Apparent dis.52 56 00 Sine, alt. 41 2 D's app. 9.9019 Same, First rem. 32.30 co-sec. 0.2697 2d rem. 20.26 co-sec. Table I. logarithm, 0.1786 Table II. logarithm, True distance, 52 50 28 Index error, Second rem. 20 26 Dis. by Naut. Alm. at 3 hours, 52 55 42 Longitude in time, 2 51 40 which reduced into longitude at the rate of one hour to fifteen degrees, four minutes to one degree, and four seconds to one mile; or more briefly by Table XII. Longitude in 42° 55' 00" east. Suppose on the 7th of April, 1817, at two hours astronomical account, in longitude 54° east, by account, the observed distance of the sun and moon's nearest limbs was 105° 16′ 20′′, the observed altitude of the sun's lower limb 42° 3', and the observed altitude of the moon's lower limb 26o 4'. Required the true longitude. Sun's obs. alt. 42° 3'-observed alt. moon's lower limb, 26° 4' Sun's app. alt. 42 15 Moon's apparent altitude, April 6th, astronomical account, 22h 24', or 10h 24', A. M. on the 7th, civil account. The reduced time being 10h 24′ from midnight on the 6th of April, by the Nautical Almanac, the moon's semi-diameter and horizontal parallax is taken out for midnight on the 6th, and noon on the 7th of April, as follows. Moon's semi-diameter at midnight, on the sixth, 16′ 2′′ Moon's semi-diameter at noon on the seventh, Difference in twelve hours, Difference in 10h 24' by Table XI. Augmentation moon's S.D. Table VIII. Moon's true semi-diameter, Moon's horizontal parallax, sixth, at midnight, 15 55 7 6 15 56 7 16 03 58 45 58 18 By Naut. Alm. dist. at noon, 7th, 104 13 56 Suppose the chronometer set to the meridian of Greenwich, and it should keep time regular, and if not, the rate or difference must be ascertained before the ship sails; a chronometer set thus to Greenwich time, say at Cape Henlopen, in longitude 75° west of Greenwich; when it is mean noon at Cape Henlopen, by chronometer, it will be five hours past noon, because the sun will be on the meridian of Greenwich earlier than at Cape Henlopen, of course they will have their noon first. A ship starting from Cape Henlopen with the chronometer set thus, after she has sailed east 15°, when it is mean noon at ship, it will be four hours afternoon by chronometer; and after she has sailed east 30°, when it is noon mean time at ship, it will be three hours afternoon by the chronometer, and when she is on the meridian of Greenwich, the ship's time and chronometer will agree, and after the ship has passed 15° east of the meridian of Greenwich, by the chronometer, it will be 11 o'clock in the forenoon when it is 12 o'clock, or noon, by ship's account. Now the time at ship is greater than Greenwich time, because the ship has the sun on the meridian before it is on the meridian of Greenwich. 11 |