Or, by taking 42° 29′ for the first altitude, and 13° 52' N. for the first declination, the tabular correction will be 83", the corrected first altitude 42° 49′, using this and the secand altitude 53° 43', the corresponding second declination 14° 16′ N. and the hour angle 1h. 44m. 15s. the latitude will be found 48° 54′ N. nearly agreeing with the former calculation. 3. Given the correct central altitude of the moon 55° 38', her declination 0° 20′ S. After an interval in which the hour angle was 5h. 30m. 49s. her correct central altitude was 29 57, and her declination 1° 10′ N. The latitude by account 23° 25′ S. Required the true latitude ? With the first altitude 55° 38′ and the first declination 0° 20' S. the tabular correction is 71" and the first corrected altitude 54° 34′ 6′′. Using this with the second altitude 29° 57', the second declination 1° 10′ N. and the hour angle 5h. 30m. 49s. the true atitude will be found 23° 23′ S. Or, by taking 29° 57′ for the first altitude, and 1° 10′ N. for the first declination, the tabular correction will be 45" and the first corrected altitude 30° 37'. Using this with the second altitude 55° 38′ the second declination 0° 20′ S. and the hour angle 5h. 30m. 49s. the true latitude will be found to be 23° 24′ S. nearly agreeing with the preceding calculations. In making the calculations of these three examples the seconds were noticed, which is always best to be done, particularly when the altitudes are nearly equal; some difference might be found in the above results if the nearest minutes only were taken. Thus, Example XII. page 144, calculating to the nearest minute, only gives the latitude 55° 28′. If the calculation be made as in Ex. I. of this appendix, it becomes 53° 25′, differing 3'. This would be avoided by taking the angles to seconds, and in some extreme case it would require the use of 6 or 7 places of decimals. TABLE shewing the variation of the altitude of an object arising from a change of 100 seconds in the declination. If the change moves the body towards the elevated pole, apply the correction to the altitude with the signs in the Table; otherwise, change the signs. LATITUDE Of same name as declination. LATITUDE Of different name from declination. Dec. Alt. 70° 60° 50° 10° 300 200 10000 100 200 300 400 500 600 700 A. Dec. 00 65 35 90 -10 11 45 601 -15 -31 14 11 70° 60° 50° 40° 30° 20° 10° 0 100 200 300 400 500 1600 170 of different name from declination. TABLE XLVIII. TABLE shewing the variation of the altitude of an object arising from a change of 100 seconds in the declination. If this range moves the body towards the elevated pole, apply the correction to the altitude with the signs in the Table ; otherwise, change the signs. LATITUDE 4062 LATITUDE of different name from declination. 100 200 300 1400 (50° 160° -9 28 73 50 25 -2 -30 59 115 89 60 27 -7 -43 79 114 125 82 35-16 -69121 0 95 103 10 20 74 91 106 30 89 107 40 140 50 85 110 60 70 36 52 58 73 86 97 104 10 20 58 77 94 109 30 70 92 111 40 16° 50 SINCE the former part of this work was printed, a new form has been given to Table XX. by which the last corrections of a Lunar Observation may be found very expeditiously. The correction in this new Table will frequently exceed those deduced from the former one by two or three seconds, on account of having introduced the fourth and fifth corrections, which were formerly omitted. In using this new Table, it will in general be sufficiently accurate to find the nearest altitudes and distance, and take out the corresponding correction, without the trouble of making a proportion for the neglected degrees and minutes. Thus in Example I. enter the new table with the 's altitude 50°, D's alu tude 700, distance 500, which are the nearest numbers in the Table, the corresponding correction is 20", as found before. In the second example the 's altitude 100, D's 20°, distance 00, give the correction 27", being 4 more than the former method. In the third example the correction is 24′′. In the fourth 22". In the fifth 17". In the sixth 19". These corrections are always additive. In using the second and third methods of working a lunar observation, this correction is to be found in the same manner, and added to the corrected distance, subtracting 18" trom the sum. Thus, in Example I. the correction 20" is to be added, and the constant quantity 18′′ subtracted, leaving 2′′ to be added instead of 1", found by the former method. TABLE XX. (New Form.) Correction in Seconds, additive- DAILO 10° 10° 20 15 13 80 500 600 700 800 900 1000 1100 120° 962 79' 67" 60" 53" 48' 41' 37' 27" 237 19" 15" 66 71 64 58 52 48 43 46 44 55678o 16 15 17 18 40 50 40 100 500 END OF THE APPENDIX. 80 EDMUND AND GEORGE W. BLUNT, HYDROGRAPHERS, HAVE OPENED A CHART AND QUADRANT STORE, No. 149 FLY-MARKET-STREET, One door above the North corner of Front-Street, NEW-YORK; where, by per sonal attention to business, they hope to receive that patronage which industry and perseverance merit. They have for sale BOOKS: BOWBITCH'S PRACTICAL NAVICATOR, 6th edition, stereotyped. THE MERCHANT'S AND SHIP-MASTER'S ASSISTANT, containing information useful to merchants, masters of ships, &c. NAUTICAL ALMANACS, from the year 1811 to 1828, both inclusive-to be continued annually. Explanation stereotyped, and English copy corrected. SEAMANSHIP AND NAVAL TACTICS, second edition. WARD'S LUNAR TABLES. CHARTS: A NEW CHART, extending from New-York to Havana, including Bahama Banks and Channels, improved by actual surveys of the Cheseapeake Bay, by order of the Navy Department, and of Capes Hatteras, Lood Out, and Fear Shoals, in conformity to an act of Congress of the United States, and conducted under the direction of J. D. ELLIOT, Esq. Capt. in the U. S. Navy, and by permission of Hon. SMITH THOMPSON, Secretary of the Navy, copied, and contains all the Surveys made on the Coast of North Carolina, to the present time (1826.) This Chart. has been since improved by a survey from Sandy Hook to Cape May, under the direction of Capt. JONATHAN COLESWORTHY, and EDMUND BLUNT, Hydrographer. It has also several PLANS of HARBOURS, from actual surveys. DO. of the Mississippi River, extending to New-Orleans, including Mobile, &c. with sailing directions, and plan of Mobile, on a large scale, from actual survey. DO. of Bahama Banks, from actual survey, made in sloop Orbit, in 1820, with sailing directions. DO. from New-York to Nova Scotia, extending from latitude 38° N. to latitude 47° N. longitude 68 W. to longitude 74 W. including the whole of St. George's Bank, improved to August, 1821, by government and other surveys, by which the latitude of the South Shoal of Nantucket was found 22′ wrong, and is here, for the first time, published correct. DO. of the Atlantic or Western Ocean, improved to 1820, with an Analysis of the aurthorities upon which the dangers have been inserted on the Chart. The Tracks extend to the Equator, and are continued on the Chart of the South Atlantic Ocean. This is the only general Chart extant which has the latitude of the South Shoal of Nantucket within 22 miles correct. DO. of the South Atlantic Ocean, containing more authentic information than any extant, part of which describes dangers lately discovered, with original plans of harbours and views, DO. of the North Coast of Brazil, showing the entrances and courses of the Rivers Para and Amazon. DO. of the West-Indies, on four sheets, which may be had separate. DO. of the Coast of Guyana. DO. of the Coast of Brazil. DO. of the Island of Bermudas, with sailing directions on the chart. DO. of the Coast of Labrador. DO. of Newfoundland. PLAN of New-London Harbour, surveyed by CHARLES MORRIS, Esq. of the United States Navy, by order of Commodore RODGERS, and to him respectfully dedicated. Repeating Circles; Brass Sextants, with Telescopes complete, in mahogany cases; Brass Sextants for the pocket; Ebony Sextants; Quadrants of superior make, with Telescopes; ditto without; Artificial Horizons; Steering, Storm, Amplitude, Azimuth, Pocket and Hanging Compasses; Day Telescopes for sea or land; Night and Day Telescopes; Night Telescopes, either to invert the object or show it erect; Cases of Instruments for Navigation and Drawing in general; Scales and Dividers, Common and Sliding Gunter's Scales; Mast-makers', Ship-carpenters', and Cordage Rutes; Marine and Common Thermometers; Log and Time Glasses; Bar and Compound Magnets; U u |
