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RULE. Turn the longitude of the place under the known meridian into time (X. 265.): add this time to the time at the given place if the longitude be west, or subtract it if east, and the sum or remainder will be the time at Greenwich. If the sum exceed 24 hours, subtract 24 hours from it, the remainder will shew the time at Greenwich on the following day: if the longitude, when turned into time, cannot be subtracted from the time at the given place, add 24 hours to the time at the given place before you subtract, the remainder will shew the time on the preceding day.

EXAMPLE I.

Find the time at Greenwich, on the 12th of August, when it is 7h.25' at a place in longitude 97°.45' west.

Time at the given place 7h.25

Long. 97°.45', in time

Time at Greenwich

= 6.31 W.

13. 56. or 56 minutes

past 1 in the morning on the 13th of August.*

EXAMPLE II.

Find the time at Greenwich, on the 1st of May, when it is 22h.40′ at a place in longitude 160° W.

Time at the given place 22h.40'.

Long. 160°, in time

10.40 W.

Sum 33 .20

24

Time at Greenwich 9.20, on May 2d.

EXAMPLE III.

Find the time at Greenwich, on the 8th of April, when it is 16 .26′ at a place in longitude 98°.45′ East.

the same time. Now, the longitudes of all places on the earth are reckoned on the equator, which is divided into 360 degrees, and the whole of it passes the sun in 24 hours; it follows that every 15° of motion is one hour in time, every degree 4 minutes, &c. (as in Prob. I. and II.) Hence, a place one degree eastward of Greenwich will have noon, and every hour of the day, four minutes sooner than at Greenwich; and a place one degree westward of Greenwich will have noon, and every hour of the day, four minutes later.

*The astronomical day begins at noon, and is counted forward to 24 hours, or the succeeding noon, when the next day begins, being 12 hours later than the civil day, which commences at the preceding midnight; thus August 12th, at 13h.56′ astronomical time, is August 13th at 1h.56' in the morning, according to civil reckoning.

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Find the time at Greenwich, on the 4th of June, when it is 5h. 26′ at a place in longitude 120° East.

Time at the given place + 24h. =29h.26′

Long. 120°, in time

Time at Greenwich

of June.

PRACTICAL EXAMPLES.

= 8.-E.

21 .26, on the 3d

1. What Greenwich time answers to noon at a place in 60° East longitude?

Answer. 20 hours, on the preceding day.

2. What Greenwich time answers to noon at a place in longitude 60° West?

Answer. 4 hours.

3. Find the time at Greenwich when it is 19h.42' at a place in 28°.30' E. longitude.

Answer. 17.48'.

PROBLEM IV.

(A) Given the time at Greenwich to find the corresponding time under any known meridian.

RULE. Turn the longitude of the place under the known meridian into time (X. 265.): add this time to the time at Greenwich if the longitude be east, or subtract it if west, and the sum or remainder will be the time under the known meridian. If the sum exceed 24 hours, subtract 24 hours from it, the remainder will shew the time at the given meridian on the following day if the longitude, when turned into time, cannot be subtracted from the given time at Greenwich, add 24 hours to the time at Greenwich before you subtract, the remainder will shew the time on the preceding day.

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EXAMPLE I.

When it is 9h.51′ at Greenwich, on the 8th of April, what hour is it in longitude 98°.45' East?

Time at Greenwich 9h.51'

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Time in long. 98°.45′ E. 16.26, on April 8th.

EXAMPLE II.

When it is 21h.26′ at Greenwich, on the 3d of June, what hour is it at a place in 120° East longitude?

Time at Greenwich
Longitude 120°, in time

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21h.26'

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Time in longitude 120° E. = 5. 26, on June 4th.

EXAMPLE III.

When it is 13h. 56' at Greenwich, on the 12th of August, find what hour it is at a place in longitude 97°.45' West. Time at Greenwich 13h. 56'

Longitude 97°.45', in time 6. 31 W.

Time in longitude 97°.45′ W. =7.25, on the 12th of
August.

EXAMPLE IV.

When it is 9h.20' at Greenwich, on the 2d of May, what hour is it at a place in longitude 160° West?

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+24h.33h, 20'

10.40 W.

22. 40, on the

Time in longitude 160° W.

1st of May, or 40 minutes past 10 in the morning on the 30th of April.

PRACTICAL EXAMPLES.

1. When may an emersion of the first satellite of Jupiter be observed at Bombay, in longitude 72°.54'.30" E. which, by the Nautical Almanac, happens at Greenwich on the fourteenth of January 1822, at 61.237.33′′.

Answer. 11.15'.11".

2. What is the expected time of the beginning of the Lunar eclipse, which happens on August 2d, 1822, at 10h.51'.40" at Greenwich, in longitude 76°.49'.30" West?

Answer. 5.44'.22".

PROBLEM V.

(B) Toreduce the declination of the sun, as given in the Nautical Almanac, to any other meridian, and to any given time of the day. RULE. The corresponding time at Greenwich being ascertained (Z. 266.), find the change of the sun's declination in 24 hours from the Nautical Almanac: Then, 24 hours this change:: the time from noon at Greenwich: the variation of the sun's declination in that time.

This variation must be added to the sun's declination at noon*, or subtracted from it, according as the declination is increasing or decreasing.

NOTE. By a similar process the change of the sun's longitude, or of right ascension, may be determined for any given time, or at any given place; and also the declination of a planet.

EXAMPLE I.

Required the sun's declination at noon, on the 12th of October 1822, at Glasgow, longitude 4°.15' W.

First, 4°.15'-17minutes, the time by which the clocks at Glasgow are slower than at Greenwich; hence when it is noon at Glasgow, it is Oh∙17′ at Greenwich.

O's declination at noon October 12th, Naut. Alm. is 7°.17′.34′′
O's declination at noon October 13th, Naut. Alm. is 7°.40'. 8"

Increase of declination in 24 hours

22′.34"

Then 24h 22'.34"::17: 16" the increase of the sun's declination in 17 minutes of time; consequently when it is noon at Glasgow, the sun's declination is (7°.17.34"+16")7°.17.50" South.

EXAMPLE II.

What is the sun's right ascension, June 5th 1822, at 13h.48'. in longitude 63°.10'E.?

Time at the given place
Longitude 63°.10', in time

Time at Greenwich

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13h. 48'. = 4.12.40′′ E.

9.35.20

O's right ascension at noon June 5th, Naut. Alm. is 4h.51′.21.7
O's right ascension at noon June 6th, Naut. Alm. is 4h.55′ 28′′.6

Increase of right ascension in 24 hours

4. 6".9

* The sun's longitude, right ascension in time, and declination are given, in the IId page of the Nautical Almanac, for every day in the year, at noon, calculated for the meridian of Greenwich.

Then 24h: 4.6′′.9 :: 9.35′.20": 1′.38′′.6
O's right ascension at noon, June 5th,

Variation of the right ascension, add

4h.51'.21".7
1.38.6

O's right ascension at 13h.48′ in long. 63°.10' E. 4.59'. 0.3

PRACTICAL EXAMPLES.

1. Required the sun's declination on the 25th of August 1822, at 8h.20', in longitude 48° West.

The declination at Greenwich, at noon, (by the Nautical Almanac) being 10°.53'.35" N. and on the 26th, 10°.32′.50" N. Answer. 10°.43′.37". N.

2. Required the sun's right ascension at noon, on the 25th of May 1822, in longitude 124° East.

The right ascension at Greenwich (Naut. Alm.) being 4.6'. 31", and on the 24th of May, 4h.2.29".

Answer. 4h.5'.29".

3. Required the sun's declination January 24th, 1822, at 181.40' in longitude 132° East.

The declination at Greenwich, at noon, (Naut. Alm.) being 19°.16.13′′ South, and on the 25th, 19°.1'.38" S.

Answer. 19°.10.14" S.

4. Required the sun's right ascension on the 16th January 1822, at 18.48', in longitude 68° West.

The right ascension at Greenwich, at noon, (Naut. Alm.) being 19h.51'.30", and on the 17th, 19h.55.47".

Answer. 19h. 54′.2".

PROBLEM VI.

(C) To reduce the declination of the moon, as given in the Nautical Almanac, to any other meridian, ana to any given time of the day.

RULE. Find the time at Greenwich corresponding to the time at the given place. (Z. 266.) Take the change of the moon's declination in 12 hours from the Nautical Almanac. Then, 12 hours: this change:: the time at Greenwich: the variation of the moon's declination in that time. This variation must be added to the moon's declination (at noon or midnight) if the declination be increasing, or subtracted if the declination be decreasing.

NOTE. By a similar process the change of the moon's right ascension*, semidiameter, and horizontal parallax may be ascertained for any given time, or at any given place.

* The moon's age and time of passage over the meridian of Greenwich are

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