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sun souths before the true sun, the clock will get before the dial, and we must add the equation of time to the time shown by the true sun.

416. When the earth is in perihelion, or—what comes to the same thing-when the sun is in perigee, the real sun moves fastest. The mean sun therefore souths before the true sun because a given meridian is brought by the earth's rotation to the mean sun before the true sun, and the dial will be behind the clock. When the sun is in apogee, the true sun will south first, and the clock will be behind the dial. The equation of time will therefore be additive or subtractive, or, as it is expressed, + or with regard to the time shown by the true sun, or to apparent time.

417. So, to refer back to Art. 415, in November we must deduct 161m. from the apparent time, and in February we must add 143m. to apparent time, to get clock time. In November, therefore, the true sun sets 16m. earlier than it would do if it occupied the position of the mean sun, by which our clocks are regulated. In February it sets 15m. later, and this is why the evenings begin to lengthen after Christmas more rapidly than they would otherwise do.

418. From an observation of the true sun with the aid of the equation of time, which is the angular distance in time between the mean and the true sun, we may readily deduce mean time. Suppose the true sun to be observed on the meridian of Greenwich, Jan. 1, 1887: it would then be apparent noon at that meridian; the equation of time at this instant is 3m. 46'69s. as given in the almanacs, and is to be added to apparent time; hence the corresponding mean time is Jan. 1, oh. 3m. 46'69; that is to say, the mean sun had passed the meridian previously to the true sun.

In Plate XII. we have a graphic representation of the equation of time. Above and below the datum lines are scales of minutes. The curve ABCD represents the portion of the equation of time due to the inequality of the real

sun's motion, and the curve 1 2 3 4 represents the inequality due to the obliquity of the ecliptic. The curve E E' E' E' is the algebraical sum of these, and represents the differences between mean time and true time all the year round.

LESSON XXXIV.-Difference of Time. How determined on the Terrestrial Globe. Greenwich Mean Time. Length of the Various Days. Sidereal Time. Conversion of Time.

419, Having said so much of solar days, both apparent and mean, we must next consider the start-points of these reckonings. We have-I. the apparent solar day, reckoned from the instant the true sun crosses the meridian through about 24 hours, till it crosses it again; II. the mean solar day, reckoned by the mean sun in the same manner. Both these days are used by astronomers. III. The civil day commences from the preceding midnight, is reckoned through 12 mean hours only to noon, and then recommences, and is reckoned through another 12 hours to the next midnight. The civil reckoning is therefore always 12 hours in advance of the astronomical reckoning; hence the well known rule for determining the latter from the former, viz. :-For P.M. civil times, make no change; but for A.M. ones, diminish the day of the month by I and add 12 to the hours. Thus: Jan. 2, 7h. 49m. P.M. civil time, is Jan. 2, 7h. 49m. astronomical time; but January 2, 7h. 49m. A.M. civil time is January 1, 19h. 49m. astronomical time. The distinction, however, between civil and astronomical reckoning is about to disappear, Greenwich civil time, counting from midnight to midnight, and from 0 to 24 hours will be adopted in the "Nautical Almanac " for 1891.

420. Now the position of the sun, as referred to the centre of the earth, is independent of meridians, and is the same for all places at the same absolute instant; but the

time at which it transits the meridian of Greenwich, and any other meridian, will be different. In a mean solar day, or 24 mean solar hours, the earth, by its rotation from west to east, has caused every meridian in succession from east to west to pass the mean sun; and since the motion is uniform, all the meridians distant from each other 15° will have passed the mean sun, at intervals of one mean hour; the meridian to the eastward passing first, or being, as compared with the sun, always one mean hour in advance of the westerly meridian. When it is 6 hours after mean noon at a place 15° west of Greenwich, it is therefore 7 hours after mean noon at Greenwich. When it is noon at Greenwich, it is past noon at Paris, because the sun has apparently passed over the meridian of Paris before it reached the meridian of Greenwich. Similarly, it is not yet noon at Bristol, for the sun has not yet reached the meridian of Bristol.

421. In civilized countries, at the present moment, not only is the use of mean time universal, but the mean time of the principal city or observatory is alone used. In England, for instance, Greenwich mean time (written G.M.T. for short) is used; in France, Paris mean time; in Switzerland, Berne mean time, and so on. This has become necessary owing, among other things, to the introduction of railways, so that with us Greenwich mean time is often called railway time. Formerly, before local time was quite given up, the churches in the West of England had two minute-hands, one showing local time, the other Greenwich time.

422. On the Continent, railway stations near the frontier of two states have their time regulated by their principal observatories. At Geneva, for instance, we see two clocks, one showing Paris time, and the other Berne time; and it is very necessary to know whether the time at which any particular train we may wish to travel in starts, is regulated by Paris or Berne time, as there is a considerable difference between them.

P

423. Expressed in mean time, the length of the day is

as follows:

Apparent solar day (Art. 419)

Mean solar day (Art. 419)

Sidereal day (Art. 538)
Mean lunar day

variable.

h. m. S.

24 O O 2356 409

24 54 O

424. It will be explained further on (Chap. VII.) that sidereal time is reckoned from the first point of Aries, and that when the mean sun occupies the first point of Aries, which it does at the vernal equinox, the indications of the mean-time clock and the sidereal clock will be the same; but this happens at no other time, as the sidereal day is but 23h. 56m. 4s. (mean time) long, so that the sidereal clock loses about four minutes a day, or one day a year (of course the coincidence is established again at the next vernal equinox), as compared with the mean time one.

425. A sidereal clock represents the rotation of the earth on its axis, as referred to the stars, its hour-hand performing a complete revolution through the 24 sidereal hours between the departure of any meridian from a star and its next return to it; at the moment that the vernal equinox, or a star whose right ascension is oh. om. os. is on the meridian of Greenwich, the sidereal clock ought to show oh. om. os., and at the succeeding return of the star, or the equinox, to the same meridian, the clock ought to indicate the same time.

426. Sidereal time at mean noon, therefore, is the angular distance of the first point of Aries, or the true vernal equinox, from the meridian, at the instant of mean noon: it is therefore the right ascension of the mean sun, or the time which ought to be shown by a sidereal clock at Greenwich, when the mean-time clock indicates ob. om. os.

427. The sidereal time at mean noon for each day is given in the "Nautical Almanac." Its importance will be easily seen from the following rules :—

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