CONTENTS. Page PROBLEM I.-To find the apparent time, the Sun's true azimuth, and the mean time, by the altitude of the Sun - - - - 6 PROBLEM II.-To find the mean time by the altitude of a fixed Star, a Planet, PROBLEM III.-To clear the lunar distances from the effects of parallax and PROBLEM IV.-To find the mean time at Greenwich answering to a given lunar distance - - - - - - - 14 Remarks on observing the lunar distances - - - - - 16 PROBLEM V.-To find the longitude by lunar observations - PROBLEM VI.—To find the altitude of a celestial object by computation - On finding the longitude by Chronometers - - On finding the errors and rates of Chronometers - - - - Remarks on the management of Chronometers Table A.* Acceleration of the fixed Stars in mean time - Introductory remarks on the Stars - - Directions for the Zodiacal Stars - - Directions for the Stars in the Northern Hemisphere Directions for the Stars in the Southern Hemisphere On finding the latitude by the fixed Stars EXPLANATIONS OF THE TABLES - - - - - - 65 Table A. To convert mean time into sidereal, &c. I. To turn degrees into time or time into degrees III. Dip of the horizon at different distances from the observer - IV. Moon's augmentation - - - - - - 2 V. Contraction of semi-diameter of Sun or Moon - - 2 VI. Corrections of the apparent altitudes of the Sun and Stars VII. To correct the mean refraction - - - - - 4 VIII. Correction of the Moon's Semi-diameter, &c. IX. Altitudes by which the Apparent Time, or horary angle, may be found with the greatest accuracy . 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 - XV. Logarithms of the apparent altitudes - - - XVI. Logarithms of the apparent distance XVII. Logarithms of the first and second corrections XIX. Proportional logarithms · XX. Correction of the apparent altitudes of the Sun and Stars - 137 XXI. Correction of the Moon's apparent altitude - - XXII. Logarithms of the Moon's apparent altitude .. XXIII. Logarithms of the sum and difference XXIV. Logarithms of numbers . - - XXVI. To find the time of a Star's passing the meridian - ABBREVIATIONS, &c. Accel. .... Acceleration. Obs....... Observed. Add. Star. 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 east, the estimated astronomical time at Greenwich is obtained ; and to this time all the articles required from the Nautical Almanac are always reduced, because, they are calculated for that meridian.t The term “ Greenwich Date," instead of Greenwich time, adopted by Inman and Raper in their works upon Nautical Astronomy, is more definite than the old term, and is therefore made use of in the following pages, to express that moment of time at Greenwich, simultaneous with any given date, at any other meridian, including the year, month, day, &c. 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 + The above remark shews, that it is of the utmost consequence, when without a Chronometer on board, that the time at Ship should be strictly attended to, as it is an element in every calculation, (except the correction of the Sun's declination for apparent noon, and the sidereal time at mean noon.) When there is a Chronometer on board (having its error and rate), the Greenwich date will, in all requisite cases, be found most conveniently, by noting the time shewn by Chronometer at the moment of any observation, such as, in the method of finding the latitude by the Polar Star, out of the meridian, given in the Nautical 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. at the noon of the month, accordiomical time, on the 4. The astronomical day begins at the instant that the tnautical 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 preceding noon, and then change the date to the preceding day. Thus, 5h. 30m. P.M. nautical time, on May the 10th, is 5h. 30m. astronomical time, on May the 9th; and 5h. 30m. A.M. nautical time, 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, I 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 semidiameter of the Sun is found in page II. of the month in the Nautical Almanac, that of the Moon, in page III. + Nautical time has been generally abolished as inconvenient, the only advantage it possessed, was finishing the “ day's work,” and date together. |