THIRD METHOD.-(Required by the Local Marine Board at Aberdeen.) Given the apparent time of change tide, and the longitude of the - place, to find the mean time of high water, A.M. and P.M.

RULE LIII.

1o. Take out of the Nautical Almanac the moon's meridian passage on the given day, and also on the preceding day; also the moon's semi-diameter, and equation of time, for the given day (roughly).

2°.

Under head (1, 2, and 3, see examples) put down the following quantities:

Under 1.

2.

3.

The time of moon's meridian passage on proposed day, as found
in the Nautical Almanac.

Put down half the sum of these times (see examples).
The meridian passage on preceding day.

3°. Correct quantity (1) by Table XVI, Norie), by entering with longitude of place at top, and difference of times under (1) and (3) at the side; thus find the time of moon's meridian passage at the place. Take out the corrections from Table (XXIX, Norie) and place it under (1). This correction is found as follows:-Enter the Table at top with moon's semi-diameter, and at the side with moon's meridian passage, under (1) corrected by equation of time to nearest minute, so as to reduce time of moon's meridian passage, which is given in mean time to apparent time.

4°. Apply the correction thus found with its proper sign, and to the given result add the given apparent time of change tide.

(a) When the quantity under (1) is less than 12 hours.

The time thus found is the mean time of high water, P.M., for the proposed day (see example 1).

24

(b) When the quantity under (1) is greater than 12 hours, and less than hours.

Work as described above, with meridian passage under (2). Then if the result is greater than 12 hours, reject 12 hours: the remainder is mean time of high water on the proposed day P.M., (see example 2). But if the result be less than 12 hours, it will be mean time of high water A.M. on the proposed day (see example 5).

(c) When the quantity under (1) is greater than 24 hours.

Work as described above, with the meridian passage under (3). Then if the result be greater than 24 hours, reject 24 hours: the remainder will be

the mean time of high water P.M. on the proposed day (see example 4). But if the result be less than 24 hours, and greater than 12 hours, reject 12 hours: the remainder will be the mean time of high water A.M. on the proposed day (see example 5).

To find the next time of high water A.M. or P.M. If the time of high water found as above is the P.M. time, subtract therefrom the difference between the meridian passages under (1) and (2); the remainder will be the mean time of high water A.M. on the proposed day.

5°. If the time of high water is the A.M. time, add thereto the difference between the meridian passages under (1) and (2), and the sum will be the mean time of high water P.M. on the proposed day.

6°. If it be necessary to add 12 hours before this difference can be subtracted, in that case the remainder will be the mean time of high water P.M. on the preceding day; there will be no high water A.M. on the proposed day. And if in adding the difference the sum be greater than 12 hours, this sum, rejecting 12 hours, will be the mean time of high water A.M. on the following day; there will be no P.M. on the proposed day.

Ex. I.

EXAMPLES.

1865, January 6th: find the times of high water, A.M. and P.M., at Shields, longitude 1° 25′ W., change tide 3h 23m.

D's mer. passage, or transit, Jan. 6d 743m

D's semid. midnight,

6th, 15′ 51′′.

Eq. time 6m.

Sub. from mean time,

7 17

6d7h43m

7h 17m

6h 50m

Time H. W. Shields

6 10 29 A.M.

Ex. 2. 1865, October 31st: find the times of high water, A.M. and P.M. at Halifax, long. 64° W., change tide 8h.

D's mer. passage or transit, Oct. 31d 9h32m

▷'s semid. midnight,

16' 37.

Added to mean time,

30

8 38

Eq. time 16.

Ex. 3. 1865, October 31st: find times of high water, change tide 2h 2m, long. 60° E.

Ex. 4. 1865, July 21st: find times of high water, change tide 5h om, long. 31° W.

Ex. 5. 1865, March 8th: find the times of high water, change tide 2h 18m P.M. apparent time, longitude 70° E.

EXAMPLES FOR PRACTICE.

Required the times of high water in each of the following examples:

WHEN the error of a chronometer on Greenwich mean time, and also its daily rate, are known, we may determine Greenwich mean time at some other instant, as when an observation is taken, by the following:—

RULE LIV.

To the time by chronometer apply the original error, adding it if the chronometer was slow, rejecting 24h if greater than 24", and putting the day one forward; but if chronometer is fast, subtract original error, increasing time shown by chronometer by 24h if necessary, and putting the day one back.

2°. Multiply the rate of chronometer by the number of days elapsed since the original error was ascertained, and add thereto the proportionate part for the fraction of a day, found by proportion or otherwise; the result is the accumulated rate in the interval.

3°. To the result found by 1o, add the accumulated rate, if chronometer is losing; but subtract if gaining: the result will be mean time at Greenwich at the instant of observation.

EXAMPLES.

Ex. 1. 1865, January 30th, P.M. at ship, time by chronometer 29d 15h 47m 485.3, which was 10m 248.7 slow on Greenwich mean time January 1st, and losing 21 daily; required the Greenwich date by chronometer.