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ON FINDING THE VARIATION OF THE COMPASS BY CELESTIAL OBSERVATIONS.
If the bearing of a celestial object, as shown by a compass, be the same as the true bearing which the object is known to have at the same time, it is evident that the points of the compass are directed to the corresponding points of the horizon, and the compass has therefore no variation. If the compass show a bearing different from the known true bearing of the object, that difference is the variation of the compass. Thus if an object bear E NE by a compass at a time when its true bearing is E, the E N E point of the compass directed to the E point of the horizon, and consequently every point of the compass is turned two points to the right of the corresponding point of the horizon, or the compass has two points easterly variation. But if an object should bear N W by a compass at the time that its true bearing is known to be W N W, the N W point of the compass, to produce this effect, must be turned two points to the left, or the compass will have two points westerly variation.
We may hence infer, generally, that when the true bearing of any object is to the left of its bearing by the compass, the compass has westerly, and when to the right, it has easterly variation.
To find the variation of the compass by the bearing of a celestial object when on the meridian.
The sun is always on the meridian at apparent noon, and the time at which any other object will pass the meridian on any given day may be found by Problem 5, page 220. Let then the error of the watch for apparent time be found, and the time by it will be known when the object is on the meridian, at which time the angle included between the meridian and the point on which the object bears will be the variation, westerly if the object is to the right, but easterly if it is to the left of the meridian.
For example, if an object on the meridian bear S 18° 40' W, the variation is 18° 40′ W; if it bear N 14° E, the variation is 14° W ; if it bear S 38° E, the variation is 38° E; if it bear N 21° W, the variation is 21° E.
To find the variation of the compass by the amplitude of the sun or a star. From the effect of refraction, celestial objects appear on the horizon when they are about 33′ below it, and therefore the altitude of the sun's centre, or the altitude of a star, should be about 33′ + the dip, when the amplitude is observed to find the variation; or the altitude of the sun's lower limb should be about 17+ the dip.
To compute the true amplitude, add the sine of the object's declination to the secant of the latitude, and the sum, rejecting 10 from the index, will be the sine of the amplitude, to be estimated from the east when the object is rising, and from the west when it is setting; and towards the north or south, according as the declination is north or south.
Then if the computed amplitude and that by the compass be both north or both south, their difference will be the variation; but if one be north and the other south, their sum will be the variation, easterly when the true amplitude is to the right, and westerly when it is to the left of the observed.
On January 24, 1822, at 6h 45m A. M., in latitude 21° 14′ N, longitude 31° W, the sun's rising amplitude was E 35° 20′ S, required the variation?
Correction for 20h 49m, (Table 30)
Q's declination at noon, January 23, 1822, 19° 30′ 26′′S.
EXAMPLES FOR EXERCISE.
In each of the following examples the variation of the compass is required?
To find the variation of the compass by the azimuth of a known
With the given time and longitude find the Greenwich time, (Problem 4, page 219,) and for that time take the declination of the object; find its polar distance, and compute its true altitude.
Add together the true altitude, the latitude, and the polar distance, and take the difference between half the sum and the polar distance; then add together the secant of the altitude, the secant of the latitude, (rejecting 10 from each of their indices) the cosine of the half sum, and the cosine of the remainder, and half the sum of these four logarithms will be the sine of half the azimuth of the object, from the south
in north, and from the north in south latitude; and towards the east or west, according as the altitude is increasing or decreasing.
Let the observed azimuth be estimated from the same point that the true azimuth is computed from; and if they are both east, or both west, their difference will be the variation; but if one is east, and the other west, their sum will be the variation; and easterly or westerly, according as the true azimuth is to the right or left of the observed one.
If on April 20, 1858, at about 9h A. M. the altitude of ☺ be 36° 50′+, bearing S 31° E, in latitude 50° 12′ N, longitude 13° W, height of the eye 21 feet, required the variation ?
In each of the following examples the variation is required?
On ship board however the direction of the needle is affected by the local attraction of the iron in the ship. If the iron be equally distributed, it produces no effect when the ship's head bears N or S from the compass, and the deviation is greatest when the head lies. E or W. In ships of war, where the guns and other masses of iron present a large attracting surface, the effect of this local attraction on the needle is very considerable; it has been observed in the channel to amount to more than half a point.
Of the various methods which have been proposed for estimating the effect of this local attraction on the different points of the compass, the following by Mr. BARLOW, of the Royal Military Academy, is the most simple and complete.
In harbour, when the ship's head bears N or S from the compass, let the bearing of some distant object be observed, and then warp the ship round till her head lies nearly E or W; and if in this situation the bearing of the object is the same as before, the effect of the local attraction is imperceptible; but if the bearing be different, the apparent change in it will be the deviation in the direction of the needle, produced by the local attraction at that point.
Take the compass on shore, and find by experiment the situation in which (if placed in the vertical plane passing through the point on which the deviation was observed on board) a plate of iron will produce, by its attraction, the same deviation; and if it be fixed in that situation, it will on every point of the compass produce the same effect on the needle that the local attraction of the ship does, and consequently if the compass with the plate so attached to it be taken on board, the effect of the local attraction will be doubled.
Let therefore an apparatus be constructed, by which the plate can be placed when wanted, in the same situation with respect to the compass, and the deviation resulting at any time from its application will show the local attraction.
If the observed deviation is to the right, it will increase easterly, and diminish westerly variation; and the contrary when it is to the left.
When the bearing of an object is taken on board by the compass, immediately apply the plate, and observe the deviation which it produces, and allow it in the same direction from the observed bearing of the object, and the result will be its bearing, independent of the local attraction.
For example, if the sun bears by the compass S 20° E, and on applying the plate the needle deviates 4° towards the right, the local attraction of the ship must have produced an equal deviation in the same direction, and consequently the bearing, independent of the local attraction, is S 16° E. If an object bear N 2° E, and the observed deviation be 6° towards the left, the bearing corrected for
deviation will be N 4° W. Hence the variation of the compass may be found on board, independent of the local attraction.
To find the variation to be allowed on a given course, let the deviation be observed by the plate, and if it is to the left, add it to the variation if westerly, and subtract it if easterly; applying it the contrary way if the deviation is to the right; and the result will be the actual variation of the compass on the given course. For example, if the variation is 20° W, and the deviation of the needle on a certain course is 6° to the right, then the actual variation on that course is 14° W.
In common merchant ships, the local attraction is in general small, and indeed it is seldom allowed for; but it unquestionably exists in all ships in a greater or less degree.
Plates for observing the deviation, with tables to assist in determining their proper situation, may be purchased of W. and J. Gilbert, 148, Leadenhall-street.
ON THE PRINCIPLES OF THE METHODS OF FINDING THE LONGITUDE AT SEA BY CELESTIAL OBSERVATIONS.
As the longitude of any place is measured by the arc of the equator, or the angle at the pole, included between the meridian of that place and the first meridian; and the difference between the time at any place and that at the first meridian is measured by a like arc of the celestial equator, or a like angle at the celestial pole, the longitude of any place would be known if the mean, the sidereal, or the apparent time at the place, and at the first meridian could be found at the same instant. Now, during the apparent diurnal revolution of the heavens, the distances of celestial objects from the horizon are continually varying, increasing from the time at which they rise till they pass the meridian, and then decreasing in like manner till they set. Hence, at a given place, any proposed altitude of a known celestial object, eastward or westward of the meridian, will correspond to a determinate instant of time; and the time at any given place may therefore be inferred from the observed altitude of a known celestial object. But an altitude for determining the time should not be observed when the object is near the meridian, as the altitude then varies so slowly that a small mistake in measuring it will produce a considerable error in the computed time; and the nearer the bearing of an object is to the east or west, the less effect will any mistake in measuring its altitude produce in the time computed from it.
Now, if a chronometer which kept mean time were set to the time at the first meridian, it would continue to show the time at that meridian to whatever place it might afterwards be carried; and