3. Correct the sun's apparent altitude for index correction, dip, semidiameter, correction in altitude, and thus get the sun's apparent and true altitudes. Subtract the true altitude from 90° for sun's zenith distance. 4. Correct the moon's observed altitude for index correction, dip, semidiameter (augmented), correction in altitude, and thus get the moon's apparent and true altitude. Subtract the true altitude from 90° for moon's zenith distance. 5. When the moon's correction in altitude is taken out of the Tables, take out also at the same opening the auxiliary angle A. 6. Correct the observed distance for index correction, and to the result add the semidiameter of the sun and moon (augmented), and thus get the apparent distance of the centres. 7. To find ship mean time.* Under sun's declination put the latitude of the ship; take the sum if their names be unlike, the difference if the names be alike. Under the result put the sun's zenith distance; take the sum and difference of the last two lines put down. Add together the log. secants of the two first quantities in this form (omitting to put down the tens in the index) and half of the log. haversines of each of the two last quantities. The sum will be the log. haversine of the ship apparent time. When the sun is west of the meridian, the time corresponding to the haversine must be taken out at the top of the page; but when the sun is east it must be taken out at the bottom. The result is apparent time at the ship: to this apply the equation of time with its proper sign and the result will be the ship mean time. 8. To calculate the true distance, and thence Greenwich mean time. * If the student have no table of haversines he may proceed as pointed out in the note p. 171, and Ex. p. 174, to find ship apparent time. Add together the zenith distances of the sun and moon, and mark the sum v. Add together the apparent altitudes of the sun and moon, and under the sum put the auxiliary angle A: take the sum and difference of the last two quantities, and mark each with the letter v. Under the apparent distance of the centres put the auxiliary angle A and take the sum and difference and mark each result with the letter v. Add together the five last of the quantities marked v. being looked for in the apparent distance or in the adjacent column, the are corresponding thereto will be the true distance of the sun and moon at the time of the observation. figures of the versines of each The five last figures in the sum column of versines under the 9. To find Greenwich mean time corresponding to this true distance. Take out of the Nautical Almanac two distances of the sun and moon three hours apart, between which is the true distance just calculated: place the first distance taken out under the true distance, and the one three hours after under the other distance taken out. Take the difference between the first and second, and also between the second and third. From the proportional logarithm of the first difference subtract the proportional logarithm of the second difference; the remainder is the proportional logarithm of a portion of time, which take from the table, and add thereto the hours corresponding to the first distance taken out of the Nautical Almanac. The result is Greenwich mean time when the observation was taken. The difference between ship mean time found above and Greenwich mean time is the longitude in time; turn it into degrees, and mark it "east if the Greenwich time is the least, and west if the Greenwich time is best." EXAMPLES. Feb. 12, 1848, at 2h 36m P.M., mean time nearly, in lat. 53° 30' N., and long. by account 15° 30' E., the following lunar observation was taken : The height of the eye above the sea was 20 feet; required (195.) March 25, 1847, at 3h 30m P.M., mean time nearly, in lat. 52° N., and long. by account 33° W., the following lunar was taken : The height of the eye above the sea was 20 feet; required the longitude. Ans., 32° 59' 30" W. (196) April 20, 1847, at 2h 0m P.M., mean time nearly, in lat. 50° 50′ N., and long. by account 1° 40′ E., the following lunar was taken : The height of the eye above the sea was 20 feet; required the longitude. Ans., 1° 20′ 30′′ E. (197). May 19, 1847, at 2h 50m P.M., mean time nearly, in lat. 51° 30' N., and long. by account 20° 40′ E., the following lunar was taken Ans., 20° 42' E. The height of the eye above the sea was 20 feet; required the longitude. (198). Feb. 6, 1851, at 3h 30m P.M., mean time nearly, in lat. 60° 20′ N., and long. by account 26° 45' E., the following lunar was taken : Obs. alt. sun's L. L. : The height of the eye above the sea was 11 feet; required the longitude. Ans., 28° 35' E. |