CHAPTER V.
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.