Ex. 5.-1876, April 18 at 8h 24m A. M. at ship, Long. by account 47° 48′ E. Time by a Chronometer 5h 36m 9s which was fast 12m 22s for mean noon at Greenwich on Jan. 5, and on Jan. 19 was fast 13m 49s for mean noon at Greenwich. Required the Mean Time at Greenwich by Chronometer. Ex. 6.-1876, June 26 at 2h 44m P. M. at ship., Long. by account 300 W. Time by a Chronometer 4h 47m 50s which was slow 6m 17s for mean noon at Greenwich on May 12, and on May 20 was slow 4m 29s for mean noon at Greenwich. Required the Mean Time at Greenwich by Chronometer Ex. 7.-1876, Nov. 16 at 2h 47m P. M. at ship, Long. by account 47° 45′ E. Time by a Chronometer 0h 4m 54s which was slow Om 48s for mean noon at Greenwich on March 10, and on Sept. 23 was fast 22m 31s for mean noon at Greenwich. Required the Mean Time at Greenwich by Chronometer. Ex. 8.-1876, Oct. 28 at 7h 28m A. M. at ship, Long. by account 99° 10′ W. Time by a Chronometer 2h 2m 40s which was fast 18m 22s for mean noon at Greenwich on June 2, and on July 15 was fast 12m 25s for mean noon at Greenwich. Required the Mean Time at Greenwich by Chronometer. Ex. 9.-1876, Dec. 2 at 2h 47m P. M. at ship. Long. by account 18° 27′ E. Time by a chronometer 10h 36m 12s which was slow 2h 58m 40s for mean noon at Greenwich on July 14, and on Sept. 1 was slow 2h 58m 6s for mean noon at Greenwich. Required the Mean Time at Greenwich by chronometer. TO CORRECT THE ELEMENTS. 71. From the observed altitude find the True Altitude (50); get also the True Declination (49) taking the declination from page II of the Almanac and the diff. for 1 hour from page I as before. 72. Subtract the True Declination from 90° when the latitude and declination are of the same name, but add it to 90° when they are of contrary names, and the sum or remainder will be the sun's Polar Distance. 73. From page I* of the Nautical Almanac, take out the * Theoretically, the Equation of Time should be taken from page II, but as errors are very likely to occur in consequence of having to refer to page I to see how it is to be applied, it is better-more especially as it makes no practical difference to take the Equation also from page I. Equation of Time opposite the Greenwich date, marking it + or as directed at the head of the column from which it is taken. Multiply its "diff. for 1 hour" by the Greenwich Time decimally expressed (this is the same as the hourly difference of the declination is multiplied by), cut off from the right as many figures as there are decimals in the two numbers multiplied, and the result will be the correction in seconds. Place this correction (to two places of decimals) under the Equation of Time, and add them together if the equation is increasing, but subtract them if it is decreasing; in this latter case, if the equation is less than the correction, the True Equation of Time, thus found, will have a contrary sign to that taken out. TO FIND THE APPARENT TIME AT SHIP. 74. Underneath the True Altitude set down the Polar Distance and Latitude; now add them together, get half the sum, and then the difference between the Half Sum and the True Alt., and let the result be called the Remainder. 75. Take out the following logs. to seconds (20 to 22) Of the Polar Distance, the Co-Secant. When the Polar dist. 76. Norie.--Take the sum of these four logs. and in Table XXXI find the Apparent Time corresponding to it, as under, viz : If it is P. M. at Ship.-Take out the time corresponding to the log. from the top of the page, (start by taking the next less log. to the given one) prefix the date at Ship, and it will now be the Apparent Time at Ship. If it is A. M. at Ship.-Take out the time corresponding to the log. from the bottom of the page, (choosing the next greatest log. to the given one) and it will be the Apparent Time at Ship, reckoning from the day before the ship's date. In the earlier additions of Norie, the time is always taken from the top, therefore when it is A. M. at ship, the time found will have to be subtracted from 24h, and the remainder will be the apparent time at ship, reckoning from the day before the ship's date. 77. Bowditch.-Take the sum of these four logs. and divide it by 2, now look for this log. in the sine column of Table XXVII, choosing the next less to the given log. if it is P. M. at ship but the next greater if it is A. M. at ship, so that the odd seconds may always be additive, then : If it is P. M. at Ship.-Take out the time corresponding in the P. M. column, to which prefix the ship's date, and you will have the Apparent Time at Ship. If it is A. M. at Ship.-Take out the corresponding time in the A. M. column, add 12h to it, and you will have the Apparent Time at Ship, reckoning from the day before the ship's date. 78. Raper.-The sum of these four logs. will be the log. Sine Square (Table 69) of the Hour Angle, then : If it is P. M. at Ship.-The Hour Angle is the Apparent Time at Ship, reckoning from the day of the ship's date. If it is A. M. at Ship.-Take the Hour Angle from 24h, and the remainder will be the Apparent Time at Ship, reckoning from the day before the ship's date. TO FIND THE MEAN TIME AT SHIP. 79. To the Apparent time at Ship apply the Equation of Time, additive or subtractive according to its sign, and the result will be the Mean Time at Ship. TO FIND THE LONGITUDE. 80. Under the Mean Time at Ship place the Mean Time at Greenwich, subtract the less from the greater (mind and look at your days), and the remainder is the "Longitude in Time," turn this into arc by multiplying it by 60 and dividing by 4, or by Table XIX Norie, Table XXI Bowditch, or Table 18 Raper, and this will be the longitude, which can be named E. or W. by the following well known couplet : "Greenwich time best, Longitude West," "Greenwich time least, Longitude East." Ex. 1.-1876, July 16th at 3h 6m P. M. Mean Time at ship, in latitude 27o 14' N., longitude by account 18° 18' W. The observed altitude of the Sun's Lower Limb was 48° 34' 10". Height of eye 18 feet. Time by a Chronometer 4h 19m 46s which was fast 8m 13s for mean noon at Greenwich on April 10th, and on May 5th was fast for mean noon at Greenwich 6m 18s. Required the longitude by Chronometer. |