is at the place corresponding to a given time at Greenwich, and the converse. To find the time at Greenwich, corresponding to any given time at a place, is required in almost every nautical problem; and even if the longitude of the place and time are only known nearly, the approximate true time at Greenwich, deduced from the estimated longitude and time at the place, is an important element in nautical astronomy. The time at Greenwich, obtained in this manner, is called an approximate Greenwich date, or more frequently the Greenwich date. To find the Greenwich date, we shall require the following rules for reducing degrees into time, and the converse. Rule III. To reduce degrees into time. (1.) Divide the degrees by 15, the quotient is hours. (2.) Multiply the remaining degrees, if any, by 4; the result is minutes in time. (3.) Divide the minutes in arc by 15; the quotient is minutes in time. (4.) Multiply the remaining minutes of arc, if any, by 4; the result is seconds of time. (5.) Divide the seconds in arc by 15; the quotient is seconds in time, carried to decimals if necessary. The sum will be the arc in time. TABLE To reduce degrees into time, and the converse. Or, thus, by means of the Table to the nearest minute. * The table is computed to the nearest minute of arc; when seconds are to be reduced (which is seldom required) the student must proceed as pointed out in the preceding example and rule. 1. Multiply the hours by 15; the result is degrees. 2. Divide the minutes in time by 4; the quotient is degrees. 3. Multiply the minutes remaining, if any, by 15; the result is minutes of arc. 4. Divide the seconds of time by 4; the quotient is minutes of arc. 5. Multiply the seconds (and parts of seconds) remaining, if any, by 15; the result is seconds of arc. The sum will be the arc in degrees. Or thus, by means of the table, to the nearest minute. 2h 18m 58s.26 = 2h 19m nearly. To find the Greenwich date, having given time at ship and the longitude. 1. Express the time at the ship astronomically (p. 65). 2. Reduce the longitude into time, and put it under ship time (p. 68). 3. If west longitude, add longitude in time to ship time; the sum, if less than 24 hours, will be the time at Greenwich, or the Greenwich date on the same day as at the ship. But if the sum be greater than 24 hours, reject 24 hours; the result will be the Greenwich date on the day following the ship date. If east longitude, subtract longitude in time from ship time, the remainder will be the Greenwich date. If the longitude in time is greater than the ship time, 24 hours must be added to the ship time before subtraction is made, and the Greenwich date will be the remainder on the day preceding the ship date. EXAMPLE. June 10th, at 6h 10m P.M., in longitude 32° 42′ W., required the time at Greenwich, or the Greenwich date to the nearest minute. July 12th, at 4h 5m A.M., in long. 63° 45′ W., required the Greenwich date. EXAMPLES. Required the Greenwich date in each of the following examples. Ship times. Answers, Greenwich dates. (21) Mar. 7, at 3h 15m A.M. Long. 15° 45′ E. Second Method of finding a Greenwich Date. The Greenwich date is more correctly found by means of a chronometer, whose error on Greenwich mean time is known. Rule VI. To the time shown by chronometer, apply its error on Greenwich mean time; adding if error is slow, and subtracting if error is fast, on Greenwich mean time; the result is the Greenwich date in mean time. Sometimes 12 hours must be added to this result, and the day put one back. This uncertainty may be removed by getting an approximate Greenwich date in the usual way by means of ship mean time and the estimated longitude; if the difference between the Greenwich dates found by the two methods is nearly 12 hours, then the Greenwich date by chronometer must be increased by 12 hours, and the day put one day back, if necessary, so as to make the two dates agree both in the day and hour nearly. The following examples will remove any doubt as to putting the day one back, or not. EXAMPLE. July 10th, 1853, at 6h 34m P.M. mean time nearly, in longitude 60° W., a chronometer showed 10h 42m 3s, its error on Greenwich mean time being 2m 10s fast; required mean time at Greenwich, or the Greenwich date. |