= 64020: + 0.33 6:40 53: Sun's right ascension at noon, September 2d, 10:44"53'.5 Sun's reduced right ascension = Observed altitude of the moon's lower limb . + 1. 0.5 10:45 54.0 9:8:36"; hence, the true central altitude of that object is 10:6:23%. Moon's right ascension at noon, September 2d,=30°58′ 8′′ Moon's corrected right ascension = 34:17:17" 16:12:13′′N. + 54. 3 17: 6:16′′N. Moon's horizontal parallax at noon, Sept. 2d, = 54.11 Correction of ditto for 640"53! = +4 Moon's horary dist., east of the merid. 4 0 0; Log. rising 5. 69897.2 = Moon's horary dist., east of the merid.=4' 0" 0: Moon's reduced right ascension 34:17:17, in time = 2.17. 9 Longitude of the place of obs., in time=450"22:72:35:30 east. Remark 1.-The longitude, thus deduced from the true central altitude of the moon, will be equally as correct as that inferred from the sun's central altitude, provided the moon's place in right ascension and declination be carefully corrected by the equation of second difference, as explained between pages 33 and 38. Whatever little extra trouble may be attendant on this particular operation, will be infinitely more than counter-balanced by the pleasing reflection that it affords the mariner an additional method of finding the longitude of his ship, either by night or by day, with all the accuracy that can possibly result from the established rate or going of his chronometer. Remark 2.-It frequently happens at sea, that, owing to clouds, rains, or other causes, ships are whole days without profiting by the presence of the sun, or obtaining an altitude of that object for the purpose of ascertaining either latitude or longitude; but it must be remembered, that there are few nights, if any, in which some fixed star, a planet, or the moon, does not present itself for observation, as if intended by Providence to relieve the mariner from the great anxiety which the doubtful position of his ship must naturally excite in him, particularly when returning from a long voyage, and about to enter any narrow sea, such as the English Channel. Under such circumstances, the three preceding problems will be found exceedingly useful; because they exhibit safe and certain means of finding the true place of a ship, so far as the going of the chronometer used in the observation can be depended upon. In this case, since a knowledge of the heavenly bodies becomes indispensably necessary, the reader is referred to "The Young Navigator's Guide to the Sidereal and Planetary Parts of Nautical Astronomy," where a familiar code of practical directions is given for finding out and knowing all the principal fixed stars and planets in the firmament. PROBLEM VII. To find the Longitude of a Ship or Place by celestial Observation, commonly called a lunar Observation. The direct progressive motion of a ship at sea is so liable to be disturbed by various unavoidable and often imperceptible causes, such as a frequent aberration from the true course, by the ship's continually varying a little, in contrary directions, round her centre of gravity; high seas with heavy swells, sometimes with and at other times against, or in directions oblique to the true course; storms, sudden shifts of wind, unknown currents, local magnetic attraction, unequal attention in the helm's-men, with many other casualties which cannot possibly be properly provided for,—that the place indicated by the dead reckoning is frequently so erroneous as to be whole degrees to the eastward or westward of the actual position of the ship. Of this every person must be fully aware, who has navigated the short run between England and the nearest of the West Indian Islands. As the best account by dead reckoning is evidently but a very imperfect kind of guess-work, it should be employed only as an auxiliary to the elementary parts of navigation, and never confided in but with the utmost caution. Hence it is that celestial observation should be constantly resorted to, because it is the only certain way of detecting the errors of dead reckoning, and of ascertaining, with any degree of precision, the actual position of the ship. If a chronometer or time-keeper could be so constructed as to go uniformly correct in all seasons, places, and climates, it would immediately obviate all the difficulties attendant on a ship's reckoning, and thus render the longitude as simple a problem as the latitude; for, such a machine being once regulated to the meridian of Greenwich, would always show the absolute time at that meridian; and, hence, the longitude of the place of observation, as has been illustrated in the four preceding problems; but those pieces of mechanism are so exceedingly complicated, and so extremely delicate, that they are liable to be affected by the common vicissitudes of seasons and climates, and also by any sudden exposure to a higher or lower degree of atmospheric temperature than that to which they have been accustomed the celestial bodies ought, therefore, to be consulted, at all times, in preference to machines so subject to mutability, and should ever be confided in by the mariner, as the only immutable and unerring time-keepers. Of all the apparent motions of the heavenly bodies, in the zodiac, with which we are acquainted, that of the moon is by far the most rapid; it being, at a mean rate, about 13:10 in 24 hours, or nearly half a minute of a degree in one minute of time. Hence, the quickness of the moon's motion seems to adapt her peculiarly to the measurement of small portions of corresponding time; and, therefore, careful observations of the angular distance of that object from the sun, a planet, or a fixed star lying in or near the zodiac, afford the most eligible and practicable means of determining the longitude of a ship at sea: for the true distance deduced from observation, being compared with the computed distances in the Nautical Almanac, will show the corresponding time at Greenwich; the difference between which and the apparent time at the place of observation will be the longitude of that place in time; and which will be east if the time at the place of observation be greater than the Greenwich time, but west if it be less. The method of finding the longitude at sea, by lunar observations, is very familiarly explained, by geometrical construction and by spherical calculation, in "The Young Navigator's Guide to the Sidereal and Planetary Parts of Nautical Astronomy," between pages 172 and 212, where it will be seen that in a lunar observation there are two oblique angled spherical triangles to work in, for the purpose of finding the true central distance; in the first of which the three sides are given, viz., the apparent zenith distances of the two objects, and their apparent central distance, to find the angle at the zenith,—that is, the angle comprehended between the zenith distances of those objects; and, in the other, two sides and the included angle are given, to find the third side, viz., the true zenith distances of the objects; and their contained angle, to find the side opposite to that angle, or the true central distance between those objects. The solution of the first triangle falls under Problem V., page 207, and that of the second under Problem III., page 202. This is the direct spherical method of reducing the apparent central distance between the moon and sun, a planet, or a fixed star, to the true central distance; or, in other words, that of clearing the apparent central distance between those objects of the effects of parallax and refraction: but, this being considered by some mariners as rather a tedious operation, the following methods are given, which, being deduced directly from the above spherical principles, will be always found universally correct; and, since they are not subject to any restrictions whatever, they are general in every case where a lunar observation can be taken. Besides this, they will be found remarkably simple and concise, particularly when the operations are performed by the Tables contained in this work. METHOD I. Of reducing the apparent to the true central Distance. RULE. Take the auxiliary angle from Table XX., and let it be corrected for the sun's, star's, or planet's apparent altitude, as directed in pages 44 and 45. Find the difference of the apparent altitudes of the objects, and, also, the difference of their true altitudes. Then, to the natural versed sines supplement of the sum and the difference of the auxiliary angle and the difference of the apparent altitudes, add the natural versed sines of the sum and the difference of the auxiliary angle and the apparent distance, and the natural versed sine of the difference of the true altitudes: the sum of these five numbers, abating 4 in the radii or left-hand place, will be the natural versed sine of the true central distance. Example 1. Let the apparent central distance between the moon and sun be 66:48:34", the sun's apparent altitude 60:15:35", the moon's apparent altitude 17:15:15%, and her horizontal parallax 59'43"; required the true central distance ? Sun's apparent alt. = 60:15:35%-Correc. 029"=true alt.=60:15′ 6′′ Moon's apparent alt. 17. 15. 15+ Correc. 54. 0 =true alt. 18. 9. 15 1 Diff. of the app. alts. 43: 0:20% H Diff. of the true alts. = 42% 5.51% |