MEAN SOLAR TIME.
SUN-DIAL TIME.—The changing directions of shadows thrown by the sun have
been utilised from very remote periods for the measurement of time, the
instrument usually employed being a sun-dial. On account of the varying
declination of the sun, it is necessary to employ as a time-measurer the
shadow of a line which lies parallel to the earth’s axis, that is, if we
wish the same hour marks to be permanently useful. Such a rod must lie
in the plane of the meridian, and be inclined to the horizon at an angle
equal to the latitude of the place. If the shadow be received on a
horizontal dial, hours may be marked upon it corresponding to the
duration of the longest day at the place where it is set up. Sometimes,
as on old churches, one sees a vertical sun-dial, the rod, or _style_,
as it is called, being still parallel to the earth’s axis, but as a dial
facing the south is only serviceable for twelve hours, another on the
north wall is necessary for times before six in the morning and after
six in the evening. As indicated by the sun-dial, it will always be noon
when the sun is on the meridian, that is, when it is due south.
The time indicated by sun-dials is distinguished astronomically as
_apparent time_, and an _apparent solar day_ is the time which elapses
between two successive southings of the sun. It is longer than the
sidereal day, for the reason that the sun moves eastward among the
stars.
NECESSITY FOR MEAN TIME.—The varying speed of the earth in its orbit, or
what comes to the same thing, the variable rate of the sun’s apparent
eastward movement, prepares us for the discovery that the intervals
between successive noons as indicated by sun-dials are unequal. That is,
the apparent solar day is not of uniform length, and our clocks could
not be regulated to indicate noon at the same moments as the sun-dial
unless they were rated afresh every day. All our daily actions are
regulated by the sun, and our time-keepers must also be controlled by
its movement if they are to be as convenient as is necessary for
purposes of everyday life. Our clocks and watches are therefore
regulated to measure twenty-four hours in the time corresponding to the
average duration of the apparent solar day throughout a year. In other
words, they are controlled by the movements of an imaginary sun, called
the _mean sun_, which is supposed to come to the meridian after equal
intervals, and in order that it may do this while having a uniform
motion, it must of necessity move along the celestial equator. In this
way the time shown by our clocks and watches never departs very greatly
from that shown by sun-dials, the maximum discrepancy being little more
than a quarter of an hour. A _mean solar day_ is thus the average length
of the apparent solar days throughout a year.
THE EQUATION OF TIME.—The difference between apparent and mean solar
time is called the _equation of time_, and a knowledge of its amount
enables us to determine mean time from an observation of apparent time.
One of the causes of this difference we have already seen to be the
varying speed of the earth in its orbital movement; this produces a
correspondingly irregular motion of the sun amongst the stars, and in
consequence the true sun comes to the meridian after unequal intervals.
Neglecting for a moment another cause of the varying length of the day,
the relation of the apparent and mean solar days would be somewhat as
follows:—Let us suppose that when the earth is at perihelion, we set our
clocks to the same time as the sun-dial. In the interval which elapses
before noon next day the true sun will have moved faster than the mean
sun, because the earth, which produces the apparent eastward movement of
the sun, is then travelling at its greatest speed. Consequently, our
meridian will overtake the mean sun before it comes up to the true sun,
and mean noon will occur before apparent noon; the difference will be
the equation of time for the day, and it must evidently be added to
apparent time in order to give mean time. This will go on for a certain
period, when, in consequence of the reduced rate of the earth’s orbital
velocity, the suns eastward motion will be less than that of the mean
sun, and the two will again come to the meridian at the same time when
the earth reaches its aphelion point; clocks and sun-dials would then
give identical times. After aphelion passage, the earth is moving
slowly, and the apparent eastward velocity of the true sun will be less
than that of the mean; our meridian will therefore come to the true sun
before it overtakes the mean sun, so that apparent noon will precede
mean noon, and the equation of time will have to be subtracted from
apparent time to give mean time. The two suns would again come together
when the earth reached perihelion, and the equation of time, so far as
this cause was concerned, would vanish. As the earth’s orbit is only
slightly elliptical, the equation of time due to this cause alone would
never amount to more than seven minutes.
This, however, is by no means the whole cause of the equation of time; a
still greater source of variation is the obliquity of the ecliptic. To
investigate the part played by this inclination of the fundamental
planes, let us now suppose that the true sun has a uniform angular
motion in the ecliptic, while the mean sun moves uniformly along the
Equator. Both these fictitious suns would have the same rate of movement
along their respective paths, since they come back to the same places
after the lapse of a year. If, then, these two suns start together at
the equinox, both would indicate noon at that time, and there would be
no equation of time. The “ecliptic sun” would then be moving at an angle
of 23½° to the Equator, as along _a b_ in Fig. 17. If the distance _a b_
represents the average daily movement of the “ecliptic” sun, and _d c_
the equal movement of the mean sun, it is clear that our meridian will
overtake the true sun at _b_ before the mean sun at _c_, so that
apparent noon will precede mean noon, and the equation of time must be
subtracted from apparent time to give mean time. The difference becomes
greater up to a certain limit, and then since both suns will traverse
90° in the same time, they will pass the meridian together at the
solstice.
[Illustration:
FIG. 17.—_Effect of Obliquity of Ecliptic upon the Equation of Time._
]
In the next quarter of a revolution, from solstice to equinox the
difference is similar, but in the opposite direction, and the same
applies to successive quadrants described throughout the year.
The net amount of the equation of time at any moment is thus the added
effects due to two causes.
In 1896 the greatest and least values of the equation of time at
Greenwich mean noon were as follows:—
M. S.
Feb. 11 14 27 to be added to apparent time.
April 14 0 7 „ „ „
May 13 3 50 to be subtracted from apparent time.
June 13 0 6 „ „ „
July 25 6 17 to be added to apparent time.
August 31 0 0 „ „ „
Nov. 2 16 20 to be subtracted from apparent time.
Dec. 24 0 7 to be added to apparent time.
A somewhat notable effect, owing its origin to the equation of time, is
seen in the times of sunrise and sunset given in our almanacs. On
November 8, for example, the sun rises at Greenwich at 6h. 58m., and
sets at 4h. 31m., thus apparently making the afternoon about half an
hour longer than the morning. As reckoned by the sun-dial, however, the
morning and afternoon would differ only by a few seconds, and the
peculiarity noted arises simply from the fact that our clocks keep time
with the mean, and not with the true sun.
DETERMINATION OF TIME.—Although the sun-dial may be used to indicate the
time of day with sufficient accuracy for some purposes, its use is
limited by the fact that it can only be employed when the sun is visible
at the place of observation. Other modes of measuring the flow of time
have, therefore, long been adopted. In early days, the rate at which a
candle burned, or at which water or sand escaped through a small
aperture, was employed as a time-measurer. Coming to more recent times,
clocks and watches serve a similar purpose, but from what has already
been stated, it is evidently necessary to regulate them according to the
results of astronomical observations.
The most precise determinations of time are made by means of a transit
instrument, that is, an instrument by which the exact moment at which a
celestial body passes the meridian can be observed. The positions of
certain fundamental stars called “clock stars” have been determined with
great accuracy, and it is therefore known to within a very small
fraction of a second at what sidereal time one of these stars will pass
the meridian. If the sidereal clock does not indicate this time when the
star is observed on the meridian, its error can be noted and corrected.
In this way the sidereal time is ascertained, and its equivalent in mean
solar time is only a matter of simple calculation.
Another method is to observe, by means of a sextant, or an altazimuth,
the time, by a clock, at which the sun or a star has a certain altitude
before noon, and the time at which it has the same altitude after noon.
Midway between these times marks the time at which the body passed the
meridian; the true sidereal time of passage is furnished by the known
right ascension, and the corresponding mean time can therefore be
calculated.
At sea, time is most frequently determined by observing the altitude of
the sun in the morning or evening, when it is nearly in an east or west
direction. The time by the chronometer corresponding to a certain
altitude of the sun is noted, and by spherical trigonometry the apparent
solar time is deduced; mean solar time is then obtained by correcting
for the equation of time. The nearer the sun is to due east or west, the
more accurate are the results obtained by this method.
TIME AT DIFFERENT PLACES.—In all these methods of finding the time,
_local time_ is alone determined, whether it be sidereal or solar. When
solar time is in question, we have seen that mean noon is determined by
the passage of the mean sun across the meridian. All places on the same
meridian will thus have equal times; but at places on different
meridians, the local times will be different. When it is noon at
Greenwich, it will be something before noon at places to the west of
Greenwich (for the reason that the sun has not yet crossed their
meridians), while at places to the cast it will be afternoon, because
the sun has already passed the meridian. As the earth rotates through
360° in a day, it will turn 15° in an hour, or 1° in four minutes. Hence
at places 15° east of Greenwich the time will be an hour in advance of
Greenwich time, while at places 15° west it will be an hour earlier. For
places in other longitudes, the difference of time is in the same
proportion. The following are the local times at several places when it
is noon at Greenwich:—
A.M. P.M.
Dublin 11.35 Paris 0.9
New York 7.4 Berlin 0.54
Toronto 6.42 Calcutta 5.53
Vancouver 3.38 Melbourne 9.40
Throughout the whole of England and Scotland, Greenwich mean time is
exclusively employed in preference to local times. This has the very
practical advantage of uniformity; and as in no case does local time
differ more than half an hour from Greenwich time, there is little
inconvenience in regard to the beginning and end of day.
Until recently, the time systems of other countries have been mainly
based on the times corresponding to their various national
observatories. At present, what is called “zone time,” in which the
hours alone differ from Greenwich time, has been adopted in several
European states, as well as in other parts of the world.
The present state of time reckoning on this much improved plan is
indicated by the following table:—
_Country._ │ _Standard time._
───────────────────────────────┼───────────────────────────────────────
England │
Belgium │Greenwich time.
Holland │
───────────────────────────────┼───────────────────────────────────────
Denmark │
Germany │Mid-European time, 1 hour fast on
Italy │ Greenwich.
Switzerland │
Norway and Sweden │
───────────────────────────────┼───────────────────────────────────────
Colony of Natal │2 hours fast on Greenwich.
───────────────────────────────┼───────────────────────────────────────
United States │4, 5, 6, 7, or 8 hours slow on
Canada │ Greenwich, according to longitude.
───────────────────────────────┼───────────────────────────────────────
Japan │9 hours fast on Greenwich.
───────────────────────────────┼───────────────────────────────────────
Western Australia │8 „ „ „
───────────────────────────────┼───────────────────────────────────────
South Australia │9 „ „ „
───────────────────────────────┼───────────────────────────────────────
Victoria, New South Wales, │10 „ „ „
Queensland, and Tasmania │
───────────────────────────────┴───────────────────────────────────────
TELEGRAPHING TIME.—An important part of the work of the chief national
observatories is the determination of correct time, and its
communication to the public at large. Railways have especially created a
demand for a uniform and accurate system of time reckoning, and to meet
this need there is usually an organised service providing an automatic
distribution of time-signals by means of the electric telegraph. The
transmission of such time-signals was first established on a large scale
in connection with Greenwich Observatory, and at the present time
signals are sent to the General Post Office, whence they are distributed
automatically to post offices and subscribers throughout the kingdom. In
addition, signals are sent direct to Westminster for the regulation of
the great clock on the Houses of Parliament, and time-balls are dropped
at certain hours at Greenwich and Deal, in order that navigators may
have the opportunity of rectifying their chronometers.
THE YEAR.—The day is too small an interval of time to be conveniently
employed as a unit for chronological purposes, so that at present the
count of time by days is practically limited to the number of days in a
month. A greater unit, but still too small, is supplied by the month,
and the necessity for a more serviceable unit early led to the adoption
of the length of the year. This is at once a natural division of time,
corresponding to the recurrence of the seasons, and sufficiently answers
all requirements for measuring extended intervals.
If we determine the exact time required by the sun to pass from one
fixed point in the heavens to the same point again, we shall find the
time in which the earth makes a complete revolution round the sun, that
is, the time in which a line joining the earth and sun sweeps through an
angle of 360°. This interval, which is called the _sidereal year_,
amounts to 365 days 6 hours 9 minutes 9 seconds of mean solar time. It
will be clear, however, that the most useful year is that which will
give us the same day of the month at the same season in all years. If
there were no precession of the equinoxes, this would be of the same
length as the sidereal year, but on account of precession the passage of
the sun from the vernal equinox to the same equinox again occupies less
than a sidereal year. In fact, this equinoctial, or _tropical year_
amounts to 365 days 5 hours 48 minutes 46 seconds; that is, about 20
minutes less than the sidereal year. This is the year which is always
understood, unless it is otherwise stated. If our calendars were
regulated according to the sidereal year, the same day of the month
would in time run through all possible changes of seasons, the 25th of
December, for instance, occurring at one time in winter, and gradually
changing through spring, summer, and autumn.
THE CALENDAR.—The earlier calendars with which history acquaints us were
mainly based on the lunar month of about 29½ days, twelve of which made
up a lunar year of 354 days. The calendar year was thus more than 11
days shorter than the actual year, and in order to bring the dates into
agreement with the seasons, arbitrary intercalations were occasionally
made by the authorities.
In the year 45 B.C. a great reform was introduced by Julius Cæsar; 365¼
days was adopted as the length of the year, and it was prescribed that
ordinary years should be reckoned as consisting of 365 days, while every
fourth year divisible by 4 without remainder should be a _leap year_ of
366 days. Matters were so much simplified by this arrangement that the
Julian calendar remained unaltered until 1582, and is even now retained
throughout Russia.
The tropical year, as we have seen, is less than 365¼ days, so that the
Julian calendar does not quite keep course with the seasons. Although
the difference is only 11¼ minutes, it amounts to an entire day in 128
years, so that if the vernal equinox occurred on the 21st of March at
one time it would occur on the 20th after 128 years. If, then, it be
desired to bring the existing dates of any particular year into
agreement with dates at a previous period, as regards the seasons, a
correction in addition to that ordained by Cæsar must be introduced. In
the time of Pope Gregory, in the year 1582, the vernal equinox fell on
the 11th of March, and the necessity of a new calendar came to be
recognised. The astronomer Clavius, with the authority of the Pope,
devised our present “Gregorian” calendar. This arrangement, first of
all, altered the actual date of the equinox from the 10th to the 21st of
March, that is, to the day on which it occurred in the year of the great
Council of the Church at Nicæa, 325 A.D. To bring about this alteration
it was necessary to drop 10 days from the calendar, and it was therefore
decided that the day following the 4th of October, 1582, should be
called the 15th instead of the 5th. To prevent subsequent changes in the
date of the equinox the Julian rule for leap year was slightly modified.
If the date number of a year is divisible by 4 without remainder it is
still to be a leap year, unless it be a century year, in which case it
must be divisible by 400 without remainder if it is to be called a leap
year.
It was not until 1752 that the Gregorian calendar was adopted in
England, and as 1700 was a leap year according to the Julian rule the
old style date was 11 days behind the Gregorian date. An Act of
Parliament decreed that the day following September 2, 1752, should be
called the 14th. The Act was carefully planned so as to prevent
injustice in the collection of rents and the like, but it was only
accepted after considerable opposition.
It has lately been pointed out that if we wish to make the day of the
year correspond with the seasons for all time, a modification of the
Gregorian calendar must be adopted. By the Gregorian rule, three leap
years are omitted every four centuries; but Mr. W. T. Lynn has drawn
attention to the fact that if one were dropped every 128 years instead,
the calendar would be sensibly perfect, and the seasons would always
commence on the same dates.