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5. To find the moon's hour angle.

To right ascension of mean sun add ship mean time, and from the sum (increased if necessary by 24 hours), subtract the moon's right ascension; the result is the moon's hour angle (rejecting 24 hours, if greater than 24 hours).

6. To find the moon's true altitude.

Under the latitude put the moon's declination, take the sum if the names be unlike, and the difference if the names be alike, call the result v. Add together the constant quantity, 6.301030, log. cos. latitude, log. cos. moon's declination, and log. haversine of moon's hour angle, reject 30 from the index, and look out the result as a logarithm, and take its natural number. To this natural number add the versine of the quantity v, found as above; the sum is the versine of the moon's true zenith distance, which find in the table and subtract from 90°; the result is the moon's true altitude.

To find the moon's apparent altitude.

Consider the moon's true altitude just found as the apparent altitude; enter the table with it, and take out the correction in altitude thus approximately; subtract this correction from the moon's true altitude, and thus get the moon's apparent altitude nearly. Then enter the table again with this corrected altitude, and thus take out the correction in altitude more exactly; subtract this correction from the moon's true altitude, and the result will be the moon's apparent altitude very nearly.

Take out at the same opening of the table the auxiliary angle A.

Correct the moon's semidiameter for augmentation. Then proceed as in arts. 6, 8, 9, p. 211.

EXAMPLE.

August 19, 1843, in lat. 50° 48′ N., and long. by account 1o 6′ W., when a chronometer showed 11h 10m 195.8 A.M.,

the observed distance of the nearest limb of the sun and moon was 76° 51′ 26′′, the error of the chronometer on ship mean time being fast 7m 29s.3, and the index correction 1'55"; required the longitude.

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Vers. sun's zen. dist. . . 0221634 Vers. moon's zen. dist.

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Sun's zenith dist.

38° 53′ 20" Moon's zenith dist.. 56° 46' 21

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(209.) September 16, 1843, in latitude 50° 48′ N., and long. by account, 1° 6′ W., when a chronometer showed 9h 34m 65.6 A.M., the observed distance of the nearest limb of the sun and moon was 96° 26′ 18′′, the index correction being+1' 32", and the error of chronometer on ship mean time being fast 7m 59s, required the longitude.

Ans., 1° 35' 30" W.

(210) October 14, 1843, in lat. 50° 48' N., and long. by account 1° 6' W., when a chronometer showed 9h 53m 57s.1, A.M., the observed distance of the nearest limb of the sun and moon was 114° 58′ 22′′, the error of the chronometer being slow 3m 27s, and the index correction + 1' 32"; required the longitude. Ans., 1° 30′ 30′′ W.

(211.) October 16, 1843, in lat. 50° 48' N., and long. by account 1° 6' W., when a chronometer showed 9h 58m 9s.8 A.M., the observed distance of the nearest limb of the sun

and moon was 91° 45′ 38′′, the error of the chronometer being slow 3m 26s.5, and the index correction + 1′30′′ required the longitude. Ans., 1° 31′ 30′′ W.

(212.) August 17, 1843, in lat. 50° 37′ 30′′ N., and long. by account 1° 6' W., when a chronometer showed 10h 42m 28s7 A.M., the observed distance of the nearest limb of the sun and moon was 99° 22′ 35′′, the error of the chronometer on ship mean time being fast 7m 443, and the index correction + 1' 55"; required the longitude.

Ans., 1° 17′ W.

(213.) May 25, 1843, in lat. 50° 48′ N., and long. by account 1° 6' W., when a chronometer showed 11h 19m 15s.1 A.M., the observed distance of the nearest limb of the sun and moon was 42° 48′ 48′′3, the error of the chronometer on ship mean time being slow 3m 29s-7, and the index correction + 3' 30; required the longitude.

Ans., 1° 5′ 45′′ W.

(214.) May 25, 1843, in lat. 50° 37′ 30′′ N., and long. by account 1° 6' W., when a chronometer showed 11h 4m 12s.2 A.M., the observed distance of the sun and moon's nearest limb was 43° 1′ 3′′, the error of chronometer on ship mean time being fast 12m 538.5, and the index correction +0' 57"; required the longitude. Ans., 1° 33' W.

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