PRELIMINARY RULES IN NAUTICAL ASTRONOMY.

CIVIL AND ASTRONOMICAL DAY.

285. The Civil Day, or common method of reckoning time, begins at midnight, and ends the following midnight, the interval being divided into two periods of 12 hours each; the first twelve hours, from midnight to noon, are denoted by A.M. (ante meridian); the latter, from noon to midnight, are styled P.M. (post meridian); thus we say 10 A.M. when an event occurred at 10 o'clock in the morning, and 10 P.M. when it occurred at 10 o'clock in the evening.

286. The Astronomical Day begins at noon and ends at the following noon, and is later than the civil day by twelve hours. The hours àre reckoned throughout, or continuously from o1 to 24". The distinction of A.M. and P.M. is not recognised in astronomical time. Thus, 11 o'clock in the forenoon of the second of January in the civil reckoning of time corresponds to January 1 day 23 hours in the astronomical reckoning; and 1 o'clock in the afternoon of the former to January 2 days 1 hour of the latter reckoning.

287. Since the civil day commences at the midnight preceding the noon which commences the astronomical day, it is evident that the civil mode of reckoning is always twelve hours in advance of the astronomical reckoning, and hence we have the following Rule for converting civil into astronomical time.

Given civil time at ship, to reduce it to astronomical time.

RULE LXXIV.

1o. If the civil time at ship be P.M., it will also be astronomical time, P.M. being omitted.

2°. If the civil time be A.M., add twelve to the hours and subtract one from the days of the month; also omit ▲.M. The result in each case is the Astronomical Date.

EXAMPLES.

Ex. 1. May 10th, at 5h 30m P.M., civil time is 5h 30m astronomical time of the same date; because the 10th astronomical day begins at noon of the 10th civil day, and 5h 30m have elapsed since that noon. But 5h 30m A.M. civil time on May 10th is 17h 30m astronomical time on the 9th of May, for the 9th day of the month, according to the astronomical reckoning, commences at noon of the 9th civil time, and ends at noon of the 10th civil day (the hours being reckoned up to 24), and 5h 30m A.M. of the 10th is 17h 30m from noon of the 9th. Ex. 2. October 7th, at 3h 20m P.M., civil time, is October 7th, at 3h 20m astronomical time. (See 1° of Rule LXXIV.)

Ex. 3. October 7th, at 3h 20m A.M., civil date, is October 64 15h 20m astronomical date; since 7d less id is 6a, and 12a added to 3h 20m is 15h 20m. (See 2° of Rule.)

Ex. 4. January 31st, at 7h 20m P.M., civil time, is January 31st, at 7h 20m astronomical time. (Rule LXXIV, 1°.)

Ex. 5. February 1st, at 6h 18m A.M., civil date, is January 31d 18h 18m astronomical date; since February 14, diminished by 14, gives January 31d, and 12h added to 6h 18m is 18h 18m. (Rule LXXIV, 2°).

Ex. 6. What is the astronomical date corresponding to 1873, January 1st, 8h A.M. The corresponding astronomical date is 1872, December 3rd 20h. In this case the year is diminished by 1, since in diminishing the day of the month by 1, the reckoning throws us back into the last month of the previous year, i.e., the day before January 1st, 1873, also 12h added to 8h is 20h.

288. Given the astronomical date, to find the corresponding civil date.

RULE LXXV.

If the hours of astronomical time be less than 12h write P.M. after it, and it will be the required civil time; but if the astronomical time be greater than 12a, add I to the days, diminish the hours by 12 and write A.M. after it: the result will be the required civil time.

Express the following astronomical dates in civil time:

289. The earth rotates uniformly on her axis once in twenty-four hours, and thus every spot on her surface describes a complete circle, or 360°, in that space of time; hence the longitude of any place is proportional to the time the earth takes to revolve through the angle between the first meridian and the meridian of the place, and thus the longitude of a place may be expressed either in are or in time.* Longitude in arc and longitude in time are easily convertable, for since 360° is equivalent to 24h (360 ÷ 24 = 15°), 15° is equivalent to 1h, 15' to 1m, and 15" to 1"; whence

In reckoning by arc, each degree is divided into sixty minutes, and each minute into sixty seconds. In reckoning by time, each hour is also divided into sixty minutes, and the minutes into sixty seconds. But a distinct notation for each of these has been adopted, degrees, minutes, and seconds being represented by ", and hours, minutes, and seconds by hms; and care should be observed not to use the same marks for both, great confusion arising from so doing.

† A third is the name given to the sixtieth part of a second.