Reduction of Altitude for Change of Ship's Position.-When the altitude of an object has been taken, and at a subsequent time and in an altered position of the ship a second altitude of the same object is observed as in the double altitude problem and in the "New Navigation," if we wish to combine these two observations it frequently happens that the first altitude has to be reduced to what it would have been if it had been taken at the altered position of the ship; in this case the azimuth or bearing of the object at the first altitude must be taken, and the course made good and distance run in the interval of the observations carefully noted.

(1) If the ship's course is directly towards a heavenly body, the effect is to raise the body r' for each mile of distance made good.

(2) If the ship's course is directly away from a heavenly body, the effect is to depress the body 1' for each mile of distance made good.

(3) If the ship's course is at right angles to the bearing of the object, the ship neither approaches, nor recedes from, the body.

(4) But the object may bear obliquely from the course the ship makes good; and thus we have an angle between the bearing and the course, which, with the distance run, gives us a plane triangle corresponding todiff. lat. dist. x cos. course

that is

reduction of altitude or correction for run (as it is sometimes called)

=

distance x cosine of angle between bearing of object and ship's course in the interval

to obtain which the Traverse Tables are generally used, as follows—

(A) Find the angle between the bearing of the sun (or star) at the first observation and the ship's course made good: enter the Traverse Table with this angle as a course, and the distance run as a distance; the difference of latitude corresponding thereto is the reduction or correction of altitude for the run, to be added when the angle is less than 8 points or 90°, but to be subtracted when the angle is more than 8 points or 90°. For example, taking the sun for illustration

The sun's bearing at the first observation being S. 531° E., and the ship's course in the interval of the observations being N. 641° E., the angle is 62°; and supposing the run to be 19 miles

Course 62° Trav. Tab. Diff. lat. 9'

Dist. 19m.

=

cor. of alt., to be added.

The sun's bearing at the first observation being S. 45° E., and the ship's course in the interval of the observations being N. 28° E., the angle is 107°, in which case, deducting it from 180°, there remain 73°, and supposing the run to be 24 miles—

Course 73° Trav. Tab. Diff. lat. 7' = cor. of alt., to be subtracted.

Dist. 24m.;

N.B. When the angle exceeds 8 points or 90°, enter the Traverse Table with its supplement or what it wants of 16 points or 180°.

(B) If the ship's course during the interval is directly towards the sun's bearing at the first observation, the distance run is the correction, to be added to the first altitude; if directly from the sun, the distance run is the correction, to be subtracted from the first altitude.

(c) If the course is exactly 8 points or 90° from the sun's bearing, the correction is o.

If, in the interval of the two observations, the ship makes but one course, the difference between the compass bearing of the sun (or star) and the compass course will be the angle; when the ship makes more than one course in the interval, the compass course made good may be also used, provided there be no deviation on the courses steered, in which latter case it would be better to find the angle between the true course made good and the true bearing of the sun (or star).

(5) If it is necessary to reduce the second altitude to the position at which the first altitude was observed, you require the ship's run (i.e., course and distance in the interval, as before) and the sun's (or star's) bearing at the second observation; the reduction or correction of altitude is obtained as already indicated, but it must be applied to the second altitude the reverse way; thus, where paragraph (A) says add, you must subtract; and where it says subtract, you must add.

When the course at the second observation is directly towards the sun (or star), the distance run is the correction, to be subtracted from the second altitude; but if directly from the sun (or star), the distance run is the correction, to be added.

In all cases the correction for run is to be applied to the true altitude. It will have been observed that the rule just given has been determined on the principle of a right-angled plane triangle. This is not strictly correct, but as the error will not exceed 1' in a run of 75 miles and with an altitude less than 50°, the navigator can consider it sufficiently near for ordinary navigation.

CONVERSION OF TIMES

1. INTERVALS OF TIME, MEAN, APPARENT, OR SIDEREAL

(1) To convert an Interval of Mean Time into an Interval of Apparent Time: From Nautical Almanac, p. I. of the month, take out the "Var. in 1h." of the equation of time, and multiply it by the hours and decimal of an hour, of the given mean interval; the result, which is the correction, is to be applied to the mean interval as follows

Look to p. II. of Nautical Almanac to see whether the equation of time is to be added or subtracted, and again whether the equation is increasing or decreasing; then

or, But,

or,

If equat. be additive to mean time and increasing.} add correction.

subtractive from

decreasing,

Example.-January 10th; convert 5h. 6m. 2s. of mean time into apparent time.

NOTE. To convert an apparent into a mean interval the application of the correction would be the reverse of the above; or use p. I. instead of p. II.

(2) To convert an Interval of Mean Time into an Interval of Sidereal Time: To the mean interval add the acceleration corresponding to the given hours, minutes, and seconds (see Nautical Almanac Table," Intervals of Mean Solar Time into intervals of Sidereal Time," etc. or Accelaration Table in Norie's Tables.

Example. Convert an interval of 6h. 12m. 42s. mean time into an equivalent interval of sidereal time.

(3) To convert an Interval of Apparent Time into an Interval of Sidereal Time: From the Nautical Almanac, p. I. of the month, and day, take out the "Var. in 1h." of the sun's right ascension, and multiply it by the interval (hours and decimal of an hour); the result is the correction to be added to the apparent interval.

Example. December 11th; the apparent interval being 7h. 42m. 3s Required the sidereal interval.

(4) To convert an Interval of Sidereal Time into an Interval of Mean Time: Subtract from the sidereal interval the retardation given in Retardation Table in Norie's Tables. Or convert the interval by the Nautical Almanac, "Table for converting Intervals of Sidereal Time into equivalent Intervals of Mean Solar Time."

Example.-Convert 8h. 18m. 14s. of sidereal time into mean time.

The foregoing Rules (1, 2, 3, 4) relate exclusively to intervals of time, and the following Rules appertain to problems connected with absolute time.

II. TO CONVERT APPARENT TIME INTO MEAN TIME

This conversion is commonly required in the problem of finding time at ship by the sun, and thence the longitude through the Greenwich date. NOTE. For this conversion the Greenwich date must either be given, or otherwise found from the ship's time and longitude.

RULE.-The Greenwich date mean time being given, correct the equation of time from p. II. of Nautical Almanac by the "Var. in 1h." and the given Greenwich time (see p 237); then apply the corrected equation of time to the apparent time at ship according to the precept standing above the equation of time on p. I. of Nautical Almanac.

Example.—Given apparent time at ship 3h. 4m. 23s. p.m., and the Greenwich date January 5d. 9h. 42m. 2s. mean time. Required the mean time at ship.

Correct Eq. + 5 54:45 to be added to App. T.

NOTE. If required, the Green. Date M.T. could, in this case, be converted into Green. App. T. by applying the Eq. of T. to it, according to precept in Naut, Alm. p. II: thus

mean time.

Example.-Given apparent time at ship 20h. 30m. 42s. (i.e. 8h. 30m. 42s. a.m.), and Greenwich date November 23d. 6h. 12m. 4s. Required the mean time at ship.

In this case the ship time expressed as civil time would be apparent time 8h. 30m. 42s. a.m., and mean time 8h. 17m. 21s. a.m.

III. TO CONVERT MEAN TIME INTO APPARENT TIME

This conversion is required in several problems, as in the "Reduction to the Meridian," and for " Time Azimuths of the Sun," etc.

The Greenwich date must either be given or otherwise found from the ship's time and longitude.

RULE.-Correct the equation of time for the Greenwich date, and apply the corrected equation of time to the given mean time, according to the precept standing above the equation of time on p. II. of Nautical Almanac. Example. Given mean time at ship 6h. 4m. 42s. p.m., and the Greenwich date January 31d. 8h. 48m. Ios. mean time. Required the apparent time at ship and at Greenwich.

IV. TO CONVERT GREENWICH MEAN TIME INTO SIDEREAL TIME AT

GREENWICH

RULE. Accelerate the sidereal time (Nautical Almanac, p. II.) for the Greenwich mean time (see p. 247); the result is the mean sun's right ascension. To the Greenwich mean time add the mean sun's right ascension, the sum (rejecting 24h if necessary) will be the sidereal time at Greenwich.

Example.-January 4d. 2h. 4m. 50s. mean time at Greenwich. Required the sidereal time at Greenwich.