or February 22d, 1732, N.S. If we inquire how any
present event may be made to correspond in date to the old style, we
must subtract twelve days, and put the year back one, if the event lies
between January first and March twenty-fifth. Thus, June tenth, N.S.
corresponds to May twenty-ninth, O.S.; and March 20th, 1840, to March
8th, 1839. France, being a Roman Catholic country, adopted the new style
soon after it was decreed by the Pope; but Protestant countries, as we
have seen, were much slower in adopting it; and Russia, and the Greek
Church generally, still adhere to the old style. In order, therefore, to
make the Russian dates correspond to ours, we must add to them twelve
days.
It may seem to you very remarkable, that so much pains should have been
bestowed upon this subject; but without a correct and uniform standard
of time, the dates of deeds, commissions, and all legal papers; of fasts
and festivals, appointed by ecclesiastical authority; the returns of
seasons, and the records of history,--must all fall into inextricable
confusion. To change the observance of certain religious feasts, which
have been long fixed to particular days, is looked upon as an impious
innovation; and though the times of the events, upon which these
ceremonies depend, are utterly unknown, it is still insisted upon by
certain classes in England, that the Glastenbury thorn blooms on
Christmas day.
Although the ancient Grecian calendar was extremely defective, yet the
common people were entirely averse to its reformation. Their
superstitious adherence to these errors was satirized by Aristophanes,
in his comedy of the Clouds. An actor, who had just come from Athens,
recounts that he met with Diana, or the moon, and found her extremely
incensed, that they did not regulate her course better. She complained,
that the order of Nature was changed, and every thing turned topsyturvy.
The gods no longer knew what belonged to them; but, after paying their
visits on certain feast-days, and expecting to meet with good cheer, as
usual, they were under the disagreeable necessity of returning back to
heaven without their suppers.
Among the Greeks, and other ancient nations, the length of the year was
generally regulated by the course of the moon. This planet, on account
of the different appearances which she exhibits at her full, change,
and quarters, was considered by them as best adapted of any of the
celestial bodies for this purpose. As one lunation, or revolution of the
moon around the earth, was found to be completed in about twenty-nine
and one half days, and twelve of these periods being supposed equal to
one revolution of the sun, their months were made to consist of
twenty-nine and thirty days alternately, and their year of three hundred
and fifty-four days. But this disagreed with the annual revolution of
the sun, which must evidently govern the seasons of the year, more than
eleven days. The irregularities, which such a mode of reckoning would
occasion, must have been too obvious not to have been observed. For,
supposing it to have been settled, at any particular time, that the
beginning of the year should be in the Spring; in about sixteen years
afterwards, the beginning would have been in Autumn; and in thirty-three
or thirty-four years, it would have gone backwards through all the
seasons, to Spring again. This defect they attempted to rectify, by
introducing a number of days, at certain times, into the calendar, as
occasion required, and putting the beginning of the year forwards, in
order to make it agree with the course of the sun. But as these
additions, or _intercalations_, as they were called, were generally
consigned to the care of the priests, who, from motives of interest or
superstition, frequently omitted them, the year was made long or short
at pleasure.
The _week_ is another division of time, of the highest antiquity, which,
in almost all countries, has been made to consist of seven days; a
period supposed by some to have been traditionally derived from the
creation of the world; while others imagine it to have been regulated by
the phases of the moon. The names, Saturday, Sunday, and Monday, are
obviously derived from Saturn, the Sun, and the Moon; while Tuesday,
Wednesday, Thursday, and Friday, are the days of Tuisco, Woden, Thor,
and Friga, which are Saxon names for Mars, Mercury, Jupiter, and
Venus.[4]
The common year begins and ends on the same day of the week; but leap
year ends one day later than it began. Fifty-two weeks contain three
hundred and sixty-four days; if, therefore, the year begins on Tuesday,
for example, we should complete fifty-two weeks on Monday, leaving one
day, (Tuesday,) to complete the year, and the following year would begin
on Wednesday. Hence, any day of the month is one day later in the week,
than the corresponding day of the preceding year. Thus, if the sixteenth
of November, 1838, falls on Friday, the sixteenth of November, 1837,
fell on Thursday, and will fall, in 1839, on Saturday. But if leap year
begins on Sunday, it ends on Monday, and the following year begins on
Tuesday; while any given day of the month is two days later in the week
than the corresponding date of the preceding year.
FOOTNOTE:
[4] Bonnycastle's Astronomy.
LETTER VII.
FIGURE OF THE EARTH.
"He took the golden compasses, prepared
In God's eternal store, to circumscribe
This universe, and all created things;
One foot he centred, and the other turned
Round through the vast profundity obscure,
And said, 'Thus far extend, thus far thy bounds,
This be thy just circumference, O World!'"--_Milton._
IN the earliest ages, the earth was regarded as one continued plane;
but, at a comparatively remote period, as five hundred years before the
Christian era, astronomers began to entertain the opinion that the earth
is round. We are able now to adduce various arguments which severally
prove this truth. First, when a ship is coming in from sea, we first
observe only the very highest parts of the ship, while the lower
portions come successively into view. Were the earth a continued plane,
the lower parts of the ship would be visible as soon as the higher, as
is evident from Fig. 10, page 70.
[Illustration Fig. 10.]
[Illustration Fig. 11.]
Since light comes to the eye in straight lines, by which objects become
visible, it is evident, that no reason exists why the parts of the ship
near the water should not be seen as soon as the upper parts. But if the
earth be a sphere, then the line of sight would pass above the deck of
the ship, as is represented in Fig. 11; and as the ship drew nearer to
land, the lower parts would successively rise above this line and come
into view exactly in the manner known to observation. Secondly, in a
lunar eclipse, which is occasioned by the moon's passing through the
earth's shadow, the figure of the shadow is seen to be spherical, which
could not be the case unless the earth itself were round. Thirdly,
navigators, by steering continually in one direction, as east or west,
have in fact come round to the point from which they started, and thus
confirmed the fact of the earth's rotundity beyond all question. One may
also reach a given place on the earth, by taking directly opposite
courses. Thus, he may reach Canton in China, by a westerly route around
Cape Horn, or by an easterly route around the Cape of Good Hope. All
these arguments severally prove that the earth is round.
But I propose, in this Letter, to give you some account of the unwearied
labors which have been performed to ascertain the _exact_ figure of the
earth; for although the earth is properly described in general language
as round, yet it is not an exact sphere. Were it so, all its diameters
would be equal; but it is known that a diameter drawn through the
equator exceeds one drawn from pole to pole, giving to the earth the
form of a _spheroid_,--a figure resembling an orange, where the ends are
flattened a little and the central parts are swelled out.
Although it would be a matter of very rational curiosity, to investigate
the precise shape of the planet on which Heaven has fixed our abode, yet
the immense pains which has been bestowed on this subject has not all
arisen from mere curiosity. No accurate measurements can be taken of the
distances and magnitudes of the heavenly bodies, nor any exact
determinations made of their motions, without a knowledge of the exact
figure of the earth; and hence is derived a powerful motive for
ascertaining this element with all possible precision.