3°. In West longitude.-ADD longitude in time to ship time-the sum if less than 24 hours, is the corresponding Greenwich date on the same day with the ship date; if greater than 24 hours, reject the 24 hours, and put the day one forward.

4. In East longitude.--From ship astronomical time SUBTRACT longitude in time, if less than the hours, minutes, &c., of ship date—the remainder is the corresponding Greenwich date in the same day as the ship date; if the longitude in time be greater than the hours, minutes, &c., of ship astronomical, ADD 24 hours to the latter, and put the day one back before the subtraction is made.

5°. When it is noon at the place.-The longitude in time, if west, is the Greenwich date (apparent time); but if east, SUBTRACT the longitude in time from 24 hours, the remainder is the Greenwich date (apparent time) after noon of the preceding day.

A bad habit prevails in writing dates, of separating the month and day from the hours, minutes, and seconds. The day of the month should always precede the minor divisions of time which give the precise instant of the day intended.

EXAMPLES.

Ex. 1, November 9th, at 4h 10m P.M., apparent time at ship, longitude 32° 45′ W.: required the corresponding time at Greenwich, or the Greenwich date.

In example 4, the added longitude changes the day of the month; and in example 5, also, a day for 2 hours) is borrowed before the subtraction is made, since the longitude in time exceeds the astronomical ship date.

U

Ship date (M.T.) 1873, Jan. 1d 3h40m20s Ship date (M.T.) 1871, Dec. 31d 21h 1m os Longitude 95° 7′ E.

In example 10, the hours, &c., of longitude to be subtracted are to be taken from a borrowed day, thus making the day of the month at Greenwich one less than at the place. See Rule LV, (5)

Required the Greenwich date in each of the following examples :

1872, January 6th, at 3h 40m 168 P.M., apparent time, long.

3 A.M.

22 P.M.

35 A.M.

5 A.M. mean time, long. 158 10 。 W. 33 P.M. apparent time, long. 170 55 15 E.

I A.M.

32 P.M. apparent time, long, 100 17 30 E
mean time, long. 148 47 30 W.
mean time,
long. 50 40 。 E.
apparent time, long. 178 51
apparent time, long. 153

REDUCTION OF ELEMENTS FROM NAUTICAL ALMANAC.

THE Nautical Almanac contains the right ascension, declination, &c., of the principal heavenly bodies for certain fixed times at Greenwich; the right ascension and declination of the sun and planets, for example, being given for every day at noon (oh om o), while for the moon these elements are given for every hour. At a place under any other meridian than that of Greenwich, or at any other time of the day than that for which any quantity is given, it is requisite to apply a correction to that taken from the Almanac, in order to reduce it to its value at the given instant. For this purpose we may either apply the common rules of proportion, or, which is in general the simplest method, make use of certain tables computed for the purpose, called tables of proportional logarithms.

TO REDUCE SUN'S

DECLINATION.

The declination of the sun is given in the "Nautical Almanac," pages I and II of each month, for every day both for apparent and mean noon at Greenwich. The difference of declination for one hour ("Diff. for 1 hour") is always annexed, and is intended to facilitate the reduction of the quantities from noon to any other time.

METHOD I.-By hourly difference.

RULE LVI.

1o. Get a Greenwich date by means of ship time, expressed astronomically, and longitude (see Rule LV, page 144), or by means of chronometer.

2°. Take out of Nautical Almanac the declination at noon of Greenwich date, noting whether the declination is increasing or decreasing; and a little to the right place the "difference for 1 hour," found in page I, N.A.

(a) When Greenwich date is given in apparent time, use page I of the month, but for mean time, use page II of the month.

(b) The tenths of seconds (") of declination may be rejected when less than five, but call them 1" when they amount to five, or above-thus 42" 7 would be 43".

3°. Multiply the "Hourly Diff." by the hours and fractional parts of an hour of Greenwich date; the product reduced to minutes and seconds is the change of declination in the time from noon.

To express the Greenwich time in hours and decimals of an hour. Divide the minutes by 6, and consider the quotient as tenths of an hour, and to this prefix the hours. For example, let it be required to express 7h 18m in hours and decimals of an hour. Then 6 is contained in 18 three times to this prefix the hours (7) and we have 7'3 hours.

4. Apply this change to the declination at noon adding it when declination is increasing, but subtracting it when declination is decreasing; the result is the declination sought.

(a) If the proportional part when subtractive exceed the declination itself, subtract the declination from the proportional part: the remainder is the declination of the contrary name.

In March when the declination changes from South to North, and in September when it changes from North to South, if the correction, by being subtractive, exceed the declination, subtract the declination from the correction, and call the remainder N. in March, but S. in September. See example 3.

METHOD II. By proportional logarithms.

1°. Find a Greenwich date.

RULE LVII.

2. Take out of the Nautical Almanac the declination for the noon at Greenwich, and that following it.

3° When the declinations are of like names, take their difference; but when of different names, take the sum: this is the daily variation of declination.

(a) When the declination is increasing, place the sign of addition (+) before the daily variation; but when the declination is decreasing, place the sign of subtraction (-) before it.

4. Under the daily variation place the hours and minutes of Greenwich time, and take from the table (Table XXI A, Raper, or XXXIII, Norie,) log. of change of declination in 24 hours and log. of hours and minutes of Greenwich time; the sum of these logs. found in the table will give the proportional part of daily change of declination.

(a) When the seconds of time (in Greenwich date) are less than 30, they may be rejected; but if above 30s, increase the minutes of time by 1m; thus Greenwich time 2h 35m 40s would in using the tables, be called 2h 36m.

(b) In using Table XXI A, Raper, or Norie XXXIII, minutes (') of declination, and hours of time (1), are found at the top of the columns; seconds (") of declination, and minutes (m) of time, at the side columns.

5° Apply the proportional part to the declination at the first noon, adding when the declination is increasing; but subtracting when the declination is decreasing; the result is the declination at the time required.

Ex. 1.

EXAMPLES.

1872, January 13th, at 3h 54m 16a P.M., app. time at ship, long. 30° 4′ E. : find the sun's declination.

Having found the Greenwich date, the sun's declination is taken from the Nautical Almanac, where it is found in page I of the month (the Greenwich date being in app. time), and on the same page and in column headed "Hourly diff." is found the change of declination for 1 hour past noon; next observe that the declination is decreasing and make a note of it. Now since the declination changes 25" 23 in 1 hour past noon, how much does it change in the Greenwich time past noon, viz., 1h 54m? First annex a cypher to the minutes (54) and divide by 60; thus 60 is contained in 540 nine times and nothing over. To this we prefix the hour, and we then have the Greenwich time 1h 54m = 14'9 expressed in hours and decimals of an hour. (See Rule VI, page 33). Set this under the hourly diff. and then proceed as in multiplication of decimals, the resulting figures are 47937, but as we have two decimals in the multiplicand and one place in the multiplier, in all three places, three figures are to be marked off from the right hand leaving 47", but as the first figure to the right of the decimal point exceeds 5, we increase the seconds by 1", whence the correction of decl. is - 48. (See Rule III, p. 26). 1872, May 21st, at 7h 50m A.M., mean time at ship, long. 149° 30′ E,: required the sun's declination.

Ex. 2.