The preceding examples of corrections of the moon's altitude and logarithms, are for the examples of the lunar observations given in this book. Lunar Observations taken on board the ship Mount Vernon, from Marseilles towards Havanna, on the 12th day of April, 1817. On the 12th of April, 1817, at 10h 10' 24", A. M. civil account, which is April 11th, by astronomical account; that is, by the Nautical Almanac, longitude by account 42° 50' west of Greenwich, observed the distance of the sun and moon's nearest limbs 44° 36′ 42′′. The observed altitude of the sun's lower limb 61° 11'. The observed altitude of the moon's upper limb 56° 50′, required the true longitude. PREPARATIONS. It is necessary to mention that the astronomical day begins at noon on the civil day, and continues twenty-four hours; so that in the place of calling it one o'clock in the morning by the astronomical account, it is called thirteen hours. Therefore 10h 10' 24" A. M. on the 12th of April, by civil account, will be 22h 10′ 24′′ astronomical account. April 11th, astronomical account, 22h 10' 24" 2 51 20 25 01 44 24 00 00 Subtract 24 hours from it; it leaves 1 1 44 April 12th, astronomical account, the following day. So that the moon's semi-diameter and horizontal parallax must be taken out on the twelfth, between noon and midnight, astronomical acccount, the Moon's semi-diameter at noon, 14' 57" Do. do. at midnight, The difference is 3" in 12 hours, and the 14 54 00 3 reduced time is little more than one hour, the proportion in onetwelth part of three seconds, which is immaterial; so that the semi-diameter and horizontal parallax may be taken out for noon. If the reduced time should be a quarter, half, one-third, twothirds, three-fourths, the proportions to be taken and proportioned accordingly; or more brief by Table XI. The difference of twelve seconds in twelve hours being the time between noon and midnight, will equal one second to each hour, and the reduced time being nearly one hour, is one twelfth part of the time between noon and midnight. The moon's horizontal parallax is on the decrease, one second is subtracted from the horizontal parallax at noon, gives 54' 47". The proportions may be found by saying, if twelve hours gives a given difference of semi-diameter or horizontal parallax, what will a given reduced time give; or by use of Table XI. When the error of the watch is found, for giving the apparent time, for the purpose of finding the longitude by lunar observation, the lunar observation will give the longitude at the time when the error of the watch was found. True distance, To find the Longitude. 44° 46′ 14′′ N. A. dist. at noon, 45 15 21 Diff. o' 29′ 07′′ prop. log. 7911 N. A. dist. at 3h. 43 51 51 Diff. 1 23 30 prop. log. 3336 See Table XII. for converting time to longitude, and Table XIII. for reducing longitude to time; see also the Nautical Almanac for the year 1817, at the end of the tables, to suit the examples in this book. The time over the first distance is twelve hours, which, added to one hour, two minutes, and forty-six seconds, makes thirteen hours, two minutes, and forty-six seconds, the time at Greenwich. Time at ship is ten hours, ten minutes, and twenty-four seconds, which, subtracted from thirteen hours, two minutes, and forty-six seconds, makes the difference two hours fifty-two minutes, and twenty-two seconds. It can also be done as follows: twenty-four hours can be added to one hour, two minutes, and forty-six seconds, which will be 25h 2'46" Then the time at ship call 22 10 24 The difference is longitude in time, as before 2 52 22 longitude, 43° 5' 30" On the 22d of April 1817, oh 16' 15", astronomical account, which is also the 22d of April by civil account, observed the distance of the sun and moon's nearest limbs, 66° 59′ 18′′. Sun's observed altitude, lower limb, 81° 36', the observed altitude of the moon's upper limb 29° 26', longitude by account 55° 20′ west of Greenwich. 22d of April by the Nautical Almanac, Longitude in time, Reduced time, or estimated time at Greenwich, Oh 16' 15" 3 41 20 3 57 35 In this case the moon's semi-diameter is taken out between noon and midnight on the 22d of April, 1817, astronomical time. Moon's semi diameter at noon, 15' 9" Ditto at midnight, 15 14 The reduced time is four hours, which is the third of twelve hours, the time between noon and midnight in the Nautical Almanac; and the third of five seconds is as near as possible two seconds, which is to be added to the semi-diameter at noon, as the semidiameter is increasing, which makes the semi-diameter fifteen minutes and eleven seconds. The moon's horizontal parallax at noon, The difference in twelve hours, 55' 30" 55 49 19 Proportional part is six seconds, and as the horizontal parallax is increasing, it is added to 55 30, which is 55 36, the horizontal parallax at reduced time. |