Great attention has been paid to the correctness of the Tables, which are carefully arranged in the most convenient order, for performing the operations for which they are chiefly intended. In the Appendix will be found, plain directions for acquiring a knowledge of the principal Fixed Stars, and examples of ascertaining the Latitude at Sea by them; with several useful Tables. The author cannot avoid taking this opportunity of strongly recommending this part of the work, to the attention of all Navigators who are not much acquainted with this highly useful part of their profession; as there can be no doubt, that many accidents which happen at sea, might be prevented, were the practice of ascertaining the place of a ship, by means of the Fixed Stars, to become general amongst Seamen. The author having used his best endeavours, throughout the work, to render it worthy the attention of Practical Navigators, most respectfully solicits a candid examination of its merits, in comparison with other works of a similar nature; and shall feel much gratified if his labours are found to contribute, in any degree, towards the improvement of an Art, on which the prosperity of this commercial country so greatly depends. Advertisement to the Fifth Edition. To this Edition Five New Tables are added, occupying abont 80 pages. By these Tables the operation of clearing an Apparent Lunar Distance, from the effects of Parallax and Refraction, may be performed in a correct and simple manner, as exemplified at Pages 55, 56, and 57, after the explanation of the Tables. Every method of correcting the Lunar Distances depends upon one or other of the two following general principles. First, From the Apparent Distance and Altitudes, together with the Moon's Horizontal Parallax, to find the True Distance on the direct principles of Spherical Trigonometry. Secondly, From the same elements to find certain corrections, by means of the Fluxional Analogies of Spherical Triangles, which being applied to the Apparent Distance will give the True Distance. The first method given in this Work depends upon the latter principle, and the method now introduced depends upon the first, or what is generally called the Spherical Principle; it is strictly correct as well as applicable to all cases, and is perhaps the shortest and most simple method of the kind ever proposed. PROBI EM I.-To find the Apparent Time by the Altitude of the Sun PROBLEM II. To find the Apparent Time by the Altitude of a Fixed PROBLEM III.-To clear the Lunar Distances from the Effects of PROBLEM IV. To find the Apparent Time at Greenwich answering Remarks on observing the Lunar Distances PROBLEM V.-To find the Longitude by Lunar Observations PROBLEM VI.-To find the Altitude of a celestial object by com- Pago. Table. VI. Corrections of the Apparent Altitudes of the Sun and Stars Page. 3 VIII. Correction of the Moon's Semi-diameter, &c. IX. Altitudes by which the Apparent Time may be found with the greatest Accuracy 5 X. Logarithms for finding the Correction of the Sun's Declination, &c. XI. Logarithms of the Latitude and Polar Distance XII. Logarithms of the Half Sum and Difference XIII. Logarithms of the Apparent Time, or Horary Angle XIV. Logarithms of the Moon's Horizontal Parallax 6 8 17 26 35 XX. Correction of the Apparent Altitudes of the Sun and Stars 137 Introductory Remarks List of the Constellations Directions for the Zodiacal Stars Directions for the Stars in the Northern Hemisphere On finding the Latitude by the Fixed Stars To find the Latitude by the North Pole Star Table I.-Right Ascension and Declination of 61 Stars Tables VI. and VII.-Difference between the Altitude of the Page. 2 4 7 8 10 10 12 14 17 18 18 19. 20 INTRODUCTION. TO prevent ambiguity in working the Examples, given to illustrate the use of the Tables, the reader is requested to attend to the following Remarks: 1. By the apparent time at Greenwich is always meant the apparent astronomical time at that meridian, and by mean time at Greenwich the mean astronomical time is to be understood. 2. When the estimated civil or nautical time is given at any meridian, it is first reduced to the estimated astronomical time at the given place, to which the longitude of that place in time being applied by addition or subtraction, according as the longitude is west or cast, the estimated astronomical time at Greenwich is obtained; and to this time all the articles required from the Nautical Almanac are always reduced. 3. As the civil time is 12 hours in advance of the astronomical time, that is, the astronomical day commences at the noon of the civil day, of the same date, it is plain that when the given civil time is in the afternoon, or P. M. it answers to the astronomical time of the same date; but when the given civil time is before noon, (or A. M.) we must add 12 hours to it, the sum will be the astronomical time for the day of the month preceding the given civil day. For example, 5h. 30m. P. M. civil time, on the 10th of May, is 5h. 30m. astronomical time of the same date. But 5h. 30m. A. M. civil time, on the 10th of May, is 17h. 30m, astronomical time, on the 9th of May; for the 9th day of the month, according to astronomical time, commences at the noon of the 9th civil day, and ends at the noon of the 10th civil day, (the hours being reckoned up to 24;) and 5h. 30m. A. M. of the 10th, is 17h. 30m. from noon on the 9th. 4. The astronomical day begins at the instant that the nautical day (of the same date) ends, consequently nautical time is always 24 hours in advance of astronomical time, therefore to turn nautical time into astronomical time, we have only to reckon the hours from the ceding noon, and then change the date to the preceding day. Thus, 5h. 30m. P. M. nautical time, on May the 10th, is 5h. 30m. astro pre on May the 10th, is 17h. 30m. astronomical time on May the 9th, and so on. 5. The noon of the astronomical day is at the instant that it begins, and the noon of the nautical day is at the instant when it ends; and as both these take place at the noon of a civil day, of the same date, it is plain that the same noon answers for any given day in either of the three methods of reckoning time. 6. The observed altitude, or the observed distance, is the angle given by the instrument used in taking the observation, allowing for the index error, if any. Thus, if the distance measured by a sextant, which has an index error of 2′ 40′′ additive, be 84° 21′ 50′′", the observed distance will be 84° 21′ 50 + 2′ 40′′, or 84 24′30′′, But if the index error of the sextant were 2′ 40′′ subtractive, and the same angle measured by it, then the observed distance would be 84° 21′ 50′′. 2′ 40′′, or 84° 19′ 10′′. 7. The apparent altitude of an object is found by applying its semidiameter, and the dip of the horizon, to its observed altitude. The dip is always subtractive. The semidiameter is to be added or subtracted, according as the lower or upper limb of the object has been observed 8. The true altitude of the Sun, or a Star, is found by subtracting the correction in altitudet from the apparent altitude. In correcting a Lunar distance, by the method given in this work, the apparent altitudes only are used. In finding the time, the true altitude of the object is always used. 9. The polar distance of an object is its distance from the elevated Pole of the observer. Hence, when the latitude of the place of observation, and the declination of the observed object, are both of the same name, (that is, both North or both South) the difference between 90' and the declination is the polar distance; but when the latitude of the place, and the declination of the object are of contrary names, the sum of 90 and the declination of the object is its polar distance. 10. The apparent distance between any two objects means the apparent distance of their centres, and is found by applying the semidiameters of those objects to the observed distance, by addition, or subtraction, according as the nearest or farthest limbs have been observed. 11. The semidiameter of the Sun is found in page III. of the month in the Nautical Almanac, that of the Moon, in page VII. for every 12 hours; namely, for Noon and Midnight, at Greenwich, when the Moon's semidiameter is required for any intermediate time, a proportional part of the difference or variation in 12 hours is to be applied to the semidiameter for Noon or Midnight: this gives the horizontal semidiameter, which is to be farther corrected by the aug The Dip or Depression of the Horizon is contained in Table II. |