To find the Latitude by the Meridian Altitude of a Fixed Star.

RULE.

I. From the Observed Altitude of the Star subtract the Correction from Table XXVII., the remainder will be the true Altitude, which being subtracted from 90°, will give the Star's Zenith Distance, which is to be called North or South, according as the observer is North or South of the Star when its Altitude is observed.

2. Find the declination of the Star by the Table of Fixed Stars, p. 432, Nautical Almanac. Then if the zenith distance and declination be both North, or both South, add them together, the sum will be the latitude of the same name with the declination; but if one be North and the other South, their difference will be the latitude, of the same name with the greater. (See N. A., p. 584.)

EXAMPLE.

1844, May 10, required the latitude where the observed meridian altitude of Arcturus, south of the observer, is 63° 24′, the height of the eye being 18 feet?

When the altitude of a Star is observed on the meridian below the Pole, the latitude is found by adding together the Star's true altitude and its polar distance. The latitude will, in this case, be always of the same name with the declination of the Star.

EXAMPLE.

1844. The altitude of y Draco, or Rastaban, observed on the meridian, below the Pole, being 14° 11', and the height of the eye 12 feet required the latitude?

The time of a Star's passing the meridian, below the Pole, is 11h. 58m. different from the time when it passes the opposite meridian; therefore 11h. 58m. being subtracted from the time of a Star's passing the meridian, as found by its R. A. from the table of Fixed Stars, p. 432 N. A. and Table XXVI., the remainder will shew the time of the preceding transit below the Pole, or if 11h. 58m. be added to the time of a Star's passing the meridian, as found above, the sum will be the time of the following transit below the Pole.

EXPLANATION

OF

THE TABLES.

TABLE A.

For converting Mean Time, Hours, &c., &c., into their Equivalents in Sidereal Time.

THE accelerations are portions of sidereal time to be added to mean time. It is also used for reducing the sidereal time mean noon, as found in the Nautical Almanac, to any other meridian. Add the acceleration in West longitude to the sidereal time mean noon; subtract it in East longitude; when the exact longitude is not found at once, it will be necessary to enter the Table, with such portions of it, as will make up the amount; and the corresponding accelerations added together, will be the acceleration for the whole longitude.

TABLE R.

For reducing Sidereal Hours, Minutes, &c., to their Equivalents in Mean Time.

'R. portions of mean time, to be subtracted.

TABLE P.

The parallax in altitude of the Planets to be deducted from the refraction corresponding to the altitude, the result is the Planet's correction of altitude. The Star's correction of altitude is the refraction. (See Example, p. 20, and Table VI.)

k

TABLE I.

To reduce Longitude into Time, or Time into Longitude.

The use of this Table will be easily understood by attending to the following Examples:

Required the longitude answering to 7h. 23m. 28s.?

This Table being chiefly intended to turn longitude into time, and the contrary, is only extended to 180°, and to 12h.; it is, however, easy to find the time answering to an arc greater than 180°, or the corresponding arc for a given time exceeding 12h.; for Example,

Let it be required to turn the arc 269° 21′ 44′′ into time?

In a similar manner may the arc be found, for any time, between 12 and 24 hours.

TABLE II.

Dip of the Horizon.

This Table contains the Dip, or Depression of the visible Horizon of the Sea, when the sight is unobstructed. The dip is always to be

back observation be used. the dip must be added to the observed altitude.

TABLE III.

Dip of the Horizon, at different Distances, from the Observer.

If the Image of the Sun, or any other celestial object, be brought in contact with the surface of the water, at any point nearer to the Observer than the most distant visible horizon, it is plain that the dip will be greater than that given in Table II.; therefore in situations near the land, when the Sun or other object is over it, the dip is to be taken from this Table. Thus, if the height of the eye of an observer be 20 feet, and his distance from the land 1 mile, the dip is 11 minutes.

The distance from the land can generally be estimated with sufficient accuracy, particularly if the distance exceeds a mile, and the height of the eye not greater than 20 feet: if the height be more than 20 feet, and distance less than a mile, it is necessary to be very exact in both the arguments.

TABLE IV.

Moon's Augmentation.

The Moon's apparent semidiameter, as given in the Nautical Almanac, is adapted to her distance from the centre of the Earth. But when the Moon is in the zenith of any place, she is nearer to an observer, in that place, than she is to the Earth's centre by about 4000 English miles (the diameter of the Earth being nearly 8000 miles), now the Moon's mean distance from the Earth's centre being about 240,000 miles, it is evident that the Moon's diameter will appear under an angle th part greater to a person who is nearer to her by 4000 miles, for 240,000 4000 = 60; and as the Moon's semidiameter, when at her mean distance from the Earth, is about 15′ 42′′, the greatest augmentation of the Moon's semidiameter will in this case be 15" 42"", that is, one 60th of 15′ 42′′. When the Moon is nearer to the Earth than her mean distance, the greatest augmentation of semidiameter exceeds 15" 42", and the contrary is the case, when the Moon's distance is greater than her mean distance from the Earth.

When the Moon is in the horizon of any place, her distance from that place is so nearly the same as the distance from the Earth's centre, that the augmentation is insensible. Supposing the Moon's distance from the Earth to remain the same, as her altitude increases she approaches an observer, and therefore, at any altitude between 0° and 90°, the augmentation will be between O", and the Moon's