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To find the local time of the Moon's Meridian Passage (or transit over a

given meridian) The mean time of transit of the moon over the Greenwich meridian on each day is nothing more than the hour angle of the mean sun at the instant, or the difference between the right ascension of the moon and the right ascension of the mean sun. If this difference did not change, the mean local time of the moon's transit would be the same for all meridians ; but as the moon's right ascension increases more rapidly than the sun's, the moon is apparently retarded from transit to transit.

Page IV. of the Nautical Almanac gives the mean time of the moon's “ Meridian Passage ” (or transit) over the meridian of Greenwich for each day; and the difference between two successive "Passages” is the retardation of the moon (varying from 44m. to 66m. according to the rate of the moon's motion) in passing over 24 hours of longitude. RULE.—Take the moon's

meridian passage

(upper) from page IV. of the Nautical Almanac for the given astronomical day.

If in west longitude take the difference between the time of “passage on the given and following day. If in east longitude take the difference between the time of " passage on the given and the previous day.

The difference being a 24-hour difference, hence, multiply it by the longitude in time, and divide the product by 24 (or by 2 and 12 successively); the result will be the correction to be applied to the Greenwich meridian passage as follows:

If in west longitude add this correction to the Greenwich meridian passage for the given day. If in east longitude subtract the correction from the Greenwich meridian passage for the given day. The result will be the meridian passage at ship.

NOTE.—In dealing with the day, it may be civil time a.m., for during half the lunar month the moon passes the meridian after midnight, but the time in the Nautical Almanac is astronomical time. Take an example : On October 4th the moon (by Nautical Almanac) passes the meridian of Greenwich at 17h. 26m. ; now this is the 5th a.m. at ship; therefore, for W. long. the day and day after would be the 4th nd 5th ; for E. long. the day and day before would be the 4th and 3rd ; in each case the actual astronomical day is the 4th, since it corresponds to the civil day 5th a.m.

The Rule just given applies equally to planets, which have the mean times of transit given in the Nautical Almanac.

For the Greenwich mean time corresponding to the time at ship.—To the time of the meridian passage at ship apply the longitude in time; add if west ; subtract if east.

Then correct the moon's declination for the Greenwich time (see p. 241).

Example. - January 29th ; long. 82° 30' W., find the local time of the moon's meridian passage, and the corresponding Greenwich date

H.

M.

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Example.February 2nd; long. 97° 30' E., find the local time of the moon's meridian passage, and the corresponding Greenwich date

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Example.April 1oth a.m. at ship, in long. 105° W., find the local time of the moon's meridian passage, and the corresponding Greenwich date

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In this example the moon passes ship's meridian on April 1oth at 4h. 22:5m. a.m.

N.B.-See Correction of Moon's Mer. Pass., Norie's Tables.

To find a Planet's Right Ascension and Declination at the time of transit

over a given meridian

Venus, Mars, Jupiter and Saturn are the only planets the navigator uses to determine the latitude by the meridian altitude (i.e., at transit). The Nautical Almanac, for the purpose of facilitating the reduction of the right ascensions and declinations of these planets, gives their “ Variations in 1 hour of longitude,” which can consequently be used in the same manner as in the “Var. in 1 hour" of the sun, and be similarly applied as regards E. and W. long. (see also Nautical Almanac explanations, “ Planetary Ephemerides at Transit ”).

Moon's Semi-diameter and Horizontal Parallax

These elements are given in Nautical Almanac, p. III. of the month, for noon and midnight, consequently they require to be interpolated for the given Greenwich time; if that time exceeds 12 hours the interpolation will naturally fall between midnight and the succeeding noon.

The corrected semi-diameter will require the augmentation due to the apparent altitude (see Table, Augmentation of the moon's semi-diameter [Table D]).

The corrected horizontal parallax will require the reduction for latitude (see Table E. Reduction of the Moon's Horizontal Equatorial Parallax for the figure of the Earth). Both these tables are in Norie's Tables.

Planet's Right Ascension and Declination for a given Greenwich Date,

mean time These elements come from the Nautical Almanac under the head of the given planet “mean time,” not “at transit at Greenwich,” unless for

latitude by the planet's meridian altitude.” They are given from day to day for Greenwich mean noon, and the difference of each element for two successive days is a 24-hour difference ; this difference must be taken as the basis of the correction for the given Greenwich date, mean time.

Thus, suppose the daily (or 24-hour) difference of declination to be 47'38":3 and you require the correction for 8h. of Greenwich time; then 47' 38":3 multiplied by 8 and the product divided by 24 (or by 2 and the resulting quotient by 12), the proportional part for 8 hours will be 15' 52":8, to be added to, or subtracted from, the declination of the given day, according as the declination is increasing or decreasing.

The correction for the right ascension is obtained in a similar manner. To find the Right Ascension of the Mean Sun, for a given time and place

The Sidereal Time of Mean Noon is also the Right Ascension of the Mean Sun at Greenwich mean noon, and may be reduced by interpolating for the constant hourly difference 9.8565s., but preferably by a table, as follows -

RULE.–From the Nautical Almanac, p. II. of the given month, column headed sidereal time,” take out the sidereal time for Greenwich noon of the given day, and accelerate it for the Greenwich mean time, using the table near the end of the Nautical Almanac entitled “ Table for Converting INTERVALS OF MEAN SOLAR Time into EQUIVALENT INTERVALS OF SIDEREAL Time."

Example.—February id. 15h. 4om. 525. M.T. at Green. ; required the Mean Sun's R.A.

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Example.—March 22d, at gh. 48m. p.m. local mean time in Long. 47° 12' W.; required the Mean Sun's R.A.

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Local Mean Time, March 22d.

Long. 47° 12' W.
Green. Mean Time 22d.

M. 9 48 3

8 I2 56

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The right ascension of the mean sun is also equal to the right ascension of the true sun + the equation of time, using the sign for the equation of time indicated for its application to mean time.

The Right Ascension and Declination of the Fixed Stars

The elements of the fixed stars are given in the Nautical Almanac for every tenth day, and can be taken out, or interpolated, at sight. The hours and minutes of right ascension, and degrees and minutes (') of declination, are placed at the head of the columns as constants, and belong equally to all the numbers below them; hence the seconds sometimes exceed 60 ; in which case increase the minutes by I and write down the number of seconds in excess of 60; thus on May 1, the declination of

Argus (Canopus) is given as 52° 37' 84", which is to be read as 52° 38' 24".

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CORRECTIONS OF OBSERVED ALTITUDES

The altitude of a heavenly body is its distance in arc from the horizon measured on a vertical circle.

The true altitude is the altitude of the object's centre above the rational horizon, as if it were measured by an observer at the centre of the earth.

The apparent altitude is the altitude of the object's centre above the sensible horizon.

The observed altitude, measured at sea by a reflecting instrument without index error, is the altitude above the visible horizon, and is reduced to the apparent, or true altitude, as may be required, by the application of certain corrections, which should be taken in the following order :

For the apparent altitude of the object's centre, apply the index error (if any), the dip, and the semi-diameter (if any).

For the true altitude of the object's centre : Having applied the corrections as specified for the apparent altitude, next apply the refraction and parallax ; and the result will be the true or geocentric altitude of the heavenly body's centre. The sun, moon, and planets have parallax, but not the fixed stars.

It is not absolutely necessary in ordinary navigation to observe the order just indicated, but when intent on attaining to the nearest amount of precision use correct methods. There are Tables in Norie's which combine most of, or all the corrections, and these are near enough for sea practice ; never attempt such slipshod work as getting the sun's zenith distance by using 89° 48' in connection with the sun's altitude.

Index Error.-Reference has already been made to the correction for index error in the quadrant or sextant : it arises from defect of parallelism

H

B

between the index-glass and horizon-glass when the index is at oo; it is, therefore, the first correction to be applied to the altitude as obtained by the instrument, to get the correct observed altitude.

Dip or Depression of the Horizon.—Dip of the horizon is the angle of depression of the visible sea-horizon below the true horizon, arising from the elevation of the eye of the observer above the level of the sea.

In the Fig. I suppose A to be the position of the observer's eye, the height of which above the level of the sea is B A; and S the position of the star whose altitude is to be found by the sextant. Then A H being the

А sensible horizontal line, the angular measure required is S A H. Draw A T H as a tangent to the earth's surface at T; then, disregarding refraction, T will be the most distant point of the surface visible from A, and the altitude of S, as obtained by the sextant, would be the angle S A H', instead of the angle S A H. The angle H A H', by which the angle S A H is increased, is the dip, or depression of the visible

Fig. I horizon, which must be subtracted from the observed altitude to give the apparer.. altitude S A H.

The sensible horizon is strictly a tangent plane touching the earth's surface extending from B, but owing to the distance of the heavenly bodies the angle at S subtended by A B (the height of the eye) is immeasurably small.

To find the Dip.-Draw C T from the centre of the earth to the point of contact T; then H A H' and the angle at C are each the complement of CAT, and are therefore equal; that is, the angle at C is equal to the angle of the dip.

Let h = the height of the eye А В

the radius of the earth (in feet) СТ d = the dip, or depression of the horizon.

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1 =

Then, in the triangle CAT, we have ACT = H A H' hence

d (the dip), and

AT
Tan. d

CT
By Euclid III. 36, we have

A T=V AB X A D Vh (2r + h) whence

var h + ho / 2h Tan. d (dip)

h

+ V

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