TO FIND THE LATITUDE BY OBSERVATION.

THE latitude of a place, being its distance from the equator, is measured by an are of the meridian contained between the zenith and the equator; hence, if the distance of any heavenly body from the zenith when on the meridian, and the declination of the object, be given, the latitude may be thence found.

The meridian zenith distance of any object may be found by observing its altitude when on the meridian, or by observing one altitude taken at a given hour from passing the meridian, or by two altitudes taken out of the meridian and the elapsed time between the observations. Each of these methods will be explained by proper

examples.

Altitudes of the sun and moon, taken at sea, require four corrections in order to obtain the true altitude of their centres; these are for semidiameter, dip, refraction, and parallax.* When a planet or star is observed, the, corrections for dip and refraction only are to be applied, as the semidiameter and parallax of a planet are but a few seconds, and may be neglected in finding the latitude at sea.

In a fore observation with a quadrant, sextant, or circle, the semidiameter is to be added if the lower limb is observed, but subtracted if the upper limb is observed. The dip and refraction are to be subtracted, and the parallax to be added, and the true central altitude will be thus obtained, which, being subtracted from 90°, will give the true zenith distance.

In a back observation with a quadrant, the semidiameter is to be subtracted if the lower limb is observed, but added if the upper limb is observed. The dip and paral lax are to be added, and the refraction subtracted, and the central altitude will be obtained, which, being subtracted from 90°, will give the true zenith distance.

In a back observation with a sextant or circle, by measuring the supplement of the altitude, (by bringing the lower limb of the image of the object to touch the back horizon,) the semidiameter and refraction must be added to the true altitude given by the instrument, and the dip and parallax subtracted therefrom, and, by subtracting 90° from the remainder, the true zenith distance will be obtained.

To find the latitude by the meridian altitude of any object.

Having obtained the true meridian zenith distance by either of these methods, you must then find the declination of the object at the time of observation. This may be found for the sun by the Nautical Almanac, or by means of Tables IV. and V., in the manner before explained. The declination of a fixed star may be easily found by inspection in Table VIII, or from the Nautical Almanac. The declination of the moon or a planet may be found, in the Nautical Almanac, in a manner which will be hereafter explained. Having the meridian zenith distance and declination, the latitude is to be found by the following rules.

CASE I.

When the object rises and sets.
RULE.

If the object bear south when upon the meridian, call the zenith distance north; but if the bearing be north, you must call the zenith distance south. Place the zenith

The semidiameter of the sun may be found in the Nautical Almanac, and is nearly 16'. The sun's parallax is found in Table XIV.; the refraction in Table XII.; the dip in Table XIII. The semidiameter and parallax of the moon may be found from the Nautical Almanac, as will be explained hereafter. It may also be observed, that it is usual to add 12' for the correction for semidiameter, dip, and parallax, in a fore observation of the sun's lower limb, taken upon the deck of a common-sized vessel; and, by subtracting the refraction from the sum, the true altitude will be obtained, nearly; and it ought always to be kept in mind, that the refraction at low altitudes is of too much importance to be neglected.

In this rule, the sun is supposed to be the fixed point, and the zenith is referred to it. Thus, if the sun bears south from an observer (or from his zenith). the zenith bears north from the sun; and it is this

distance under the declination, and, if they are of the same name, add them together but if they are of different names, take their difference; this sum or difference will be the latitude, which will be of the same name as the greatest number.

CASE II.

When the object does not set, but comes to the meridian above the horizon twice in 24 hours. Many stars are always above the horizon of certain places of the earth, and, in high latitudes, the sun is sometimes above the horizon for several days, in which case the meridian altitude may be observed twice in 24 hours; that is, once at the greatest height above the pole, and again at the lowest height upon the meridian below the pole. In the former case, the latitude is to be found by the preceding rule, but in the latter by the following:

RULE.

Add the complement of the declination to the meridian altitude; the sum will be the latitude, of the same name as the declination.

NOTE.-When the sun or star is on the equator, or has no declination, the zenith distance will be equal to the latitude of the place, which will be of the same name as the zenith distance. When the sun or star is in the zenith, the declination will be equal to the latitude, and it will be of the same name as the declination.

To find the latitude by the meridian altitude of the sun or star.

The refraction, being small, is here neglected.

↑ The parallax, being sinall, is here neglected, and the sun's semidiameter is supposed to be 16'.

20 41 N.

* The parallax, being small, is here neglected, and the sun's semidiameter is supposed to be 16'. + The declinations of these bright stars are given for every 10 days in the Nautical Almanac. When great accuracy is required, these declinations should be used instead of the numbers in Table VIII.

We have observed, in the directions for finding the meridian altitude of an object, that an error will arise if the ship be in motion, or the sun's declination vary. The amount of this correction may be estimated in the following manner:

Find the number of miles and tenths of a mile northing or southing made by the ship in one hour, and also the variation of the sun's declination in an hour, expressed also in miles and tenths. Add these together, if they both conspire to elevate or depress the sun; otherwise take their difference, which call the arc A. Find, in Table XXXII., the arc B, expressed in seconds, corresponding to the latitude and declination; then the arc A, divided by twice the arc B, will express the time in minutes from noon, when the greatest (or least) altitude is observed. Moreover, the square of the arc A, divided by four times the arc B, will be the number of seconds to be applied to the observed altitude to obtain the true altitude, which would have been observed if the ship had been at rest.

Thus, if the ship sail towards the sun south 11 miles per hour, and the declination increases northerly 1' per hour, we shall have A=11+1=12. If the latitude is 42° N., and the declination 2° S., we shall have by Table XXXII. B=2′′. In this case, the time from noon is 123 minutes, and the correction of altitude 144 = 18 seconds only.

The declination of this star is given for every day in the Nautical Almanac; when great accuracy is required, this declination should be used instead of that in Table VIII.

The refraction, being small, is neglected.

22

TO FIND THE LATITUDE BY A MERIDIAN ALTITUDE OF THE MOON.

THE latitude may be found at sea, by the moon's meridian altitude, more accurately than by any other method, except by the meridian altitude of the sun; but to do this, it is necessary to find the time of her passing the meridian, and her declination at that time. To facilitate these calculations, we have given the Tables XXVIII. and XXIX., the uses of which will evidently appear from the following rules and examples.

To find the mean time of the moon's passing the meridian.

Find, in the Nautical Almanac, the time of the moon's coming to the meridian of Greenwich for one day earlier than the sea account,* and also the time of her coming 'to the meridian of Greenwich the next day, when you are in west longitude, but the preceding day when in east longitude; take the difference between these times, with which you must enter the top column of Table XXVIII., and against the ship's longitude in the side column will be a number of minutes to be applied to the time taken from the Nautical Almanac, for the day immediately preceding the sea account, by adding when in west longitude, but subtracting when in east longitude; the sum or difference will be the true time of passing the meridian of the given place.

EXAMPLE.

Required the time of the moon's passing the meridian of Philadelphia, April 19, 1836, sea account.

The day preceding the sea account is April 18; on this day, the moon passed the meridian of Greenwich at 1h 55m.6, and, being in west longitude, we find the time of her passing the meridian the next day 2 43.0. The difference between these two times is 47.4, which is to be found at the top of Table XXVIII.; the nearest tabular number is 48; under this, and opposite 75°, (the longitude of Philadelphia,) is the correction 10m, nearly, to be added to 1h 55m.6, to obtain the time of passing the meridian at Philadelphia, April 19 2 05.6, sea account, or April 184 2h 05m.6, P. M., civil account.

To find the moon's declination when on the meridian.

Find the time of the moon's coming to the meridian as above; turn the ship's longitude into time by Table XXI., and add it thereto if in west longitude, but subtract it in east; the sum or difference will be the time at Greenwich. Take out the moon's declination from the Nautical Almanac, for the nearest hour preceding the Greenwich time, and also the variation for 10 minutes in the next column.

* Taking the time one day earlier than the sea account, reduces it to astronomical time used in the Nautical Almanac. We may observe that the time of the moon's coming to the meridian, is given in the Nautical Almanac to tenths of a minute, instead of seconds of time. This is done to facilitate the calculation of the right ascension and declination, by using common decimal fractions instead of sexa. gesimals.

Longitude may be turned into time, without the help of Table XXI., by multiplying the degrees and minutes of the longitude by 4, and considering the product as minutes and seconds of time respectively; and, by the inverse process of dividing by 4, we may turn time into degrees, &c. Thus, 80° x 4320m 5h 20m; and 15° 16' x 461m 04 1h 1m 4. In like manner, 1h 20m or 80m, being divided by 4, gives 20°, and 196m, being divided by 4, gives 49°, which agree with the table. If the ship be furnished with a chronometer, regulated for mean time at Greenwich, we may avoid the labor of this part of the operation by taking the time at Greenwich, as shown by the chronometer, at the very moment when the meridian altitude of the moon is observed.

If the time at Greenwich fall exactly upon any hour, the declination can then be taken from the Nautical Almanac, by mere inspection, without any reduction. We may also remark, that the reduc sion of the declination for the minutes and tenths of a minute of time, can be found by means of Table