BOOK VI.

CONTAINING

Various Methods of finding the Latitude of a Place, and the Variation of the Compass.

CHAP. I.

of finding the Latitude of a Place.

INTRODUCTION.

THE situation of a place, with respect to the equator, was anciently determined, by ascertaining the length of the longest day, and by the comparative length of the shadow of a Gnomon at that time. This instrument was afterwards used in many astronomical observations, such as for determining the obliquity of the ecliptic, the times of the tropics and equinoxes, the length of the year and seasons, &c. The method of reckoning the latitude in degrees and minutes being introduced, instruments for observing altitudes were divided accordingly. The Astrolabe, (a circular ring, having a moveable index and sights, was applied to observe altitudes at sea. It was, however, supplanted by the Cross Staff, and that again by the Quadrants of Davis and Hadley, in succession.

The most simple, and at the same time the most accurate method of determining the latitude of a place, is by an observation of the meridian altitude of the Sun, or of any other of the celestial bodies; and, therefore, such observations should not be neglected, when possible to be observed. It, however, frequently happens, that the meridian altitude cannot be observed, by reason of clouds, fog, &c.;

or

or that the declination of the object is unknown. In these cases, therefore, recourse must be had to other methods.

PROBLEM I.

Given the Sun's Meridian Altitude, to find the Latitude of the Place of Observation.

RULE.

Find the true altitude of the Sun's center, by Prob. x. page 104. Call it S or N, according as the Sun is south or north at the time of observation, which, subtracted from 90°, will give the zenith distance of a contrary denomination.

Reduce the Sun's declination to the meridian of the place of obser vation, by Prob. v. page 99. Then, the sum or difference of the zenith distance and declination, according as they are of the same, or of a contrary denomination, will be the latitude of the place of observation, of the same name with the greater*.

EXAMPLES.
I.

October 17, 1810, in longitude 32° E. the meridian altitude of the Sun's lower limb was 48° 53' S. height of the eye 18 feet. Required the latitude?

November 6, 1811, in longitude 158° W. the meridian altitude of the Sun's lower limb was 87° 37'N. height of the eye 12 feet. Required the latitude?

*A method very often practised at sea, especially by coasters, is, to correct the observed altitude, by adding 12′; and from thence, and the declination, the latitude is to be found. Or, subtract the altitude from 89° 48', and the declination applied to the remainder will be the latitude. These methods may no doubt give the latitude tolerably exact in some cases, but in others, the mariner will be deceived above half a degree; and in any case they are seldom free of error.

VOL. I.

2 s

Mer.

Mer. alt. Sun's 1. limb 87° 37′ N. O's dec. p. N. Alm. 15° 48'.8S.

Semidiameter

Dip and refraction

3.3

Reduced declination 15 56.4S.

The dip of the horizon, in Table 111. answers to a free or unobstructed horizon; but if the land intervenes, and the ship at no great distance therefrom, the dip will be considerably greater, and that in proportion to the nearness of the ship to the land. This dip may be found as follows:

Let two persons observe the Sun's altitude at the same instant, the one being as near the mast head as possible, and the other on deck immediately under. Then to the log. of the sum of the heights of the observer above the sea, add the ar: co. of the log. of their difference, and the log. sine of the difference of altitude; the sum will be the log. sine of an arch. Now, half the sum of this arch, and the difference of altitude, will be the dip answering to the greatest height; and half their difference will be that corresponding to the height of the lowest observer.

If the distance of the ship from the land is known, the dip may found in Table 1v.

This remark, in a similar case, is to be applied to the following problems.

EXAMPLE.

Being close in with the land, September 28, 1812, a person on deck, 16 feet above the water, observed the meridian altitude of the Sun's lower limb to be 29° 51'S. and another observer on the cross trees 68 feet above the sea, found the altitude at the same instant to be 30° 8'S. Required the latitude?

Given the Meridian Altitude of a Fixed Star, to find the Latitude of the Place of Observation.

RULE.

Reduce the observed to the true altitude, by Prob. Ix. page 103, and find the star's zenith distance. Take the declination of the star from Table LII, and reduce it to the time of observation. Now, the sum or difference of the zenith distance and declination, according as they are of the same, or of a contrary name, will be the latitude of the place of observation.

EXAMPLE.

December 1, 1812, the meridian altitude of Sirius was 59° 50′ S. height of the eye 14 feet. Required the latitude?

Given the Meridian Altitude of a Planet, to find the Latitude of the Place of Observation.

RULE.

Compute the true altitude of the planet, as directed in last problem*. Take its declination from the Nautical Almanac, and reduce

Being sufficiently accurate for correcting altitudes observed at sea.

2s 2

it

it to the time of observation. Then the sum or difference of the zenith distance and declination of the planet will be the latitude as before.

EXAMPLE.

April 25, 1812, the meridian altitude of Saturn was 68° 42′ N. and height of the eye 15 feet. Required the latitude?

Given the Meridian Altitude of the Moon, to find the Latitude of the Place of Observation.

RULE.

Take the number from Table xx. answering to the given longitude, and daily variation of the Moon's passing the meridian; which being applied to the time of transit at Greenwich, by addition or subtraction, according as the longitude is west or east, will give the time of passage over the meridian of the ship.

Reduce this time to the meridian of Greenwich, and find the Moon's declination answering thereto, by Prob. vII. page 102, and the horizontal parallax and semidiameter, by Prob. vIII.

Correct the observed altitude of the Moon's limb, by Prob. xi. page 105. Hence, the Moon's zenith distance will be known; the sum or difference of which, and the declination, will be the latitude of the place, as before.

EXAMPLE.

June 21, 1812, in longitude 30° W. the meridian altitude of the Moon's lower limb was 81° 15′ N. height of the eye 16 feet. Required the latitude?