proportional logarithm of the second correction; these corrections being found in Table XXII. are to be placed under the former corrections. Enter Table XX. and seek in the side column the nearest minute of the correction of Table XIX. opposite thereto and under the distance in the column marked Table XIX. will be a number of seconds which reserve. Enter the Table again, and find at the side the nearest minute to the sum of the correction of Table XIX. and the second correction opposite to this sum and under the distance in the column marked Table XIX. +2d. Cor. will be a number of seconds; the difference between this and the former reserved number of seconds will be a correction to be placed under those already found. Then by adding all these corrections to the apparent distance decreased by 20 the true distance will be obtained nearly.* To determine the Longitude from the true distance. If the true distance of the observed objects can be found in the Nautical Almanac, in either of the pages 3, 9, 10, 11 of the month, opposite to the given day, or to that which immediately precedes or follows it, the time will be found at the top of the page. If the true distance cannot be found in the Nautical Almanac, take out the two distances, one of which is the next greater and the other the next less than the true distance; take the difference between these two distances, and also the difference between the distance which stands first in the Nautical Almanac and the true distance. Then the Proportional Logarithm of the former difference (Table XXII.) being subtracted from the prop. log. of the latter difference, the remainder will be the prop. log. of a portion of time to be added to the time standing over the first distance in the Nautical Almanac, and the sum will be the true time at Greenwich. The difference between this time and the apparent time at the ship turned into degrees and minutes by Table XXI. will be the true longitude of the ship from Greenwich at the time of observation, and the longitude will be East if the time at the ship be greater than that at Greenwich, otherwise West.t To exemplify the preceding rules there will now be given six examples of correcting the apparent distance by this new rule, in which examples we shall also include the preparation and the determination of the longitude from the true distance. EXAMPLE I. Suppose that on the 2d of January, 1820, sea account, at 6' past midnight, apparent time in the longitude of 121° 30' E. by account, the observed distance of the farthest limb of the moon from the star Aldebaran was 47° 48' 53", the observed altitude of the star 50° 35', and the observed altitude of the moon's lower limb 70° 35'. Required the true longitude? *The distance obtained by this rule is not perfectly correct, since several small corrections must be applied to obtain the true distance to the nearest second, viz. (1) The refraction taken from Table XII. which was made use of in constructing Tables XVII. XVIII. and XIX. ought to be corrected for the different heights of the Barometer and Thermometer, as directed in page 103. (2) A correction must be applied for the spheroidal figure of the earth. And (3) a very small correction equal to the fourth correction of Witchell's method given in page 62 of the Appendix of the second edition of the Requisite Tables of Maskelyne must also be applied.-But to notice all these corrections would increase the calculation very much, and the result of a single observation, in which all these things were noticed, would probably not be so accurate as the mean of two or three observations, taken at different times of the day, in which these corrections were neglected, and the time necessary to take and work the latter observations would not be much greater than to work a single observation in which all the corrections were noticed. It may be necessary to observe that if the times at the ship and Greenwich fall on different days the latest day is to be reckoned the greatest, though the hour of the day may be the least; thus 17th Suppose that on the 20th September, 1820, sea account, at 7h. 23′ 45′′, P. M. apparent time, in the longitude of 166° 30′ W. by account, the observed distance of the nearest limb of the moon from the star Antares was 81° 3' 18", the observed altitude of the star 12° 34', and the observed altitude of the moon's lower limb 20° 26'. Required the true longitude? • This Log.=Log. Table XIX. 2260+Log. Table C. 9=2269. This Corr. Corr. Table XIX. 41' 49+ Corr. Table A. 13+Corr. Table B. 6=42′ 08′′. Suppose on April 25th at 2h. A. M. sea account, in the longitude of 1660 E. by account, the observed distance of the moon's farthest limb from Antares was 76° 32′ 15′′, the observed altitude of the star 23° 34', the observed altitude of the moon's lower limb 17° 59'. Required the true longitude? * This Log.=Log. Table XIX. 1883+Corr. Table C. 5.-1888. This Corr. Corr. Table XIX. 5' 5"+ Corr. Table A. 2"+Corr. Table B. 2"-5' 9", ↑ This Log.=Log. Table XIX. 2426 Corr. Tab. C. 6=2482. Suppose that on the 31st October, sea account, at about 1h. P. M. in the longitude of 750 W. by account, the following observations of the sun and moon were taken. Required the true longitude? App. Dist. 69 14 Sine 9.9708 Ap. Alt. 46 02 Rem. 20° 12' Co-s 0.4618 same Sum 1-2 Sum 1 Rem. 2 Rem. 132 24 9.9708 App. Dist. less 2-67 13 52 0.4618 Table XVIII. 0.3941 Table XIX. Table XVIII. log. 1.8848 Table XIX. log.* 2457 1 Cor. 2 Cor. 2.3180 2 Cor. 15' 14" P. L. 1.0724 Table XX. 59 11 10 52 52 '15 14 22 * This Log.=Log. Tab. XIX.2454+Cor. Tab. C. 3=2457. This Corr. Corr. Tab. XIX. 10′ 12"+Corr. Tab. A. 40+Corr. Tab. B.0"=10′ 52′′. |