The correction in Table LI., corresponding to latitude 50: north, and Declination 0: is 1:38" 8 Red. for lat. 1:5 and decl. 25′22′′ = 3. 2 Correct latitude of the place of observ. 519 5 5 North. Hence it is evident, that the latitude may be determined by this method to all the accuracy desirable in nautical operations. It pos sesses a decided advantage over that by doublé altitudes; and, since the calculation is so extremely simple, the mariner will do well to avail himself thereof on every occasion; because the latitude, thus deduced, will be equally as correct as that resulting from the observed meridional altitude, provided the observation be made within the prescribed limits. When, however, the latitude and the declination are of different names, it will not produce any sensible error in the result, if the altitude be observed a few seconds without those limits, as may be seen in Example 1, page 415. But it is to be remembered, that the mean time of observation must be well determined, because a trifling error in the interval from apparent noon would sensibly affect the resulting latitude. EE PROBLEM X. Given the Latitude by Account, the Altitude of the Moon's lower or upper Limb, observed near the Meridian, the mean Time of Observation, and the Longitude; to find the true Latitude. RULE. To the mean time of observation apply the longitude in time by Problem III., page 342, and the mean time at Greenwich will be obtained to which let the mean sun's right ascension be reduced by Problem V., page 344.-Let the moon's semidiameter and horizontal parallax be reduced to the Greenwich time by Problem XV., page 361; her right ascension and declination by Problem XVI., page 364: and let the observed altitude of her lower limb be reduced to the true central altitude by Problem XXIV., page 376. To the mean time of observation add the mean sun's reduced right ascension; the sum, abating 24 hours if necessary, will be the right ascension of the meridian; the difference between which and the moon's reduced right ascension will be her horary distance from the meridian. Now, with the moon's reduced declination, and the latitude by account, 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 moon's horary distance from the meridian, compute the correction of altitude; and hence, the latitude of the place of observation, by Problem IX., page 413. Note. The limits within which the altitude of the moon should be observed, are to be determined in the same manner, precisely, as if it were the sun that was under consideration; observing, however, to estimate the interval from the moment of transit over the meridian of the place of observation, instead of from noon. Example. At sea, January 23rd, 1836, at 3:53 12: mean time, in latitude 51:15 north, by account, and longitude 45: west, the mean of several observed altitudes of the moon's lower limb, reduced to the true central altitude, was 39:15:3" south; required the true latitude? D's reduced declin.=1:33:26′′N. Tabular correction 1:37 0 Prop. logarithm. 1:40""3 3.3 1:37:0 . 2.0467 0:48:47: Twice its prop. log. 1. 1340 Correction of the moon's altitude. Moon's meridional altitude = Moon's meridional zenith distance Moon's reduced declination. True latitude, as required = . 51:15 4 North. PROBLEM XI. To deduce the Latitude from the Altitude of a Planet taken near the Meridian. RULE. Reduce the mean time of observation to the meridian of Greenwich by Problem III., page 342; to which, let the mean sun's right ascension be reduced by Problem V., page 344; and the geocentric right ascension and declination of the planet by Problem XVII., page 366.-Find the planet's horary distance from the meridian by Problem XXII., page 373; and let its observed central altitude be reduced to the true altitude by Problem XXV., page 377.-Now, with the latitude by account, and the planet's reduced declination, enter Table LI. or LII., according as they are of the same or of contrary denominations, and take out the corresponding correction, agreeably to the Rule in page 139; with which, and the planet's distance from the meridian, compute the correction of altitude, and, hence, the latitude of the place of observation, by Problem IX., page 413. Note. The measure of the interval between the time of observation and the time of transit,-that is, the number of minutes and seconds contained in the planet's distance from the meridian, must not exceed the number of degrees and minutes contained in that object's meridian zenith distance at the place of observation, as particularly pointed out in page 414. See explanation to Tables LI. and LII., page 138, and thence to 143. Example. At sea, January 4th, 1836, at 10:47 56: mean time, in latitude 45:28 south, by account, and longitude 60:12 east, the mean of several observed central altitudes of the planet Jupiter, reduced to the true altitude, was 19:52:38" north of the observer; required the true latitude of the place of observation? Jupiter's geocentric right ascension, reduced to the Greenwich time, is 64548, and his declination 23:6:37 north. Ditto meridian distance 1 420: Twice its prop. log. . 1:32:47 Prop. log. = 0.2878 19.52.38 North. 21:25:25 North. 68:34:35 South. Latitude of the place of observation= 45:27:58" South. Note.-The latitude may be deduced in the same manner from the altitude of a fixed star when near the meridian; taking care, however, that the interval between the time of observation and the moment of transit, viz., the star's horary distance from the meridian, does ne exceed the limits prescribed in page 414. PROBLEM XII. To deduce the Latitude from the Altitude of a Celestial Object observe near the Meridian below the Pole. RULE. If the object be the sun, let its horary distance from the meridian be reckoned from apparent midnight; but, for any other celestial object, let its horary distance from the meridian be reckoned from the mean time of its transit below the pole. Now, let the correction answering to the latitude and the declination be always taken out of Table LII., in the same manner as if those elements were of different denominations:-then, the resulting correction of altitude being applied by |