8h 17m 35'5 60 Ex. 5. Convert 8h 17m 35.5* into arc. Ex, 6. Convert 11h 39m 50s7 into arc. 11h 39m 505.7 To find the Greenwich date, the time at any other place and the longitude being given. RULE XLII. 1o. Express the ship time astronomically (Rule XXXIX, page 113). 2o. Convert the longitude into time (Rule XL, page 114). 3°. In West longitude.-ADD longitude in time to ship time—the sum if less than 24 hours, is the corresponding Greenwich date on the same day with the ship date; if greater than 24 hours, reject the 24 hours, and put the day one forward. 4°. In East longitude.-From ship astronomical time SUBTRACT longitude in time, if less than the hours, minutes, &c., of ship date—the remainder is the corresponding Greenwich date in the same day as the ship date; if the longitude in time be greater than the hours, minutes, &c., of ship astronomical, ADD 24 hours to the latter, and put the day one back before the subtraction is made. 5°. When it is noon at the place.—The longitude in time, if west, is the Greenwich date (apparent time); but if east, SUBTRACT the longitude in time from 24 hours, the remainder is the Greenwich date (apparent time) after noon of the preceding day. EXAMPLES. Ex. 1. November 9th, at 4h 10m P.M. apparent time at ship, longitude 32° 45′ W.; required the corresponding time at Greenwich, or the Greenwich date. In example 4, the added longitude changes the day of the month; and in example 5, also, a day (or 24 hours) is borrowed before the subtraction is made, since the longitude in time exceeds the astronomical ship date. In example 10, the hours, &c., of longitude to be subtracted are to be taken from a borrowed day, thus making the day of the month at Greenwich one less than at the place, See Rule XLII, 5°, page 116. Required the Greenwich date in each of the following examples : at 3h 40m 16s P.M., apparent time, long. 1. 1865, January 6th, 66° 56′ o" W. 2. 22 February 13th, at 8 40 4 o W. 3. February 1st, at 5 10 20 30 E. 4. March 15th, April 11th, at I 40 45 E. long. 14151 15 W. 12 8. November 1st, 9. December 1st, long. 114 30 o W. o E. دو 33 P.M. apparent time, August, at 6 31 32 P.M. apparent time, long. 100 17 30 E. September 1st 13. December 28th, 4 36 A.M. at Noon, June 1st, at Noon, 17. March 2nd, at Noon, at Noon, I A.M. mean time, long. 148 47 30 W. 51 o E. o W. 40 5 o E. 10 。 E. REDUCTION OF ELEMENTS FROM NAUTICAL ALMANAC. THE Nautical Almanac contains the right ascension, declination, &c., of the principal heavenly bodies for certain fixed times at Greenwich; the right ascension and declination of the sun and planets, for example, being given for every day at noon (oh om o3), while for the moon these elements are given for every hour. At a place under any other meridian than that of Greenwich, or at any other time of the day than that for which any quantity is given, it is requisite to apply a correction to that taken from the Almanac, in order to reduce it to its value at the given instant. For this purpose we may either apply the common rules of proportion, or, which is in general the simplest method, make use of certain tables computed for the purpose, called tables of proportional logarithms. 1° TO REDUCE SUN'S DECLINATION. FIRST METHOD-By proportional logarithms. RULE XLIII. Get a Greenwich date by means of ship time, expressed astronomically, and longitude (see Rule XLII, page 116), or by means of chronometer. 2o. Take out of the Nautical Almanac the declination for the noon at Greenwich, and that following it. (a) When Greenwich date is given in apparent time, use Page I of the month, but for mean time, use Page II of the month. (b) The tenths of seconds (") of declination may be rejected when less than five, but call them 1" when they amount to five, or above-thus 42" 7 would be 43′′. 3°. When the declinations are of like names, take their difference; but when of different names, take the sum: this is the daily variation of declination. (a) When the declination is increasing, place the sign of addition (+) before the daily variation; but when the declination is decreasing, place the sign of subtraction (-) before it. 4. Under the daily variation place the hours and minutes of Greenwich time, and take from the table (Table XXI A, Raper, or XXXIII, Norie) log. of change of declination in 24 hours, and log. of hours and minutes of Greenwich time; the sum of these logs. found in the table will give the proportional part of daily change of declination. (a) When the seconds of time (in Greenwich date) are less than 30s, they may be rejected; but if above 30s, increase the minutes of time by im; thus, Greenwich time 2h 35m 40s would, in using the tables, be called 2h 36m. (b) In using Table XXI A, Raper, or Norie XXXIII, minutes (') of declination, and hours of time (h), are found at the top of the columns; seconds (") of declination, and minutes (m) of time, at the side columns. 5°. Apply the proportional part to the declination at the first noon, adding when the declination is increasing; but subtracting when the declination is decreasing; the result is the declination at the time required. (a) If the proportional part, when subtracted, exceed the declination itself, subtract the declination from the proportional part; the remainder is the declination of the contrary name. In March when the declination changes from South to North, and in September when it changes from North to South, if the correction, by being subtractive, exceeds the declination, subtract the declination from the correction, and call the remainder N. in March, but S. in September. See examples, 3 and 6. 1o. 2°. SECOND METHOD-By the hourly difference. RULE XLIV. Find a Greenwich date, as before. Take out of Nautical Almanac the declination at noon of Greenwich date, and a little to the right place the "difference for 1 hour," found in - page 1, N.A.* 3°. Multiply this last quantity by the hours and fractional parts of an hour of Greenwich date; the product, reduced to minutes and seconds, is the change of declination in the time from noon. 4. Apply this change to declination at noon, adding it when declination is increasing, but subtracting it when declination is decreasing; the result is the declination sought. *In the Nautical Almanac for 1863 and following years, the quantities given in the column marked "Diff. for 1 hour," are not the 1-24th part of the daily variation as heretofore, but the hourly change which the declinatian is undergoing at the time of sun's transit, and is obtained by dividing the change of the declination (Page I) between the day before and the day after the given day by 48. In order, therefore, to the accurate determination of the declination at any given time (including, of course, the second difference), the "Diff. for 1 hour" must be reduced to a time midway between that for which the declination is given and that for which it is required, that is, for the middle time between noon of the given day, and the given time on that day. Example.-Greenwich date, January 25d 8h, the middle time between noon 25th and 25d 8 is 25d 4h. Having found middle time, take out of Nautical Almanac the hourly difference for noon of given day and hourly difference for next day, take the difference of them, which is daily change of hourly difference, and take proportionate parts of this change for middle time, which apply to hourly difference at noon of given day, adding when hourly difference is increasing, and subtracting when decreasing. By using the hourly difference as heretofore, a not inconsiderable error may arise (sometimes amounting to 12"). It is surprising that no explanation has been given in the Nautical Almanac as to the above new plan for hourly differences, which is a very ingenious method for finding the declination as correct as by using second differences; yet nautical men will not, it is presumed, trouble themselves by proportioning for hourly differences. The better plan would be to proceed according to the preceding rule (Rule XLIII), using Norie's Table XXXIII, or Raper's XXI A; and it is to be hoped that this method will be adopted at the examinations by the Marine Boards, remarks apply to the equation of time and to the sun's right ascension, The same |