Jupiter's declination, February 1st = 19: 3′ 0′′N. + 5.51 Jupiter's apparent central altitude = 58:17:18? S. Parallax, Table VI. = 0. 1 } Diff.= -0.33 Jupiter's true central altitude = 58:16:45 S. Jupiter's meridional zenith distance =31:43:15 N. Latitude of the place of observation 50:52 6 N. Example 2. March 16th, 1825, in longitude 75: E., at 2:49 apparent time, the meridional central altitude of the planet Venus was 31:10: N., the height of the eye above the level of the horizon 18 feet, and the planet's horizontal parallax 23 seconds; required the latitude? Apparent time of observation, March= 16: 2:49 5. 0 15:21:49: 17:15: 0N. + 1. 5.57 18:20:57" N. 31:10: 0 N. 31: 5:56 N. = 1.15 - 31: 4.41′′N. 58:55:19 S. 18. 20.57 N. Latitude of the place of observation 40:34:22: S. Note. The principles of finding the latitude by the meridional altitude of a celestial object may be seen by referring to "the Young Navigator's Guide to the Sidereal and Planetary Parts of Nautical Astronomy," between pages 98 and 105. PROBLEM IV. Given the Meridional Altitude of a fixed Star, to find the Latitude of the Place of Observation. RULE. Find the true altitude of the star, by Problem XVII., page 327; and hence its meridional zenith distance, noting whether it be north or south. Take the declination of the star from Table XLIV., and reduce it to the time of observation. Now, if the star's meridional zenith distance and its declination be of the same name, their sum will be the latitude of the place of observation ; but if they are of contrary names, their difference will be the latitude, of the same name with the greater term. Example 1. January 1st, 1825, in longitude 85:3: W., at 12:39 26: apparent time, the meridian altitude of Procyon was 44:49: S., and the height of the eye above the level of the horizon 16 feet; required the true latitude? Latitude of the place of observation = 50:56: 3 N. Example 2. January 2d, 1825, in longitude 165:30. E., at 10:14" 33 apparent time, the meridian altitude of Rigel was 30:39: S., and the height of the eye above the level of the sea 21 feet; required the true latitude? 51: 2:26′′N. Latitude of the place of observation = Note. The principles upon which the above rule is founded, are given in "the Young Navigator's Guide to the Sidereal and Planetary Parts of Nautical Astronomy," between pages 98 and 105. PROBLEM V. Given the Meridional Altitude of a Celestial Object observed below the Pole, to find the Latitude of the Place of Observation. RULE. Find the true altitude of the object, as before; to which let the polar distance of that object, or the complement of its corrected declination, be added, and the sum will be the latitude of the place of observation, of the same name with the declination. Example 1. June 20th, 1825, in longitude 65: W., the meridian altitude of the sun's lower limb, observed below the pole, was 9:12., and the height of the eye 20 feet; required the latitude? Observed altitude of the sun's lower limb = Dip of the horizon for 20 feet 4. 17 } Diff. = Apparent altitude of the sun's centre = 5:34" } Difference = True meridian altitude below the pole = 9:12: 0 +11.29 9:23:29% 5.25 Sun's corrected polar distance, or co-declination=66.32.17 N. Example 2. June 1st, 1825, in longitude 90: E., at 11:26 40: apparent time, the observed altitude of Capella, when on the meridian below the pole, was 11:48, and the height of the eye above the level of the sea 25 feet; required the latitude? Capella's true meridian altitude below the pole = 11:38:44" Remarks.-1. When the polar distance or co-declination of a celestial object is less than the latitude of the place of observation (both being of the same name), such celestial object will not set, or go below the horizon of that place in this case, the celestial object is said to be circumpolar, because it revolves round the pole of the equator, or equinoctial, without disappearing in the horizon. 2. If 12 hours, diminished by half the daily variation of the sun's right ascension, be added to the apparent time of the superior transit of a fixed star, it will give the apparent time of its inferior transit over the opposite meridian; that is, the apparent time of its coming to the meridian below the pole. 3. The least altitude of a circumpolar celestial object indicates its being on the meridian below the pole. PROBLEM VI. Given the Altitude of the North Polar Star, taken at any Hour of the Night, to find the Latitude of the Place of Observation. Although the proposed method of finding the latitude at sea is only applicable to places situate to the northward of the equator, yet, since it can be resorted to at any time of the night, it deserves the particular attention of the mariner. Of all the heavenly bodies, the polar star seems best calculated for finding the latitude in the northern hemisphere by nocturnal observation; because a single altitude, taken at any hour of the night by a careful observer, will give the latitude to a sufficient degree of accuracy, provided the apparent time of observation be but known within a few minutes of the truth: however, an error in the apparent time, even as considerable as 20 minutes, will not affect the latitude to the value of half a minute, when the polar star is on the meridian, either above or below the pole; nor will it ever affect the latitude more than about 8 minutes, even at the star's greatest distance from the meridian. But, as it is highly improbable, in the present improved state of watches, that the apparent time at the ship can ever be so far out as five minutes, the latitude resulting from this method will, in general, be as near to the truth as the common purposes of navigation require. RULE. To the sun's right ascension, as given in the Nautical Almanac, or in Table XII. (reduced to the meridian of the place of observation, by Problem V., page 298,) add the apparent time of observation; and the sum (rejecting 24 hours, if necessary,) will be the right ascension of the meridian, or mid-heaven; with which enter Table X., and take out the corresponding correction. Find the true altitude of the star, by Problem XVII., page 327; to which let the correction, so found, be applied by addition or subtraction, according to the directions contained in the Table, and the sum or difference will be the approximate latitude. Enter Table XI., with the approximate latitude, thus found, at top of the page, and the right ascension of the meridian in one of the side columns; in the angle of meeting will be found a correction, which, being applied by addition to the approximate latitude, will give the true latitude of the place of observation. Remark.-Since the corrections of the polar star's altitude, in Table X., have been computed for the beginning of the year 1824, a reduction therefore becomes necessary, in order to adapt them to subsequent years and parts of a year. The method of finding this reduction is illustrated in examples 1 and 2, pages 17 and 18. Example 1. January 2d, 1825, in longitude 60: west, at 8:10 40: apparent time, the observed altitude of the polar star was 52:15:20%, and the height of the eye above the level of the sea 16 feet; required the latitude? |