time, we must say as 12 is to its variation in 12, so is the proposed time to the variation due to that time.

In like manner must the moon's semidiameter be reduced, by proportion to the time of observation, since it sensibly varies in the course of a few hours. We shall begin, therefore, with finding in this way the true horizontal parallax and semidiameter for the time of observation, reduced to the meridian of Greenwich.

Longitude of the ship in time 5h 10m after Greenwich time.

Hor. par. at noon (Naut. Alm.) 58′ 17′′ Semidiam. at noon

15' 53"

Hor. semidia. at reduced time 15 55.7" | Hor. par. at reduced time 58 26.5

These two examples will serve for specimens of the corrections to be applied to an observed altitude, in order to deduce from it the true altitude of the body's centre. In the case of the moon, the corrections, when the utmost accuracy is sought, are rather numerous, as the last example shows. But, in finding the latitude at sea, it is usual to dispense with some of these, more especially with the corrections for temperature, for the contraction of the moon's semidiameter, and for the spheroidal figure of the earth; because an error of a few seconds in the true altitude will introduce no error worth notice in the resulting latitude. When, however, the object of the observers is to deduce the longitude of the ship, all the data, furnished by observation, should be as accurate as possible; for the problem is one of such delicacy that by neglecting to allow for the influence of temperature would alone introduce in some cases an error of from 30 to 40 miles in the longitude.

When the object observed is a star, several of the foregoing correc

tions vanish: the only corrections, in this case, requisite are those for dip and refraction, modified as usual for the temperature.

(78.) To determine the latitude at sea from the meridian altitude of any celestial object whose declination is known.

The determination of the latitude, by a meridian altitude, is the easiest, and in general the safest, method of finding the ship's place on the meridian; for both the observations and the subsequent calculations being few, they are readily performed, and with but little liability to error in the result; this method, therefore, is always to be used at sea, unless foggy or cloudy weather render it impracticable.

The declination of the object observed is supposed to be given in the Nautical Almanack for the meridian of Greenwich; it may therefore be reduced to the meridian of the ship, by means of the longitude by account, which will always be sufficiently accurate for this purpose, although it should differ very considerably from the true longitude, because declination changes so slowly that even an error of an hour in the longitude would cause an error in the declination too small to deserve notice.

Having then thus found the distance of the object from the equinoctial, and having, by means of the observed altitude properly corrected, obtained the distance of the same object from the ship's zenith, the distance of the zenith from the equinoctial, that is, the latitude, immediately becomes known.

1. Let S be the object observed, the zenith Z being to the north of it, and the object itself north of the equinoctial EQ, then the latitude EZ is equal to the zenith distance, or coaltitude ZS + the declination, and it is north.

2. Let S' be the object, still north of the equinoctial, but so posited that the zenith is south of it, then the latitude EZ is equal to the difference between the zenith distance S′Z, and declination S'E, and is still north.

3. Let now the object be at S", south of the equinoctial, and the zenith to the north of the ob- s ject, then the latitude EZ is equal to the difference between the zenith distance S"Z and declination S"E, and it is north.

We have here assumed the north to be the ele

E

S

vated pole, but if the south be the elevated pole, then we must write south for north, and north for south. Hence the following rule for all

cases.

Call the zenith distance north or south, according as the zenith is north or south of the object.

If the zenith distance and declination be of the same name, that is, both north or both south, their sum will be the latitude; but, if of different names, their difference will be the latitude, of the same name as the greater.

EXAMPLES.

1. If on the 2d of May, 1833, the meridian altitude of the sun's lower limb be 47° 18', height of the eye 20 feet, and longitude by account 32° E.: required the latitude, the sun being south at the time of observation.

Observed alt. of O's L. L.

Dip. of the horizon

App. alt. of O's L. L.

47°18' 0"

4 17

46 13 43.

The longitude in time is 2h 8m east, so that time at Greenwich is 2h 8m before the noon of the 2d of May; hence, to find the corresponding declination, we have, by the Nautical Almanack,

24h: 2h 8m:: 18′ 1′′ : 1′38′′;

so that, 1′ 38′′, the variation in 2h 8m, must be subtracted from 15° 23′ 21" N., the declination of the sun on May 2, at noon; hence the proper declination is 15° 21′ 43′′ N.

2. On the first of January, 1820, the meridian altitude of Capella was 27° 35', the zenith being south of the star, and the height of the eye 22 feet; required the latitude.

3. On the 19th of February, 1823, the ship being in longitude 40° W., the observed meridian altitude of the moon's lower limb was 55° 6'; the zenith north of the moon; and the height of the eye 16 feet: required the latitude.

Here the time of observation at the ship is not given, it must therefore be calculated, and we have these data for this purpose, viz. that the ship is 40° W. of Greenwich, and that the moon is on its meridian. The following process therefore immediately suggests itself.