tral altitude is 22:47:24", on the assumption that her horizontal parallax, at the time of observation, was 18 seconds of a degree. Planet's m.z.dist.=24:35:24" Nat. co-sine=909309 387355 Venus' horary dist.,west of the merid.=4'36"55 Log. rising 5. 80981.1 Remark. Should the horizontal parallaxes of the planets be ever given in the Nautical Almanac, the mariner may then deduce the apparent time from their altitudes, by the above Problem, to a very great degree of accuracy, provided the longitude of the place of observation be known within a few minutes of the truth, or that there be a chronometer on board to indicate the time at Greenwich. However, even admitting that those parallaxes are still to remain unnoticed, the apparent time, computed as above, will always be sufficiently near the truth for the purpose of determining the longitude at sea. PROBLEM VI. Given the Latitude and Longitude of a Place, the estimated Time at that Place, and the Altitude of the Moon's Limb; to find the apparent Time of Observation. RULE. Reduce the estimated time of observation to the meridian of Greenwich, by Problem III., page 297; to which let the sun's right ascension be reduced, by Problem V., page 298; and let the moon's right ascension, declination, semi-diameter, and horizontal parallax be reduced to the same time, by Problem VI., page 302. Reduce the observed altitude of the moon's limb to the true central altitude, by Problem XV., page 323; then, With the latitude of the place of observation, the moon's reduced declination, and her true central altitude, compute her horary distance from the meridian, by any of the methods given in Problem III., pages 384 to 392. Now, let the moon's horary distance from the meridian, thus found, be applied to her reduced right ascension, by addition or subtraction, according as she may have been observed in the western or eastern hemisphere, and the right ascension of the meridian will be obtained; from which (increased by 24 hours, if necessary,) subtract the sun's reduced right ascension, and the remainder will be the apparent time of observation. Note.-When the moon's horary distance, east of the meridian, exceeds her right ascension, the latter is to be increased by 24 hours, in order to find the right ascension of the meridian. And it is to be borne in mind, that the moon's right ascension and declination must be corrected by the equation of second difference, Table XVII., as explained between pages 33 and 38.* Example 1. January 4th, 1825, in latitude 50:10 N., and longitude 60: W., the mean of several observed altitudes of the moon's lower limb, east of the meridian, was 29:25:23", that of the corresponding times, per watch, 7:2818, and the height of the eye above the surface of the water 17 feet; required the apparent time? * For the effects resulting from the equation of the mean second difference of the moon's place in right ascension and declination, see " The Young Navigator's Guide to the Sidereal and Planetary Parts of Nautical Astronomy," page 171. 98: 6:53′′ Moon's right ascension at noon, January 4th, Moon's semi-diameter at noon, January 4th, 16: 9" Moon's declination at noon, January 4th, = + 5 +8 16:22" 22:35:39"N. Corrected prop. part of ditto for 112818-1. 10. 18 Moon's corrected declination= 21:25:21 N. Moon's horizontal parallax at noon, January 4th,= 59:17" Moon's true horizontal parallax= · + 16 Observed altitude of the moon's lower limb=29° 25' 23"; hence, her true Moon's horary dist., east of the merid. 430"41:Log.rising 5.79245.6 Moon's horary dist. east of the merid. 4:30"41: Right ascension of the meridian = 2:30 56: 19. 2.38 Apparent time of observation = . 7:28 18: Example 2. January 30th, 1825, in latitude 10:20 S., and longitude 100:50 E., the mean of several altitudes of the moon's lower limb, west of the meridian, was 7:23:30%, that of the corresponding times, per watch, 13:33 20:, and the height of the eye above the surface of the water 20 feet; required the apparent time? Moon's semi-diameter at noon, January 30th, = Correction of ditto for 650" = 15:46" Augmentation, Table IV., = + 5 + 2 15:53 Moon's true horizontal parallax= 58: 8" Observed altitude of the moon's lower limb 7:23'30"; hence, her true central altitude is 8:25:54". १ Remainder 680118 Log.-5.832584 Moon'shorary dist. west of the merid. 5 333 Log. rising 5.878621 Moon's cor. R. A. 80:35:33", in time=5. 22. 22 Remark. If there be a chronometer on board to indicate the time at Greenwich, the apparent time of observation, at any given place, may be very correctly ascertained by the above problem. But, since the chronometer shows the equable or mean time at Greenwich, this time must be reduced to apparent time, by applying the equation of time thereto with a contrary sign to that expressed in the Nautical Almanac. Thus, in the above example, if the chronometer give the mean time at Greenwich = 7:344, then the reduced equation of time, viz., 1344, being subtracted therefrom, shows the apparent time at that meridian to be 6:50:0. Hence, when the equation of time in the Nautical Almanac is marked additive, it is to be applied by subtraction; but when marked subtractive, it is to be applied by addition to the mean time (per chronometer) at Greenwich, in order to reduce it to apparent time. SOLUTION OF PROBLEMS RELATIVE TO FINDING THE It sometimes happens at sea, particularly in taking a lunar observation, that the horizon is so ill-defined as to render it impossible to observe the altitudes of the objects to a sufficient degree of exactness; or, perhaps, that one or both of the objects are directly over the land, at the time of measuring the lunar distance, and the ship so contiguous thereto as to |