VARIATION BY AMPLITUDE.

To the apparent time at ship (if a. M. add 12 hours, and call it a day less) apply the longitude in time to find Greenwich time with Greenwich date, take out declination, and correct it as in meridian altitude; then to the log. Sine of the true declination add the log. Secant of the latitude, the sum (rejecting 10 from the index) will give the Sine of the true amplitude to be named ; E. if A. M., W. if P. M., and N. or S., like the declination. If the true and observed amplitudes are of the same names, the difference is the variation; but if different names, the sum of the two is the variation. If the true amplitude is to the right of the observed on the compass, the variation is E.; but if to the left, the variation is W.

If the observed amplitude is given in points, it must be reckoned from the E. or W.

EXAMPLE.-1864, May 12th, at 6h. 15m. A. M., apparent time at ship, in latitude 20° 10′ N., longitude 30° 00′ W., the observed rising amplitude was E. 33° 30′ N. Required the variation.

CHRONOMETER TIME.

To the time shown by chronometer, apply the original error, adding if slow, and subtracting if fast; then find the accumulated rate, and add if the chronometer is losing, and subtract if gaining, which will give the true Greenwich time; with the Greenwich time, take out the declination and correct it, as in the preceding problems, which will give the true declination; to it add 90° 00' 00", if latitude and declination are different names, and subtract it from 90° 00′ 00′′, if same names; the result will be the polar distance; correct the alt. for index error, and apply the cor. from Table IX., as in the preceding problems; then use the following formula to find the horary angle in Table XXXI.

After obtaining the horary angle, if A. M. at ship, take it from 24h. 00m. 00s., and call the apparent time thus found a day less than DATE AT SHIP. If P. M. at ship, do not take h. angle from 24 hours, but place the same DATE AS AT SHIP before the h. angle, which is the apparent time at ship; apply the corrected equation of time, adding or subtracting, as given in the Nautical Almanac; the result will be the mean time at ship; and the difference between the mean time at ship and the true Greenwich time, is the longitude in time of the ship, which turn into degrees, &c.; and name it E. if the Greenwich time is least, and W. if it is greatest.

In taking out Cosecant of an arc above 90° 00′ 00′′, take 90° from it, and take Secant of the remainder.

In taking out Cosine of an arc greater than 90° 00′ 00′′, take 90° from it, and take Sine of the remainder.

EXAMPLE.-1864, July 25th, A. M. at ship, in latitude 40° 30' N., the observed altitude of the Sun's 1. 1. was 36° 25′ 10′′, index error + 3', height of the eye 16 feet, time by chronometer 24d. 20h. 58m. 24s., which had been found to be 16m. 12s. fast on Greenwich mean time, on April 1st, and losing daily 1.5. Required the longitude.

The work of this question is given in the next page.

D

N. B.-The daily rate in this question is so small, that the nearest day has been taken, without calculating for the hours, &c.

VARIATION BY AZIMUTH.

Find the Greenwich time and true declination as in amplitude, and find p. distance as in chronometer time; then use the

following formula.

(Diff. between p.dis. & Sum)

After obtaining the

(azimuth) log Sine

Add.

azimuth, multiply by 2, which will be named always the opposite to the latitude, and E. if A. M., and W. if P. M., at ship.

give the true azimuth, to

If the true azimuth and the observed azimuth are both from the N., or both from the S., their difference is the variation; but if opposite names, one must be taken from 180°, in order to bring it the same name as the other. Mark both the true and observed off on the compass; recollect, true to the right of observed variation is E., and true to the left of observed variation is W.

If the observed azimuth is given from the E., or from the W., towards the N. or S., thus, E. 20° 10′ N., or W. 15° 20′ S., it should be taken from 90°, and reckoned from the N. or S. 1. EXAMPLE.-Suppose the observed azimuth is given E. 20° 10′ N.

Then E. 20° 10′ N. taken from 90 00

gives N. 69 50 E.

2. EXAMPLE.-Suppose the observed azimuth is given W. 16° 45′ S.

Then W 16° 45′ S.

taken from 90 00

gives S 73 15 W.

If the observed azimuth is given in points, reckon from the N. or S., as the case requires.

EXAMPLE.-1864, December 13th, mean time at ship 3h. 10m. P. M., in latitude 30° 45′ S., longitude 145° 45′ W., the observed bearing by azimuth compass was N. 80° 10′ W., altitude of the Sun's 1.1. 26° 36′ 10′′, index error + 1′ 45′′, height of the eye 12 feet. Required the variation.