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Given the Greenwich Date, Mean Time, Longitude, and Daily Reckoning,

to find the Ship Date Under the circumstances it is most appropriate, in connection with the time at Greenwich and the time at ship, to use the terms “Greenwich date ” and “ Ship date ”inasmuch as time is too often taken to imply merely hours, minutes, and seconds, to the neglect of the day to which those data belong. It is only by using the term date, which implies day, hours, minutes, and seconds, that a proper comparison between the times at the various meridians can be made ; and in the absence of a due appreciation of this fact it is by no means certain that the student will have obtained correct elements from the Nautical Almanac, or a correct determination of longitude, as arising out of the difference between the ship date and Greenwich date. This is the reverse process to that given in the preceding examples; and the Greenwich date is taken to be the time by chronometer corrected for error and daily rate, and is hence always Greenwich mean time.

1. To the Greenwich date add the longitude in time, if longitude is east.

2. From the Greenwich date subtract the longitude in time, if longitude is west.

If the ship date exceeds 12h., subtract 12h. from it, for civil time a.m., and add i to the astronomical day for the ship day.

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N.B.-When questions are set with time shown by chronometer, the ship time with the longitude in time applied to it will show whether the chronometer is showing astronomical time or whether 12 hours are to be added to it.

THE NAUTICAL ALMANAC AND

ASTRONOMICAL EPHEMERIS The first “Nautical Ephemeris " for the year 1767 was projected on the basis proposed by Dr. Nevil Maskelyne—the Astronomer-Royal of that day—and was published by order of the Commissioners of Longitude, together with the “ Tables requisite to be used with the Nautical Ephemeris." The Ephemeris took its present form as “The Nautical Almanac and Astronomical Ephemeris in 1834, and an alteration in the “ difference columns ” was made at a later date.

It is well here also to notice that the term difference as “Diff, for I hour," etc., which was used in the earlier editions of the Almanac, has been changed into the term “variation,” as “ Var. for 1 hour," " Var. for 10 m.,” etc.

The Nautical Almanac is computed for the meridian of Greenwich, and, consequently, it contains the right ascensions and declinations of the sun, moon, planets, and fixed stars, the equation of time, lunar distances, and various other solar, lunar, and stellar elements, for given instants of Greenwich time.

Eighteen pages (I. to XVIII.) of the Almanac are given to each month for various elements or quantities relating to the sun and moon. It is probable that pp. I. and II. are more used than any other parts of the work, since those pages relate to the sun—its right ascension, declination, and semi-diameter-together with the equation of time ; p. I. being adapted to Greenwich apparent noon, and p. II. to Greenwich mean noon; the “ Var. in 1 hour” given on p. I. of the month is the variation (that is difference) at noon that the quantity is undergoing at that instant; but this “variation" is applicable to its proper quantity taken from either page, as required.

Before the student begins to use practically the various elements or quantities set down in the pages of the Nautical Almanac, it is earnestly recommended that he should attentively read, and become perfectly familiar with, the "explanation of the articles ” given at the end of that work.

In this Epitome the Nautical Almanac can only be referred to incidentally, in relation to the necessary elements or quantities that are taken from it for the purpose of working the various problems in navigation.

Before we can find from the Almanac the values of any of these quantities for a given local time, we must invariably find the corresponding Greenwich date (see pp. 233 to 234). When this time is exactly one of the instants for which the required quantity is put down in the Almanac, nothing more is necessary than to transcribe the quantity as there set down. But when, as is mostly the case, the time falls between two of the times of the Almanac, the required quantity must be found by interpolation. To facilitate this interpolation, the Almanac contains the rate of change, or variation (that is difference) of each of the quantities in some unit of time. To use the variation (difference) columns with advantage, the Greenwich

time must be expressed in that unit of time for which the variation (difference) is given : thus, when the variation is for one hour, the time must be expressed in hours and decimal parts of an hour; when the variation is for one minute, the time must be expressed in minutes and decimal parts of a minute, etc.

Simple Interpolation. In the greater number of cases in practice it is sufficiently exact to obtain the required quantities by simple interpolation; that is, by assuming that the variations of the quantities are proportional to the differences of the times, which is equivalent to assuming that the variations given in the Almanac are constant. This, however, is never the case; but the error arising from the assumption will be smaller the less the interval between the times in the Almanac; hence, those quantities which vary most irregularly, as the moon's right ascension and declination, are given for every hour of Greenwich time; others, as the moon's semidiameter and horizontal parallax, are given for every twelfth hour, viz., for noon and midnight; others, as the right ascension and declination of the sun, are given for each noon, as are also most of the planetary elements; while others, as the right ascensions and declinations of the fixed stars, are given for every tenth day.

The following examples illustrate simple interpolation when the Greenwich date mean time is determined or given

RULE.—When the quantity, as the sun's declination or the equation of time, has the “ Var. in 1 hour ” given.

1. Take from the Nautical Almanac for the nearest preceding mean time date the required quantity, and the corresponding “ Var. in 1 hour.”

2. Multiply the “ Var. in 1 hour ” by the hours and decimal of an hour of the Greenwich date ; the product is the correction.

3. Add this correction (properly reduced) to the Nautical Almanac quantity, if that quantity is increasing, but subtract it if decreasing.

4. Also, note that if the Greenwich date is nearer to a subsequent than to a preceding Almanac date it will be more accurate to interpolate back from the subsequent date, in which case subtract the correction if the quantity is increasing, but add it if the quantity is decreasing.

NAUTICAL ALMANAC, 1914 EDITION The “Abridged Edition for the use of Seamen ” of the Nautical Almanac supplies the seaman with all the astronomical data he requires for finding his position, etc., at sea by observations of the sun, moon, planets, or stars; or for rating his chronometers on shore by observations of the sun or stars.

Quantities are given to a degree of accuracy comparable with that obtainable in the data by sextant observations; as a general rule to o''I of arc and o.Is. of time. The Almanac gives, at Greenwich mean noon throughout the year and in certain cases for greater convenience at every even hour of Greenwich mean time, the positions, with reference to the equator, of all the heavenly bodies the seaman makes use of, in terms of declination and right ascension, together with the equation of time. The values at any other Greenwich mean time may be found, either by the ordinary methods of interpolation or by making use of certain auxiliary tables, or in certain cases by inspection only.

The chief alterations are
Page I. Apparent time no longer given : Greenwich mean noon takes

its place. The declination is given in degrees, minutes, and tenths, and the acceleration from 1 to 24 hours is given on each page in a column parallel and adjacent to the right ascension of the mean sun.

Page II. is occupied by the moon and the transit of the first point of Aries.

Pages III., IV., V., VI. tabulate the right ascension mean sun, declination, and equation of time for every even hour, therefore the necessary correction can be found at sight.

Pages VII., VIII., IX., and X. are given to the moon's right ascension and declination for every even hour, with the difference for two hours between.

Pages XI. and XII. tabulate the data relating to the four planets, Venus, Mars, Jupiter, and Saturn.

Pages 146 to 153 are given to stars.

The right ascension and declination are given of all stars of magnitude 3.0 and upwards, at intervals of ninety days. In most cases the values for any day can be taken out by inspection.

The Pole Star Tables are much extended, and a table of Rising and Setting is added (pp. 160-161).

The rearrangement has been made to cut out such Tables and ephemeris as were not used by sailors, and to simplify the remainder.

Correct the Following Elements Given the following: October 5d. 8h. 42m. 28. Greenwich date, mean time ; correct for that date the sun's declination, the equation of time, and the sun's right ascension.

Here the numbers appertaining to each element are taken from Nautical Almanac, p. II. of October, because the time given is mean time, but the “Var. in 1 hour" must be taken from p. I. under the heading “ Var. in I hour.”

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H.

M.

S.

Var. in ih.

9:114 Sun's right ascension...... 12 44 50.09
8.7
Cor. for 8.7h.

+ I 19:29
6,0 ) 7.9.2018 Cor. sun's R.A.

12 46 9:38 Im.198.29 NOTE.--In the first example the method of obtaining the correction is given in full ; in the subsequent examples the method is abbreviated; but the student can verify the result by multiplying as required.

When the given Greenwich time is nearer to a subsequent than to a preceding Almanac date, it will be more accurate to interpolate back from the subsequent date.

Example.-February 22d. 18h. 42m. 35. Greenwich date, mean time.

Here it is preferable, for accuracy, to refer the time to noon of the next day, and reckon it as 5h. 18m.=5:3h. before noon of the 23rd ; and for that time find the correction, which is to be added if the element is decreasing, but to be subtracted if increasing.

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To find the Declination of the Sun at the time of its transit over a given

meridian, also the Equation of Time at the same instant When the sun is on the meridian at any place in west longitude the Greenwich apparent time is precisely equal to the longitude. That is, the Greenwich apparent time is after the noon of the same date as the local date, by a number of hours (and decimal of an hour) equal to the longitude.

When the sun is on the meridian at any place in east longitude, the Greenwich apparent time is before the noon of the same date as the local date, by a number of hours (and decimal of an hour) equal to the longitude.

Hence, to obtain the sun's declination and the equation of time for apparent noon at any meridian, take these elements from the Nautical Almanac (p. I. of the month) for Greenwich apparent noon of the same date as the local date, and apply a correction equal to the “ Var. in 1 hour multiplied by the number of hours (and decimal of an hour) in the longitude, observing to add or subtract the correction thus obtained, according as the element in the Nautical Almanac may indicate, for a time before or after noon.

Rule for Sun's Declination at noon, local date
Turn the longitude into time, as hours and decimal of an hour.

From Nautical Almanac, p. I. of the month, take out the sun's declination for the ship date, and also the “ Var. in ih." for the same date.

Multiply the “ Var. in Ih.” by the longitude in time, and the product will be the correction, to be applied to the declination as follows-

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