elliptic, and is consequently, at different parts of her orbit, nearer to, or farther from the earth, which occasions an apparent augmentation or diminution of her semi-diameter; on which account her semi-diameter and horizontal parallax for every noon and midnight are set down, page 7, of the month, in the Nautical Almanack, and may be found for any intermediate time by taking proportional parts. It is evident, that to obtain the true angular distance, the observed distance must be corrected for the semi-diameter of the ob-. jects. If the nearest limbs of the sun and moon are observed, the sum of the semi-diameters must be added; if the farthest limbs are observed, the sum must be subtracted from the observed distance, to obtain the distance of their centres. The same rules hold good in respect to adding or subtracting the moon's semi-diameter, according as her nearest or farthest limb is used when the observation is made between the moon and a star, observing that the star has no semi-diameter. To work an observation, or to find the Latitude of a Place, by the Tables of the Sun or Star's Declination, and the Zenith Distance. The latitude of any place is its distance from the equator, either north or south, counted in degrees, &c. upon an arch of the meridian, contained between the zenith and the equator. The zenith is that point directly over our heads, and is 90 degrees distant from the horizon. The zenith distance is the distance of any object from the point directly over our heads, which is always the complement of the altitude; it is said to be south, if the sun or star be south, and north, if the sun or star be north of the observer. To the observed altitude add the difference between the semi-diameter and the dip, the sum will be the apparent altitude of the sun's centre; but must be subtracted if a back observation is used. From the apparent altitude subtract the refraction, the remainder. will be the true altitude of the sun's centre: this being subtracted from 90 degrees, gives the true zenith distance, with which, and the declination, the latitude is found by the following rules. See Globe, facing page 46. NOTE. For the dip and refraction, see Tables 8 and 7. 1st. When the sun or star is in the zenith, the declination is the latitude; and is of the same name as the declination, north or south. 2d. When the sun or star is on the equator, consequently hath no declination, the zenith distance is the latitude of the place: if the zenith distance be south, the latitude is north; but if north, the latitude south. 3d. When the zenith distance is north, and declination north. f they be both equal, you are on the equator, therefore in no Litude. 4th. When the zenith distance is south, and declination south, then, if the zenith distance is equal with the declination, you are on the equator. The foregoing need no examples. 1st. But, when the zenith distance is south, and the declination north, the declination added to the zenith distance gives the latitude north. 2d. When the zenith distance is north, and the declination south, the declination added to the zenith distance gives the latitude south. 3d. When the zenith distance is south, and the declination south, if the zenith distance is more than the declination, subtract the declination from it, and the remainder gives the latitude north. 4th. When the zenith distance is north, and the declination north, if the zenith distance be more than the declination, subtract the declination from the zenith distance, the remainder is the latitude. south. 5th. When the zenith distance is north, and the sun hath north declination, the zenith distance being less than the declination, subtracting the zenith distance from the declination, gives the latitude north. 6th. When the zenith distance is south, and declination south, if the zenith distance is less than the declination, the zenith distance subtracted from the declination gives the latitude south; for it is plain in these two last cases, the observer is between the sun and equator. The preceding six rules are exemplified in their regular order below. Zenith distance 56 42 O 0 10 56 41 0 90 0 0 33 19 0 South29-70 150 North. SP With the chord of 60 describe a circle to represent the meridian; through the 49 10 0 North. centre draw the diameter E Q, to repre Latitude sent the cquater, and at right angles thereto, another diameter; mark the upper end, NP, for the north pole, and the lower, SP, for the south pole; set off the declina , 15°55′, taken from the line of chords, from E to D; take from the line of the zenith distance, 33o 19', and set it off from D to Z. Then will EZ meahe line of chords, 49° 10', the latitude required. Draw the figure as before; take the declination, 21" 22', from the line of chords; set off from E towards the south pole to D; take the zenith distance on the line of chords, and set it from NP D to Z; then will E Z, measured on the same line of chords, be the latitude required. EXAMPLE III. Suppose, on the 20th Jan. 1810, the meridian altitude of the sun's lower limb to be 42° 30' south, the eye being elevated 18 feet above the water. Required the lat. Sun's observed altitude. Semi-dia. 16′ 0′′ Dip } 405 Latitude 42 30 0 South. 27 77 0 North. Draw the figure as before; set off the declination, 20° 12', from E to wards the south pole to D. Secondly, set off the zenith distance, 47° 19', contra from D towards the north, to Z; then will EZ measure on the line of chords 27° 7', the latitude. EXAMPLE IV. Suppose, in 1810, the altitude of the star Aldebaran, when on the meridian, be found 40° 27' north, when the decl. is 16° 7' 8" north, the eye being elevated 18 feet above the sea. Required the lat.? ° Observed latitude Dip for 18 feet Apparent altitude 40 27 0 *D 0 40 NP Draw the figure as before; set off star's declination, 169 7′ 8′′ from D; next set off the zenith distance 49° 38', from D to z; then will Z E, measured on the line of chords, be 33° 30′ 52", the latitude required, which is south. In the two last examples it is plain the observer is between the sun and the equator. Suppose on the 12th of March 1810, by a back observation, the observed altitude of the sun is 25° 12' south, the eye being 40 feet above the horizon: required the latitude in the longitude of 64° east and 64° west. As the declination in the tables is calculated for the meridian of Greenwich, it is plain that when a ship is to the eastward, and the declination decreasing, it must be more at the ship than at Greenwich; consequently the proportional parts of the daily difference must be added to the declination of that day; but when the ship is to the westward of London, the proportional parts must be subtracted, to find the true declination at the place of observation; but had the declination been increasing, the proportional parts must have been subtracted when to the eastward, and added when to the westward, to obtain the true declination at the ship; whence it follows, that no latitude can be truly ascertained without finding the sun's declination at the place of observation, as above, which is but too often neglected. Here it may be observed also, that in a back observation, the sun being brought over the observer's head, the upper edge appears to him the lower one; and though the sun appears to the south of him, yet the zenith distance is north. The same may be observed if he is north of the sun. The back observation is seldom used, unless there is a high land, or other obstructions, between the observer and the sun. The foregoing rules are for observing the sun, or a star, when they are at the greatest altitude, or upon the meridian above the pole; but as in some parts of the earth the sun does not set for several days, and some stars never set, in that case they may be observed when they are at the lowest, or upon the meridian below the pole. To work which observation, take the following RULE.-Add the complement of declination to the true meridian altitude: the sum is the latitude, of the same name that the declination is of. Suppose, on the 12th of June, 1810, an observer in a hig! |