peatedly and continually finding the time and correcting his timepiece by observation on celestial bodies whose apparent positions are given in the Nautical Almanac ; while in the former case he need check his chronometer only occasionally.

The time adopted in the Nautical Almanac is astronomical time reckoned from and to mean noon at Greenwich; civil time is twelve hours in advance of astronomical time; and nautical time is twelve hours in advance of civil time. Hence the nautical day ends at the noon when the astronomical day of the same date begins, or, as the sailors say, the Nautical Almanac is always a day behindhand. The nautical day, like the civil day, is divided into two periods of twelve hours, distinguished by A.M. and P.M.; but the astronomical day consists of twenty-four hours, counting from noon to noon. For example:

The civil time, April 20th, 9 o'clock A.M., is, by astronomical time, April 19th, 21 o'clock.

The civil time, April 20th, 4 o'clock P.M., is, by astronomical time, April 20th, 4 o'clock.

In the same way also:

The nautical time, July 20th, 10 o'clock A.M., is, by astronomical time, July 19th, 22 o'clock.

The nautical time, July 20th, 3 o'clock P.M., is, by astronomical time, July 19th, 3 o'clock.

(Nautical time will probably be eventually abolished.) Mean solar time (whether civil, nautical, or astronomical), being a purely artificial arrangement, based on an average day in the year, or an average interval. between two consecutive passages of the sun over the meridian of a place, instead of an actual real interval which gives apparent local time; the equation of time

(which is given in the Nautical Almanac), or difference between apparent and mean time, is the correction necessary in reducing observations made with apparent local time to mean local time; the latter may then be compared with Greenwich mean time for the same moment, and the difference between them is the longitude of the place of observation expressed in time. Apparent local time might be obtained most simply by observing the moment of transit of the sun's centre over the middle wire of a transit instrument fixed in the plane of the meridian; that moment is apparent local noon. (The observation, however, would require correction for instrumental adjustments; for this read the paragraph on the adjustment of the Transit Instrument.) The result would then be reduced to mean time by applying the equation of time; and if it is just before noon, by adding twelve hours and altering the date it is reduced to astronomical time; if, however, it is just after noon, the date and hour remain unchanged in astronomical as in civil time. At sea, where the moment of apparent local noon is important, the process is more rough; as the sun mounts in the sky to about the same altitude as it was at noon on the preceding day, the chief mate shouts to the sailing-master, 'It's topping, sir,' and the skipper gets ready his sextant; when the sun just appears to get stationary without ascending or descending, the altitude is observed with the sextant, the chronometer time is noted, and that is taking a meridian altitude at sea, and fixing local apparent noon. The more precise way of doing this is to take several observations, recording altitudes and times both just before and just after the sun tops, and to interpolate the mean as a check on the apparent noon indicated by a maximum altitude.

Sidereal time corresponds to right ascensions of celestial bodies in the same way as solar time corresponds to terrestrial longitudes, the former being reckoned from the first point of Aries, or the intersection of the ecliptic with the equator, the latter from the meridian of Greenwich; the one being convertible into the other by expressing hours, minutes, and seconds of time by their equivalents in degrees, minutes, and seconds of measure of the circle, thus 1 hour=15°, I min.=15′, I sec. = 15".

The interval between two successive transits of a star over the meridian of a place is a sidereal day, and represents correctly the time of one revolution of the earth on its axis. A sidereal day of 24 hours sidereal time is thus equal to 23h. 56m. 4'092s. of mean solar time. As right ascensions are expressed in sidereal time, observatory clocks are regulated to keep to it, and they thus show the right ascension of the meridian of the place at any moment.

If therefore a transit-instrument be correctly adjusted to the meridian of a place, the transit of a star or planet across its mean wire fixes the moment when its right ascension in time is true sidereal time for the place. The right ascensions and declinations of the principal stars and planets are given in the Nautical Almanac for various intervals of time, and can hence be interpolated for any date; the annual variation of the right ascensions and declinations of stars being small, the proportional part for any date can be obtained by applying the fraction of the year corresponding to the date; this is also given in the Nautical Almanac.

The two above-mentioned processes afford the means. of checking or correcting either local mean solar time,

X

or local sidereal time, or, using both operations, of checking one by the other and comparing the clock with the chronometer; they happen, however, generally to assume either that the meridional direction has been already carefully determined or approximately arrived at. In the case of mean solar time being required to be deduced from observations on the moon, stars, or planets, and their right ascensions given in the Nautical Almanac, it must of course be always borne in mind that the Sidereal Time of Mean Noon, or moment for comparison of time given in the Nautical Almanac for the given astronomical day, must be reduced to the local meridian by applying the acceleration due to longitude, adding it for west and subtracting it for east longitude. The reduction of the right ascensions in the Nautical Almanac to the given moment can be effected by simple proportion, even in the extreme case of the moon, whose right ascensions are given for every hour.

The method of observing the sun at equal altitudes before and after noon avoids this difficulty; it may be roughly done as follows. Set up a transit-theodolite in perfect adjustment with its vertical circle clamped to an altitude of some even number of degrees or minutes exceeding that of the sun at some time in the morning; when the sun rises to this altitude, note the time and altitude, and take some more similar observations in the morning at other convenient altitudes, without moving the instrument throughout the day; in the afternoon observe a set of times and altitudes corresponding to the former in number and altitude. The mean of the times of all the observations will be nearly apparent local noon, but a correction has to be applied on account of the change of the sun's declination in the interval between the mean

of the morning set of observations and the mean of the afternoon set.

The calculation of this correction is based on the following principle. Let SS' be a circle of declination, PZ a meridian of the place, and aaa a circle of altitude in the attached figure 39. If the declination remains un

FIGURE 39. CORRECTION FOR EQUAL ALTitudes.

changed in the interval under consideration, the polar distance PS' in the afternoon remains = PS, the polar distance in the morning; but if the declination has decreased, the polar distance P has increased, and is greater than PS; while, under contrary circumstances, Ps, the new polar distance is less than PS; the corresponding changes of declination being represented by o's' and os, and the corresponding required corrections being represented by the arcs o'S', oS' on the circle of declination; while ZP is the complement of the latitude of the place.

Then if the required correction in angular seconds d=change of declination in the interval,

P the angle SPS', and Q=polar distance PS

x=d (cotg colat x cosec

P

2

– cotg Q × cotg

xcotg).