increased by 24 hours, whence the approximate Greenwich date is obtained by applying the longitude in time. Then, by applying a correction for the hours and minutes of the Greenwich date, a more exact value of the right ascension of the mean sun is obtained (compare Art. 68), which, when subtracted from the right ascension of the star, will give the local mean time of the star's transit or meridian passage.

EXAMPLE 1.-At what time will the star Regulus (a Leonis) be on the meridian of a ship in longitude 115° 48′ E, December 30, 1899? R. A. + 24h

SOLUTION.

34h 2m 59.6$

18h 30m 53.8$

15h 32m 5.8s

=

EXAMPLE 2.-At what time will the star Antares (a Scorpii) be on the meridian of Leghorn, Italy (longitude 10° E), on August 5, 1899?

=

8h 55m 16.7s

1m 78

8h 56m 23.7s 16h 23m 12.8s

7h 26m 49s P. M. Ans.

L. M. T. of transit, Aug. 5 NOTE.-Since the difference between these two values of the mean time does not amount to more than 2 or 3 minutes, it may, for most practical purposes, be considered sufficiently correct, in determining the mean time when a star will be on the meridian, to subtract the right ascension of the mean sun, or sidereal time at Greenwich mean noon, without correction from the right ascension of the star.

77. To Find, Approximately, the Apparent Time of a Star's Meridian Passage. It is evident that when mean time of a star's meridian passage is known, the

the

corresponding apparent time is found by applying the equation of time taken out and corrected for the Greenwich date; or, the approximate apparent time of a star's meridian passage may be found directly by the following rule:

Rule. From the right ascension of the star subtract the right ascension of the true sun, as found in the Nautical Almanac on the page marked I; the remainder is the approximate apparent time of the star's meridian passage.

EXAMPLE 1.-Find the apparent time of the meridian passage of Fomalhaut (a Pis. Aust.) on October 8, 1899.

EXAMPLE 2.-Find the apparent time of the meridian passage of Rigel (3 Orionis) on September 6, 1899.

NOTE. For observations at sea, it is advisable to select a star whose transit occurs during the morning or evening twilight, because then the sea horizon is well defined and the result will therefore be more trustworthy.

78. The preceding articles relating to the transitions of

m

n

FIG. 6

stars apply to the meridian passage above the pole, or when the celestial body is situated at S, Fig. 6, P being the celestial pole. To obtain the time of transit when the star is on the meridian mn below the pole, or at S', 12 sidereal hours (= 11h 58m 2s mean time) is added to the time given for the upper transit. For any celestial object, it can be shown that the mean time of lower meridian passage is equal to (12 + right ascension of object) right ascen

sion of the mean sun.

It is evident that the rules given

for determining the time of the meridian passage of stars

are applicable also to the planets; but, since the apparent motion of the planets is irregular, it is more convenient to find the time of their transits according to instructions given in Art. 64.

79. Cautionary Remarks.-In dealing with times of meridian passage at sea, it is well to remember that the ship's clocks that are regulated at each noon, when observations of the sun are taken, show correct apparent time at that instant only; also, that these clocks will be too fast if the ship sails westward from noon to the time of observation, and too slow if the ship sails eastward, by 4 minutes of time for every degree of longitude traversed. Hence, when the apparent time for a star's transit is determined, an appropriate allowance should be made for the ship's run by adding 4 minutes of time for each degree of longitude sailed. eastward, or by subtracting the same number of minutes for every degree of longitude sailed westward.

EXAMPLES FOR PRACTICE

1. The local apparent time of a place in longitude 81° 15′ E, April 3, 1899, is 8h 45m A. M. Required, the corresponding mean time.

2. The mean time at a ship in longitude 81° 15′ W, April 21, 1899, is 3h 5m P. M. Find the corresponding apparent time.

Ans. L. App. T., Apr. 21 = 3h 6m 22.9s

3. The mean time at a ship in longitude 36° 30′ E, June 20, 1899, is 1h 40m 42s P. M. Find the sidereal time.

Ans. Sid. time 7h 34m 29.7s

4. The Greenwich mean time August 1, 1899, is 5h 15m 25s. Find the corresponding local sidereal time at a ship in longitude 124° 37′ W. Ans. L. Sid. time 5h 37m 19.3s

=

5. On January '18, 1899, in longitude 174° 30′ E, a sidereal clock indicated 19h 26m 14s. Find the corresponding local mean time.

6. Find what bright star was the next to pass the meridian after midnight December 2, 1899, at a place in longitude 30 W.

Ans. Capella (a Auriga)

7. Find, approximately, the apparent time of meridian passage of the star Vega (a Lyræ) on June 30, 1899. Ans. 11 56.8m P. M.

8. What stars of the first magnitude will cross the meridian of an observer in longitude 124° 30′ E between 8:30 and 9:30 P. M. on March 2, 1899? Procyon (a Canis Minoris) Pollux (3 Geminorum)

Ans.

LATITUDE

DETERMINATION OF LATITUDE

LATITUDE BY MERIDIAN ALTITUDE

1. The simplest and most reliable method of determining the latitude of a ship at sea is that deduced from an observed meridian altitude of a celestial body. Three distinct reasons may be put forth in support of this statement: first, that the measurement of a meridian altitude of a celestial body, particularly the sun, can, as a general rule, be made with the utmost accuracy; second, that an error in the estimated longitude and, consequently, in the time, has no appreciable effect on the resulting latitude; third, that the necessary calculations are few and simple.

2.

Desirable Objects for Latitude Observations. The most desirable object to select for latitude observations is the sun, which is on the meridian of the ship at apparent noon each day. Hence, when the weather permits, the opportunity of measuring the sun's altitude at that instant should never be disregarded at sea.

A star of known declination is also a very suitable object provided the observer has sufficient training in measuring altitudes at night. With the star's appearance, the sea horizon generally becomes too obscure to be sufficiently well defined, and, as a rule, it requires considerable practice before altitudes of stars as measured from the sea horizon can be considered trustworthy. It goes without saying that only stars of the first and second magnitudes should be used for Copyrighted by International Textbook Company.

214

Entered at Stationers' Hall, London