the mean solar day, and time thus regulated is called mean solar time, or MEAN TIME, which is that shewn by clocks and watches.

476. The sun being generally either behind or in advance of the position which he would have occupied if he had moved uniformly, mean time is in general either fast or slow, on apparent time. The correction for this irregularity, that is, the difference between the sun-dial and the mean solar clock, is called the EQUATION OF TIME. Mean time is, therefore, deduced from apparent time, by applying the equation of time. See the Nautical Almanac, p. I. or II., or

Table 62.

477. THE SIDEREAL TIME AT MEAN NOON is the right ascension of the meridian at the instant when the sun, if he moved uniformly, would be on it.

It is evident that this element, from its nature, varies uniformly; now, since the sun's R.A. varies irregularly, and since the equation of time, which is the correction that removes this irregularity, must also vary irregularly, it follows that the unequal variations of the equation of time and the sun's R.A. are together equivalent to the single and uniform variation of the sid. time at mean noon; and herein consists the great convenience of employing the sidereal time at mean noon, which has been given in the Nautical Almanac only since 1834.*

478. (1.) Let One the place of the sun, at about 4 P.M., m the place where he would be if he always moved uniformly; then M is apparent time (No. 474), m M is mean time, and m is the equation of time. The equation is here additive to app. time, as is the case from January to March, and from July to August. (See Table 62.)

(2.) Let be the first point of Aries; then, while the sun and revolve, the sun moves contrary to the diurnal rota

m

P

N

M

tion, or is always increasing his R.A., or the arc No, by nearly 1° a-day. The complete revolution of constitutes a sidereal day; that of, an apparent solar day; and that of m, a mean solar day.

After 24 sidereal hours the sun has still to describe about 1°, or one 360th part of the circle to complete it; the time necessary for which is about one 360th of 24 sidereal hours, or 4 sidereal minutes. Thus the solar day is longer than the sidereal day by about 4". The mean solar day being divided into 24 hours, the sidereal day is 23h 56m 4s of such a day.

(3.) When m is on the meridian at M, the arc M m v,

or the

*This element, which is the R.A. of a mean, or imaginary sun, is a very different thing from the R.A. of the sun at mean noon, with which it has been confounded: the latter can differ only a few seconds from the R.A. O at apparent noon, but may differ from the Sidereal Time at mean noon by the whole amount of the equation of time, or sixteen minutes.

sun's mean R.A., is the sidereal time at mean noon. When m has arrived at m in the figure, this quantity has changed by an amount proportional to the mean time M m.

The moves sometimes more quickly, at others more slowly; the point m (which is merely an imaginary situation of O, deduced by calculation, from knowing the limits within which the irregularities of its motion are confined) moves equably. Hence m, the difference of these two, changes unequally.

(4.) By No. 472 (3) the sidereal time, or place of the point, is obtained from the hour-angle of any celestial body. By applying to the place of the sid. time at mean noon, we obtain the place of m, or mean time.

Thus Mean Time is found from the hour-angle of a star.

479. Since the sun m passes over 150 of the circle in one mean hour, he arrives at the meridian of a place 15° west of N M one hour after he has passed N M, that is, at one o'clock of the time at any place, or all places, of which N M is the meridian. In like manner he passes a meridian 15° east of M one hour before he arrives at M, that is, when the time on M is 11 o'clock in the forenoon, or 23 hours after the noon of the day before.

Thus the beginning of the day, and therefore the hour or time of the day, at one place differs from that of another place by the difference of longitude of the places; the time at the easternmost of the two being in advance of, that is, greater than, the time at the other. Hence when the times proper to two places at the same instant are known, their diff. long. is determined, or the relative positions of their meridians.*

480. The Civil Day is dated from midnight, and the twelve hours are computed twice over; the Astronomical Day is dated from noon, and runs through the twenty-four hours.

Ex. 1. October 3d, 3h 18m P.M., civil time, is the same astronomical time.

Ex. 2. January 3d, 4h 25 A.M. civil time, is reckoned January 2d, 16h 25m astronomical time.

Ex. 3. April 1st, 11 A.M. is, astronomically, March 31st, 23 hours.

481. The GREENWICH DATE is the time at Greenwich corresponding to any given time elsewhere.†

The diff. long. is found as well by means of the motion of a star as of the sun, that is, by means of a clock or chronometer regulated to sidereal time, as well as by one regulated to mean time. For although the absolute interval of time employed by a star in moving from one meridian to the other is less than that employed by the sun, yet it is divided into the same number of hours, minutes, and seconds, but which are of smaller magnitude and thus the difference of time results, in numbers, the same.

Here terminates all requisite description of the terms used in the rules in the present volume. The other terms which occur in the Nautical Almanac will be described in the Theory.

In this chapter we have sometimes spoken of the earth as fixed and the heavens as movable, although this is contrary to fact, because the appearances alone furnish us with the measures of time, without any regard to the actual state of things.

Again, we have considered the earth as a sphere instead of a spheroid (No. 180). The consequences of the oblateness, in an astronomical point of view, are that the planes of the

482. It will be found a useful exercise of what has preceded to verify the following remarks:

:

(1.) No star of which the pol. dist. is less than the lat. can set; and no star of which the pol. dist. exceeds 90° plus the colat. (S M, fig. p. 144) can be visible.

(2.) When the pol. dist. is less than the lat. the star passes the meridian both above and below the pole.

(3.) When the pol. dist. is less than the colat. the star passes the meridian between the zenith and the pole, and does not pass the prime vertical.

(4.) When the declin. is 0, or the pol. dist. 90°, the body rises and sets in the E. and W. points. The hour-angle at rising and setting is 6, and the body is seen raised on the prime vertical by the effect of refraction; unless it is the moon, which, from her parallax being greater than her refraction, is not seen at the precise time of her rising and setting.

The object is above the horizon for 12 hours, and 12 hours below it.

In this case the amplitude is 0, except from the effect of refraction.

(5.) When the pol. dist. exceeds 90°, the celestial body rises and sets on that side of the E. and W. points which is farthest from the elevated pole; the hour-angle at rising and setting is less than 6o: the time during which the body is above the horizon is less than 12 hours, while it is more than 12 hours below the horizon. The body does not pass the prime vertical above the horizon; and the amplitude is reckoned towards the S. in N. lat., and towards the N. in S. lat.

(6.) When the pol. dist. is less than 90°, the celestial body rises and sets on the same side of the E. and W. points as the elevated pole; the hour-angle at rising and setting is greater than 6h. The body is more than 12 hours above the horizon, and less than 12 hours below it. The amplitude is reckoned towards the N. in N. Lat., and towards the S. in S. Lat.; the body passes the prime vertical twice. The hour-angle at the passage of the prime vertical is less than 6". (See Table 29.)

(7.) A star having a certain declination always rises and sets in the same points, and passes the meridian and prime vertical, or any other circle of altitude at the same altitude, without regard to its R. A.

circles of altitude (excepting the meridian) do not pass through the centre, and that the length of the radius, or line drawn from the centre to the place of the observer, is different in different latitudes. The first of these conditions produces no sensible effect in practice, because the Time is not affected by it, and the same Latitude (though differing from the latitude on a sphere by the quantity in Table 52) results alike from all observations, of whatever kind, of a body not affected by parallax,- and thus the oblateness, however great, would always be neglected in determining a place by observation of the stars or the sun. By the second condition the parallax of the moon is affected, and a further correction of her apparent place becomes necessary.

We have also described the first point of as fixed, whereas it has a very slow motion. The stars, also, though called fixed, have slow proper motions. These and other points not necessary to our present subject will be treated more at large in the Theory.

(8.) As the place of a star or any celestial body is determined by its R. A. and Decl., and as, at the place of the spectator, the position of the celestial equator, to which both these are referred, is fixed, it is easy to know whereabout any star is to be looked for at any time. When, as is commonly the case, the time (mean or apparent) is given, the sun's hour-angle is known; and therefore, when he is invisible, his place on the equator may be estimated. By means of the sun's place, and his R. A., the place of the first point of Aries may be estimated; then the star's R. A. gives the place of its meridian on the equator, and its declination the place of the star with respect to the equator. When the sidereal time is given, the place of the first point of is at once known, just as the place of the

sun is known from the apparent_time.*

*The position of the equator, and the relations among the Latitude of the place, the Time, and the Hour-angle, Altitude, and Azimuth of a celestial body, are best illustrated by a celestial globe. The broad horizontal rim represents the Rational Horizon (No. 420 (1)). The brass meridian of the globe being laid N. and S., and the Pole elevated, by the degrees marked on it, to the latitude (No. 448), the globe represents the celestial sphere as shewn in figs. 1, 2, p. 120. The position of the sun is found by marking the sun in his place in R. A. and Decl., by the help of the divisions on the globe, and then setting the sun at his proper hour-angle by means of the hour-circle near the pole. The Alt. or Zen. Dist. is measured by a graduated slip of brass, or by a thread, as in the note, p. 144. It is unnecessary to enter further into details, as the reader who well understands the definitions above will find no difficulty in solving any useful "problem on the globe" which can be proposed, without burdening his memory with technical rules.

In the absence of a globe, distinct ideas may be obtained of the actual positions of the celestial bodies by a circular card, as a compass-card, having the hours marked on the edge, and an axis, as a pencil, put through the centre perpendicular to the card. If this axis be laid N. and S., and the north end (in north lat.) raised up till it is inclined to the horizon at an angle equal to the latitude, it will represent the polar axis round which the celestial bodies revolve, the card representing the equator. The Oh being brought up to the meridian, the hour of the day at the edge will shew the place of the sun's meridian at the time. If the Oh be made the first point of T, the hours become hours of R.A.; if, then, the be marked on the edge, on its proper R. A., and then turned round to the position proper to the hour of the day, the place of the first point of T is seen.

Suppose, now, a small telescope were placed on the axis making an angle with the plane of the equator, or the card, equal to the declination of some star, then, while this star revolves parallel to the equator, the telescope, kept at the same angle, could at any time be directed towards the star by merely turning the axis round A large instrument is constructed on this principle, and is called an Equatoreal!

CHAPTER II.

INSTRUMENTS OF NAUTICAL ASTRONOMY.

I. THE REFLECTING INSTRUMENTS.

II. THE ARTIFICIAL HORIZON. III. THE CHRONOMETER.

I. THE REFLECTING INSTRUMENTS.

483. THESE are instruments for measuring angles between two objects, by bringing the reflected image of one of them to coincide with the other seen directly. They are necessary for observing altitudes of the heavenly bodies at sea, where the spectator has no fixed point of reference except in the horizon. On shore, and often on a field of ice, the fixed point required in observing altitudes is obtained by means of the artificial horizon.

484. The instruments of this class which are in most common use are the quadrant, sextant, and reflecting-circle. For conve nience, we shall describe the adjustments generally under the two former; and as every person in possession of an instrument will be instructed by the maker or some expert person in the names of the different parts, and also in the mode of handling it, and packing it in the case without danger of distortion, we shall confine ourselves merely to matters of general reference.

1. The Quadrant and Sextant.

485. The quadrant contains an arc of more than 45°, and measures a few degrees more than 90°;* it is usually made of wood, and the graduated arc, which is ivory, reads to minutes, and sometimes to 30". The sextant measures a few degrees more than 120°; it is made of brass, and sometimes reads to 10". The quadrant serves for common purposes at sea, but the sextant is required for taking a lunar observation.

The observer should be in the habit of employing good instruments of their kind, as inferior instruments naturally induce careless and imperfect observation.

486. The sextant made of a very small size, and thence called the Pocket Sextant, is adapted to the use of surveyors, travellers, and others, on occasions in which minute accuracy is not necessary.

*This depends on the properties of light, which will be considered in the "Theory."