Example 2. February 4th, 1825, at 3:36:20: apparent time, the observed central altitude of the planet Venus was 36:24:25"*, in latitude 52:12: N., by account, and longitude 45:40: W., and the height of the eye above the level of the horizon was 26 feet; allowing the horizontal parallax of the planet, at that time, to be 17", the true latitude of the place of observation is required? Refrac. (Tab. VIII.) 1:17"-Parall. (Tab. VI.) 0:14" = 36:24:25 S. - 4.52 36:19:33′′ S, - 1. 3 True central altitude of Venus = 36:18:30 S. This is the mean of several altitudes. The altitude of Venus may be taken very correctly when the sun is above the horizon, provided the atmosphere be fine and clear. Cor. in Tab. LII., ans. to lat. 52°N. and dec. 0 = Correction answering to lat. 52:12 N. and dec. 0:24:19S.= 1:30′′.9 2.0749 Computed correction = 1"30".9 Prop. log. = Given the Latitude by Account, the Altitude of a fixed Star observed near the Meridian, the apparent Time of Observation; and the Longitude, to find the true Latitude. RULE. Turn the longitude into time, and apply it to the apparent time of observation, by addition or subtraction, according as it is west or east ; and the sum, or difference, will be the corresponding time at Greenwich. To this time let the sun's right ascension at noon of the given day be reduced by Problem V., page 298. Let the star's right ascension and declination (Table XLIV.) be reduced to the night of observation, by the method shown in page 115; and let the star's observed altitude be reduced to the true altitude, by Problem XVII., page 327. To the apparent time of observation add the sun's reduced right ascension, and the sum (abating 24 hours, if necessary,) will be the right ascension of the meridian; the difference between which and the star's reduced right ascension will be that object's distance from the meridian at the time of observation. Now, with the latitude by account, and the star's reduced declination, enter Table LI. or LII., according as they are of the same or of a contrary denomination; and take out the corresponding correction, agreeably to the rule in page 139; with which, and the star's distance from the meridian, compute the correction of altitude; and, hence, the latitude, by Problem IX., page 354. Note. The interval between the time of observation and the time of transit must not exceed the limits pointed out in the three preceding Problems; viz., the number of minutes and parts of a minute contained in the star's distance from the meridian, is not to exceed the number of degrees and parts of a degree contained in that object's meridional zenith distance at the place of observation. See explanation to Tables LI. and LII., from page 138 to 143. Example 1. January ist, 1825, at 8:52"17: apparent time, in latitude 52°46' N., by account, and longitude 56:15 W., the observed altitude of the star Menkar was 39°42′40′′, and the height of the eye above the level of the sea 26 feet; required the true latitude of the place of observation? Star's observ. alt., reduced to its true alt., is 39:36:39 S. Correction in Table LI. answering to lat. 52°N. and dec. 3°N. 1"36".0 -2.7 +0.5 133.8 1 1:15 Prop. log. 0.4682 39.36.39 S. Menkar's meridional zenith distance = 49:22: 6′′N. Latitude of the place of observation 52:46 2"N.; which differs but 2" from the truth. Example 2. September 1st, 1825, at 13:28 42: apparent time, in latitude 49:30'S. by account, and longitude 22:10:30" E., the observed altitude of the star B Pegasi, or Scheat, was 11:37:59", and the height of the eye above the level of the sea 19 feet; required the true latitude of the place of observation? Scheat's declination, January 1st, 1824, = 27: 7:35′′N, + 0.32 Correction in Table LII., answ. to lat. 49:S. and dec. 27:N. = = Correction to latitude 49:30:S. and declination 27:8:7"N. = 110".0 Scheat's meridional zenith distance = .76:37:59"S. 27. 8. 7 N. Latitude of the place of observation = 49:29:52" S.; which differs 8" from the truth. Remark. The latitude may be also very correctly inferred from the altitude of a celestial object observed near the meridian below the pole. In this case, the meridian distance of the object is to be reckoned from the apparent time of its transit below the pole; the correction answering to the latitude and the declination is always to be taken out of Table LII., in the |
