evidently not affected by refraction or parallax, which acting in vertical lines cause the true place of the moon to be elevated above its apparent place (the parallax from her vicinity to the earth, being a greater quantity than the correction for refraction), and that of the sun or star, to be depressed below its apparent place. Let M' and S' represent the corrected places of these bodies, and we have then ZM' and ZS-the zenith distances corrected for refraction and parallax-and the angle Z' before found, to find the true lunar distance M'S' in the triangle ZM'S'. The apparent time represented by the angle ZPS may be found in the triangle ZPS, having SS, PS, and ZP the co-latitude, if the exact error of the chronometer at the moment is not already known; and this time, compared with the Greenwich time at which the lunar distance is found from the "Nautical Almanac" to be the same, gives the difference of longitude east or west of the meridian of that place. The example below will show all the steps of the operation. On May 4th, 1838, at 10h 41m 45.88 by chronometer, the following observations were taken in latitude 51. 23.40′ north, to find the longitude; the chronometer having been previously ascertained the same evening to be 3m 34s too fast. Double altitude 74° 42' 35"-taken with a sextant; index error 22". Altitude Spica Virginis 28° 15′ 58"-with alt. and az. inst.; index error 28". Distance D * 31° 25′ 55′′—with repeating circle. Barometer standing at 29.9", and thermometer at 61°. 1st-Then in the triangle ZMS we have the three sides to find the angle MZS. + 8.49 14 53.75 (b) ZS = 61 44 38. ar. comp. sin. 0.0551028 (c) ZM = 52 53 47.3 ar. comp. sin. 0.0982439 Then to correct the zenith distances for refraction and parallax: ▷ Apparent zenith distance ZM = Refraction Parallax ZM', Corrected zenith distance ZS, Spica Virginis apparent zenith distance 52 53 47.3 + 1 14.1 Mean Refraction D 1 16.05 By the "Nautical Almanac" it appears that the Greenwich mean time answering to this distance, must be between 9 P.M. and midnight. The difference between the prop. log. at 9 and midnight being 0, the correction of 2nd differences is nothing. * The interval of time past 9 P.M. might of course have been found by a common proportion, without the aid of prop. logarithms. |