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As these two results come out near to each other, the correct Greenwich date is July 10th, 10h 39m 53o.
Aug. 3rd, 1853, at 5h 42m P.M. mean time nearly, in long. by account 150° 30′ W., a chronometer showed 3h 23m 15s, and its error on Greenwich mean time was 10m 10s-4 slow; required the Greenwich date.
In this example 12 hours must be added to the Greenwich date by chronometer, without putting the day one back.
March 10th, 1853, at 2h 10m A.M. mean time nearly, in longitude 20° 42′ E., a chronometer showed Oh 2m 50s, and its error on Greenwich mean time was 45m 16s slow; required the Greenwich date.
In this example 12 hours must be added, and the day put one back, to bring the chronometer Greenwich date more nearly alike to the estimated Greenwich date.
EXPLANATION AND USE OF THE NAUTICAL ALMANAC.
THE NAUTICAL ALMANAC contains the declination, right ascension, &c., of the principal heavenly bodies, for certain fixed times at Greenwich. The declination and right ascension of the sun and planets are given for every day at Oh Om Os; for the moon, for every hour at Greenwich. To obtain these quantities for any other time, we may either apply the common rules of proportion; or-which is in most cases the simplest method-make use of certain tables computed for the purpose, called tables of proportional logarithms. The tables of proportional logarithms contained in most collections of nautical tables are the following:
1. The proportional logarithms (properly so called). 2. The Greenwich date proportional logarithm of the
3. The Greenwich date proportional logarithm of the
4. The logistic logarithms.
Their use will be best seen in the following rules and examples.
Rules for taking out of the Nautical Almanac the sun's declination, &c.
The sun's change of declination, and the method of determining its amount at any given time, may be illustrated by means of a figure.
Let A x be the celestial equator, a o the ecliptic, s, and Su
the places of the sun on the 27th and 28th April, 1846, at Greenwich mean noon; then at 10 o'clock on the
27th it must be at some intermediate point, as at s; and s, R, S,, R,, are the declination of the sun on the 27th and 28th at noon, and s R the declination at the required time. Draw s, m, parallel to the equator, then s,, m,, is the change of the sun's declination in 24 hours, and s m the change in 10 hours, and if we suppose the sun's motion in the ecliptic during the 24 hours to be equable, and s, m,, a few minutes only, so that the lines drawn in the figure may be considered as straight lines, we have this proportion:
sm: s, m,, :: 10h : 24h
Hence s m is easily found, since s, m,, the change in 24 hours, is known by means of the Nautical Almanac. And in a similar manner may be explained the method of taking out, for any required time at Greenwich, the other quantities given in the Nautical Almanac.
To take out the sun's declination.
First method. By proportional logarithms.
1. Get a Greenwich date; thus, put down the ship mean time expressed astronomically.
2. Under which put the longitude in time.
3. Add in west, subtract in east longitude (adding or subtracting 24 hours, according to the Rule I, p. 71).
4. Take out of the Nautical Almanac the sun's declination for two consecutive noons between which the Greenwich date lies.
5. Take the difference of the declinations when their names are alike; but when the names of the declinations are unlike, take their sum; thus finding the change of declination in 24 hours.
6. Add together Greenwich date logarithm for the sun and proportional logarithm of the change in 24 hours; the result is the proportional logarithm of change of declination for the given time, which take from the Tables and apply to the declination at first noon, either by subtracting or adding it, according as the declination is seen to be decreasing or increasing.
Second method. By hourly differences.
Another method of taking out the sun's declination, is to make use of the hourly changes of declination given in the Nautical Almanac.
1. Find a Greenwich date as before.
2. Take out of the Nautical Almanac the declination at noon of the Greenwich date, and put down a little to the right thereof the difference for one hour found in page 1 of the Nautical Almanac. Multiply this quantity by the hours in Greenwich date, and the fractional parts of the hour if necessary, the product will be the change of declination in the time from noon; apply this, reduced to minutes and seconds, to the declination taken out, adding it if the declination is seen to be increasing, and subtracting if decreasing. The result is the declination of the sun at the time required.*
* The corrections of the quantities taken out of the Nautical Almanac are often made by inspection: the results thus obtained are generally considered sufficiently correct.