CHAPTER X.

VARIATION OF THE COMPASS.

Art. 323. It was many years after the discovery of the compass before it was suspected that the magnetic. needle did not point accurately to the north pole of the world; but about the middle of the sixteenth century observations were made in England and France which fully proved that the needle pointed to the eastward of the true north.

The angle which measures this difference of direction is called the Variation of the Compass, and is named easterly when the north point of the compass needle is drawn to the eastward of true north, and westerly when drawn to the westward of true north.

Although charts are now constructed on which are drawn lines of equal variation, for the assistance of the Navigator, still it is absolutely necessary to be able to find the variation at any time in order to correct the courses steered by compass.

The amount of the variation is determined by comparing the True Azimuth of some celestial or terrestrial object with the observed Compass Azimuth of the same object; then the variation is found by taking the difference between the compass azimuth and the true azimuth, and is marked E. or W., according as the compass azimuth falls to the left or right of the true azimuth.

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There are several methods of finding the true azimuth, and hence the variation; those useful to the Navigator

1. By Amplitudes.

2. By Time Azimuths.

3. By Altitude Azimuths.

4. By the True Bearing.

1.-BY AN AMPLITUDE.

Art. 324. The method by amplitudes consists in observing the compass-bearing of the sun or other celestial body when its centre is in the true horizon; or, in other words, at its true rising or setting. Since the object can only be referred to the visible horizon, and being subject to vertical displacement from refr. ction, parallax, and dip, it is necessary to observe its centre in the visible horizon and to apply a correction.

Art. 325. The Observation.--With cbjects having appreciable discs, like the sun and the moon, no prepara tion is needed except being ready at the compass a few minutes in advance, and keeping the sight-vanes pointed in the right direction.

If the Sun is to be observed at the rising, when the upper limb appears in the sea horizon, take the bearing by compass; and continue to take bearings of the centre bisecting the disc, noting each bearing until the lower limb appears. At the setting, commencing when the lower limb touches the horizon, proceed in the same manner until the upper limb disappears. The mean of the bearings, reckoning from the E. or W. point, will be the observed amplitude.

The Moon.-Proceed in the same manner as in observing the sun if the luminous portion of the disc is bright enough for the rising to be anticipated in time to get the bearing of the upper limb as it comes upon the horizon. Otherwise it would be better to wait until a sufficient altitude has been reached to observe an azimuth.

There should also be noted with this observation, as well as with a 1 others for determining the variation, the ship's head by the standard compass, the angle of heel if an iron vessel, and if to starboard or to port.

Art. 326. THE COMPUTATION.

To correct the observed amplitude.—Enter Table 40 with the latitude and declination to the nearest degree, and apply the correction there found to the observed amplitude.

For the sun, a planet, or a fixed star, at the rising in N. Lat. and at the setting in S. Lat., to the right; or, at the setting in N. Lat. and rising in S. Lat., to the left.

For the moon apply half the correction in the contrary manner.

The result will be the corrected compass amplitude, which, by comparison with the true amplitude, will give the variation.

To find the true amplitude. To the log secant of the latitude add the log sine of the declination; the sum (rejecting 10 in the index) is the log sine of the true amplitude; or the angular distance from the east or west point toward the north in north declination, but toward the south in south declination.

By Inspection. Enter Table 39 with the declination at the top and the latitude in he side column; under the former and opposite the latter will be the true amplitude. When great accuracy is required in.erpolate for minutes of latitude and declination.

To find the variation.-If the corrected compass amplitude and the true amplitude be of the same name, their difference will be the variation; if of different names, their sum will be the variation. The variation will be E. or W. according as the compass amplitude falls to the left or right of the true amplitude.

EXAMPLE. At sea, June 5, 1875, in Lat. 11 29' N., Long. 30 W., about 6 10 a m., the observed bearing of the sun at rising was E. 31 N.; Greenwich date, June 4, 20, O's Dec., 22° 32′ N.

EXAMPLE. At sea, May 30, 1875, in Lat. 25° 3' S., Long. 22° W., about 6h 42m a. m., the observed bearing of the sun at rising was E. 18° 30' N.; Greenwich date, May 29, 20h; O's Dec., 21° 44′ N.

EXAMPLE. At sea, November 27, 1875, in Lat. 40° 27′ N., Long. 207 W., about 4h 43m p. m., the observed bearing of the sun at setting was W. 17 S.; Greenwich date, November 27, 6; O's Dec., 21.2 S.

EXAMPLE. At sea, December 18, 1875, in Lat. 31° 35′ S., Long. 60 13′ E., about 7h p. m., the observed bearing of the sun at setting was N. 83.4 W.; Greenwich date, December 18, 3; O's Dec., 23 .4 S.

Degree of Dependence.—In low latitudes this method is susceptible of great precision, the observations not being affected by the relative temperatures of the sea and air, verticality of the sight vane, horizontality of the compass bowl. In high latitudes refraction renders it less trustworthy.

2. BY TIME AZIMUTHS.

Art. 327. In this method there are given in the triangle of position PZX, Fig. 70, the hour angle ZPX, deduced from the local time of observation; the co-declination PX, and the co-latitude PZ, to find PZX, the azimuth of the body at X.

Hence it will be seen that the data required are:

The hour angle deduced from the local time of the observation;
The declination taken from the Nautical Almanac; and

The latitude as brought up by the reckoning, or as known by obser

vation.

In finding the variation for a single heading of the ship, any celestial object sufficiently bright to be seen through the sight-vanes of the compass may be employed in time azimuths with more or less convenience.

During the day the sun is to be observed, or the moon by day or night, the planets Venus, Mars, Jupiter, and Saturn, or the brightest fixed stars, according to circumstances. As a general rule, an object should be selected which is relatively low in altitude, not only that, in being seen through the sight vanes directly rather than by reflection, the compass azimuth is more reliable, but because the condition is more favorable for a reliable true azimuth, when the data are somewhat reliable.

Art. 328. The Observation.—Take a set of bearings of the object with the standard compass as quickly as possible, bisecting it each time if it has a sensible disc, and noting the times with a watch whose error in

N

FIG. 70.

E

local time is known. Note the heading of the ship with the same compass, and the corresponding headings with the other compasses; also the angle of heel if the ship is iron-built.

The mean of the bearings is the compass azimuth; the mean of the times is the corresponding watch time of the observation.

Art. 329. Finding the True Azimuth.-This method of finding the true azimuth consists of two parts: Ist, the preparation of the data; and 2d, the solution of the triangle of position.

The second part may be accomplished by logarithmic computation, by Time Azimuth Tables, of which there are several reliable ones, or by the Graphic Method, such as Godfray's. The method by computation alone is here given:

Preparation of the Data.

1. Find the Green wich date corresponding to the local time of observation.

2. Take out the declination of the body from the Nautical Almanac, and note the polar distance and the co-latitude.

3. Find the hour angle of the body by rules heretofore given.

First Case. If the half-sum of the polar distance and co-Lat. is less than 90°.

Take the sum of the angles X and Y if the polar distance is greater than the co-Lat.; take the difference if the polar distance is less than the co-Lat.

Second Case. If the half-sum of the polar distance and co-Lat. is greater than 90°.

Always take the difference of X and Y, which subtract from 180, and the result will be the True Azimuth. In either case, mark the True Azimuth N. or S. according to the latitude, and E. or W. according to the hour angle.

It may sometimes be convenient to use the supplement of the True Azimuth, by subtracting it from 180o and reversing the prefix N. or S., in order to make it correspond to the Compass Azimuth less than 90°. EXAMPLE. December 3, 1879, a. m., in Lat. 30° 25′ N., Long. 5h 25m 428 W., the observed bearing of sun's centre was N. 135° 30′ E., and the Greenwich mean time was, December

2h
3, 36m 118.

EXAMPLE. December 8, 1879, a. m., in Lat. 30° 25′ N., Long. 5h 25m 428 W., the observed bearing of the moon's centre was N. 133° 30′ W., and the Greenwich mean time of observation 3h 24m 54.

EXAMPLE. April 9, 1879, in Lat. 42° 16' S., the observed bearing of the sun's centre was S. 105° 30′ E.; Sun's H. A., 3h 44m 169; true altitude, 18 40′; Dec., 7° 38′ N.

EXAMPLE. At sea, February 23, 1875, Lat. 60° 53′ N., Long. 174° 15' W., at 1h 5m a. m., local app. time; the observed bearing of Jupiter was S. 49 E. Required the Apparent Variation and the Deviation. Greenwich date, February 23, ob 7m.

Art. 330. SWINGING SHIP AT SEA.-The method of Time Azimuths affords a convenient and reliable manner of ascertaining the Deviation of the Compass at Sea for different headings of the Ship. Since the opportunity can be chosen, the sun should be the body selected for the observations; it should be low in altitude, and, if possible, when the hour angle is greater than 45.

Having a fine day and a smooth sea, either steam or sail the ship around, steadying her a minute or two on each heading in order to allow the compass-card to come to rest. Take the bearing of the sun's centre on each heading, noting the time, also noting the corresponding headings with the steering compasses and the angle of heel. This may be done for every point of the compass, every other point, or every fourth point, as deemed desirable. The same may be done when in sight of any prominent point of land whose true bearing can be established.

Art. 331. RULE. To get the serial True Azimuths by Computation.

1. Find the Greenwich date for the middle local time of the set of observations.

2. With this date take out the sun's declination and the equation of time.

3. Deduce the co-Lat. and middle polar distance to the nearest minute.

4. Prepare the sun's hour angles, marking them E. if A. M., W. if P. M.

5. Find the value of S and D, or the half-sum and half-difference of the Mid. P. D. and the co-Lat. ; then to the log sine of D add the log cosecant of S; the result will be the Log A. To the log cosine of D add the log secant of S; the result will be the Log B.

6. Now proceed in tabular form by ruling several vertical columns, and, dividing each hour angle by 2, place the series of 1⁄2 in proper order in Col. I. Place the log cotangent of each 1⁄2t in Col. 2. Add Log A to each log cot1⁄2 and place the resulting log tangents X in Col. 3; also, do the same with Log B and place the resulting log tangents Y in Col. 4. Then take out for each log tan X the corresponding angle X and place them in Col. 5; also, for each log tan Y the corresponding angle Y and place them in Col. 6. 7. Then, remembering the precepts with regard to X and Y, place the resulting True Azimuths in Col. 7, marking them N. or S. according to the latitude, and E. or W. according to the hour angle.

8. Place in proper order the several Compass Azimuths in Col. 8; the total compass errors in Col. 9, and then, knowing the magnetic variation, the series of Deviations in Col. 10.

EXAMPLE. May 13, 1875, in New York Bay, Lat. 40° 41' N., Long. 74° 2′ W., about 5h 45m p. m., made the following observations of the sun, on a careful swinging of the ship for Compass Deviations. Watch error on local mean time, 47 fast. Magnetic Variation, 7.9 W.

Art. 332. In this method there are given in the triangle of position, Fig. 69

to find the angle

ZX, the zenith distance,

PX, the polar distance, and

PZ, the co-latitude,

PZX, the azimuth of the body X.

Art. 333. The Observation.-Take several bearings of the celestial body with the Standard Compass bisecting it each time if it have a sensible disc, taking its altitude simultaneously, noting the times with a watch. Note the heading of the ship by the Standard Compass and the correspon ing headings by the Steering Compasses, also the angle of heel, if an iron ship, and whether to starboard or to port.

The mean of the bearings is the Compass Azimuth; the mean of the altitudes is the observed altitude. Art. 334. To find the True Azimuth.-With the Greenwich date corresponding to the mean of the times, take out the declination of the body, and, if the moon, its Semi-diameter and Horizontal Parallax. Get the true altitude by applying the proper corrections to the observed altitude.

Then compute the True Azimuth from the following formula:

in which S half-sum of the polar distance latitude and true altitude. Or, in words :

Add together the polar distance, the latitude, and the true altitude; take the difference between the half-sum and the polar distance, and note the remainder. Then add together the log secant of the latitude, the log secant of the altitude (rejecting 10 in each index), the log cosine of the half-sum, and the log cosine of the remainder; half the sum of these four logarithms will be the log cosine of ha f the true azimuth, which, being doubled, will give the true azimuth, reckoned from the north in north lati ude, but from the south in south latitude.

EXAMPLE. December 3, 1879, in Lat. 30° 25' N., Long. 5h 25m 428 W., at 9h 10m 298 a. m., the observed bearing of the sun's centre was N. 135° 30′ E., and its true altitude 24 59'.