since the moon is nearer the earth when observed than when it was in the horizon, the horizontal semidiameter must also be corrected for augmentation (p. 104). The correction of the moon's apparent altitude for parallax and refraction is found inserted in most of the nautical tables: it is entered with the corrected horizontal parallax at top, and the apparent altitude at the side. Hence this rule. 1. Get a Greenwich date. 2. Correct the moon's semidiameter and horizontal parallax, taken from the Nautical Almanac, for the Greenwich date (p. 78). 3. Add to the semidiameter the augmentation, taken from the table of augmentation. 4. Correct the observed altitude for index correction, dip, and semidiameter, as in the preceding rules (p. 106). 5. Add the moon's correction in altitude, taken out of table. the proper 6. The result is the moon's true altitude. EXAMPLE. April 7, 1853, at 4h 47m P.M., mean time nearly, in long. 10° W., the observed altitude of the moon's L. L. was 72° 15' 0", the index correction was 4' 20", and height of eye above the sea 15 feet: required the true altitude. 4h 47m 0 40 W. (93.) July 12, 1848, at 9h 18m P.M., mean time nearly, in long. 44° 40′ W., the observed altitude of the moon's L. L. was 27° 56′ 40′′, the index correction + 2' 20", and height of eye above the sea 20 feet, required the true altitude. Ans., 28° 56' 9". (94.) May 15, 1848, at 10h 25m P.M., mean time nearly, in long. 55° 40′ W., the observed altitude of the moon's L. L. was 21° 14' 10", the index correction + 2′ 20′′, and height of eye above the sea 15 feet, required the true altitude. Ans., 22° 15′ 17′′. (95.) May 15, 1848, at 10h 22m P.M., mean time nearly, in long. 41° 30′ W., the observed altitude of the moon's U. L. was 45° 20′ 30′′, the index correction + 4' 10", and height eye above the sea 20 feet, required the true altitude. of 113 SECTION II. RULES FOR FINDING THE LATITUDE, LONGITUDE, ERROR AND RATE OF CHRONOMETERS, AND VARIATION OF THE COMPASS. CHAPTER VI. RULES FOR FINDING THE LATITUDE. To find the latitude by the meridian altitudes of a heavenly body above and below the pole. Let NW SE represent the horizon of the spectator, z the zenith, N z s the celestial meridian, N P the altitude of the pole, w Q E the celestial tor. equa of the pole) latitude of spec tator.* Let A B A' be a parallel of declination described by a heavenly body about the pole P, then A'N AN N P Z W E Q above pole star's polar distance and A P = A' P = star's polar distance .'. A'N PN A'Plat. and A N = adding A' N or lat. = PN + A P = lat. + star's polar distance + AN = 2 lat. (A' N + AN) = half sum of latitudes. * For ZN = PQ (each being 90°) or, PN + PZ = PZ + ZQ .. PNZQ= latitude of spectator. See "Problems in Astronomy," by the Author. If the heavenly body when passing the meridian above and below the pole, is on different sides of the zenith, so that the altitudes are taken from opposite sides of the horizon, subtract the greater altitude from 180°, so as to reduce it to an altitude taken from the same point of the horizon as the other altitude (see Exercise 2, p. 115). Hence this Rule XXVII. To find the latitude by the meridian altitudes of 1. Correct the altitudes for index correction, height of eye, refraction and parallax (or as many of these as are applicable to the case), and thus get the true meridian altitudes. 2. Add together the true meridian altitudes (reckoning from the same point of horizon), and half the result will be the latitude of the spectator. EXAMPLES. 1. The meridian altitudes of a Ursa Majoris were observed above and below the north pole to be 74° 10′ 10′′ and 32° 42′ 15′′ respectively (zenith south at both observations), index correction - 2′ 10′′, and height of eye above the sea 20 feet, required the latitude. A 2. The meridian altitudes of a Auriga (Capella), were observed above and below the north pole to be 81°10′ 52′′ (zenith north of star), and 3° 42′ 52" (zenith south), index correction 3′ 10′′, and height of eye above the sea 14 feet, required the latitude. Dip (96.) The meridian altitudes of a star were observed above and below the north pole to be 69° 20′ 45′′ and 6° 14' 30" respectively (zenith south at both observations), index correction 1′ 45", and height of eye 16 feet, required the latitude. Ans., lat. 37° 37′ 35′′ N. |
