be obferved to be 67° 5' 36", at the fame time the altitude of the fun's lower limb fhould be 31° 48′ 15", the moon's 23° 48′ 15′′, the eye of the obferver being 18 feet above the furface of the fea. Required the true longitude of the place? Anfwer. 11° 20' 15" weft. Suppofe, at fea in longitude of 10° weft by account, on June the 5th, 1805, the mean of five obfervations were taken; viz. at 3 h. 17 m. 20 f. P.M. the diftance of the fun and moon's nearest limbs were 106° 18 m. 12 f. the error of the fextant 2 m. 37 f-the altitude of the moon's upper limb 20° 4′ 6′′, the error of the quadrant I'm. the altitude of the fun's lower limb 45° 22′ 3′′, the error of the inftrument 48 f.-the eye being 21 feet above the sea. quired the true longitude? Anfwer. 5° 59' weft. Re Suppose, on the 1ft. of January 1806, in longitude 8o east of Greenwich, by account at 5 h. 56 m. A.M. per watch well regulated, the diftance of the moon's fartheft limb from the ftar Pollux fhould be 62° 52′ 28", the altitude of the moon's lower limb being 15° 19′ 14′′, and the ftar's altitude 29° 51′ 39′′, the eye of the obferver being 18 feet above the furface of the fea, and the true longitude fhould be required? Anfwer. 7° 36′ 30′′ east.' NOTE. In vefels which afford only one obferver, it will be found fufficiently exact for practice to have a quadrant at hand, in order to take the altitudes of the objects immediately after the diftance is obferved, as the difference of altitudes which take place during the time spent in the operation will be nearly infenfible. It is recommended to take the altitude of the fun firft. But as it may fometimes happen, owing to the obfcurity of the horizon, that the altitudes cannot be taken, the following methods are given to obtain them by calculation: To find the Sun's true Altitude. It fometimes happens that the distance of the celestial objects may be taken, but for want of a good horizon, or affiftants, their altitudes cannot be taken at the fame time; to fupply fuch deficiencies, obferve the three following cafes. CASE I. The apparent time, the fhip's latitude, longitude, and the fun's declination given, to find the true altitude of his centre. RULE. If the fhip's co-latitude, and the fun's declination, be both north or both fouth, take their fum; but if one be north and the other fouth, their difference is the fun's meridian altitude. With the apparent time from noon, enter Table XXIII. and from the column of rifing take out the logarithm corresponding to it. To this logarithm add the log. co-fine of the latitude, and the log. co-fine of the fun's declination. Their fum, rejecting 20 in the index, will be the logarithm of a natural number, which, being fubtracted from the natural fine of the fun's meridian altitude, will leave the natural fine of his true altitude at the given time. EXAMPLE I. Required the true altitude of the fun's centre, in latitude 49° 57' N. when its declination is 19° 26', at 6 h. 56 m. 30s. in the morning? Nat. fine true alt. 40276=23°45′. EXAMPLE II. What will be the true altitude of the fun's centre at London, when its declination is 20° 49′ S. at 3 h. 21 m. 30s. apparent time in the afternoon? H. Decl. at that time 20 49 S. CASE II. The Apparent Time, the Latitude and Longitude given, to find the Altitude of any of the known fixed Stars. RULE. Turn the longitude into time, and add it to or fubtract it from the time at the fhip, according as it is east or weft, the fum or difference will be the time at Greenwich. Take the fun's right afcenfion from the Nautical Almanack, proportion it to the time at Greenwich, and add it to the apparent time at the fhip, which will give the right ascension of the meridian, or mid-heaven. Find the ftar's right afcenfion and declination in Table XX. and take the difference between its right afcenfion and the right afcenfion of the meridian, which will be the distance of the ftar from the meridian. Having the ftar's distance from the meridian, with its declination and the fhip's latitude, the true altitude is found in the fame manner as has been fhewn in the laft examples of finding the true altitude of the fun. EXAMPLE. What will be the true altitude of Aldebaran, April 11, 18c6, at 5h. 56m. 20s. P. M. apparent time, in latitude 55° 58' N. and long. 3° 6' W.? App. time at fhip H. M. S. 5 56 20 Long. 3° 6' W. in time 0 12 24 CASE III. The apparent Time, the Latitude and Longitude of the Ship being given, to find the true Altitude of the Moon's Centre. RULE. Turn the longitude into time, and if it be weft add it to, but if it be eaft fubtract it from, the apparent time at the ship, and it will give the time at Greenwich. Take the fun's right afcen. out of the N. A. and proportion it to Greenwich-time, which, being added to the time at the ship, the fum will be the right afcenfion of the meridian or mid-heaven. Take out of the N. A. the moon's right afcenfion and declination, and proportion them to the time at Greenwich. Turn the moon's right afcenfion into time, and take the difference between it and the right afcenfion of the mid-heaven, which will be the diftance in time of the moon from the meridian. Having the fhip's lat. together with the moon's declin, and dift. from the meridian, the true altitude is found, in the fame manner as has been fhewn in finding the true altitude of the fun and star. EXAMPLE. What will be the moon's true akitude April 28, 1809, at 6h. 20m. P. M. in lat. 42° 34′ S. and long. 84° 30' weft of Greenwich by account? 51 16 N. fine 78014 In the last example, proportional parts are taken in finding the right afcenfion, declination and log. rifing. Hh 2 By By the three laft cafes the true altitudes of the objects are found, therefore if the apparent altitudes be wanted, the difference between the fun's parallax and refraction must be added to the fun's true altitude, the refraction must be added to the true altitude of a ftar, and the difference between the moon's refraction and parallax in altitude must be fubtracted from the true altitude of the moon thus foun', to obtain the refpective apparent altitudes of their centres. To find the Longitude by the Eclipfes of Jupiter's Satellites. On the day preceding the evening on which it is propofed to obferve an eclipfe, look for the time when it will happen at Greenwich, in page 3d of the month in the Ephemeris. Find the diff. of longitude either by a good map, fea chart, or dead reckoning. Let the watch be regulated by the fun with all poffible exactness to the apparent time. Turn the difference of longitude into time, and add it to, or fubtract it from, the apparent time, according as it is east or west of Greenwich, the fum or difference will be nearly the time when the eclipfe is to be looked for in that place. But as the longitude is uncertain, it will be proper to begin 20 or 30 minutes before. Obferve the hours, minutes and seconds of the beginning of the eclipfe, called immerfion, that is, the very inftant that the fatellite appears to enter into the fhadow of Jupiter; or the emerfion, that is, when it appears to come out of the fame. The difference of time between the obferved immerfion, or emerfion, and that set down in the Nautical Almanack, being turned into degrees, will give the difference of longitude between Greenwich and the place of obfervation. Thefe obfervations made on the firft fatellite, or that which moves nearest to the body of Jupiter, is the most proper for determining the longitude; and here it may be obferved, that its emerfions are not vifible from the time of Jupiter's conjunction with the fun to the time of his oppofition to the fun, and that its immerfions are not vifible from the time of the planet's oppofition to the fun, to the time of its conjunction. The configurations, or the pofitions in which Jupiter's fatellites appear at Greenwich, are laid down every night when visible, in page the 12th of the month in the Ephemeris. EXAMPLE. Suppose on Jan. 8, 1809, in long. 18° 23′E. by account, an emerfion of Jupiter's firft fatellite was obferved at 11h. 3m. apparent time, required the longitude? At Greenwich that day the emerfion began at H. M. S. 9 50 26 II 3 0 |