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of the horizon, but if it be the lower hole, hold the quadrant so that the sun's image may be bisected by the line joining the silvered and transparent parts of the horizon glass.

The sun's limb ought to touch that part of the horizon immediately under the sun, but as this point cannot be exactly ascertained, it will be therefore necessary for the observer to give the quadrant a slow motion from side to side, turning at the same time upon his heel, by which motion the sun will appear to sweep the horizon, and must be made just to touch it at the lowest part of the arch; the degrees and minutes then pointed out by the index on the limb of the quadrant will be the observed altitude of that limb which is brought in contact with the horizon.

When the meridian or greatest altitude is required, the observation should be commenced a short time before the object comes to the meridian ; being brought down to the horizon, it will appear for a few minutes to rise slowly; when it is again to be made to coincide with the horizon by moving the index forward; this must be repeated until the object begins to descend, when the index is to be secured, and the observation to be read off.

From this description of the quadrant and its use, the manner of adjusting and using the sextant will be readily apprehended. Our limits will not allow a particular description of this excellent instrument.

The Artificial Horizon.

In many cases it happens that altitudes are to be taken on land by the quadrant or sextant; which, for want of a natural horizon, can only be obtained by an artificial one. There has been a variety of these sorts of instruments made, but the kind now described is allowed to be the only one that can be depended upon. It consists of a wooden or metal-framed roof, containing two true parallel glasses of about 5 by 24 inches, fixed not too tight in the frames of the roof. This serves to shelter from the air a wooden trough filled with quicksilver. In making an observation by it with the quadrant or sextant, the reflected image of the sun, moon, or other object is brought to coincide with the same object reflected from the glasses of the quadrant or sextant: half the angle shown upon the limb is the altitude above the horizon or level required. It is necessary in a set of observations that the roof be always placed the same way. When done with, the roof folds up flatwise, and, with the quicksilver in a bottle, &c. is packed into a portable flat case.

SECTION III.

WARIATION OF THE COMPASS.

The variation of the compass is the deviation of the points of the mariner's compass from the corresponding points of the horizon, and is termed east or west variation according as the magnetic needle or north point of the compass is inclined to the eastward or westward of the true north point of the horizon. The true amplitude of any celestial object is an arch of the horizon contained between the true east or west points thereof and the centre of the object at the time of its rising or setting ; or it is the degrees and minutes the object rises or sets to the northward or southward of the true east or west points of the horizon. The magnetic amplitude is an arch contained between the east or west points of the compass and the centre of the object at rising or setting; or it is the bearing of the object by compass when in the horizon. The true azimuth of an object is an arch of the horizon contained between the true meridian and the azimuth circle passing through the centre of the object. The magnetic azimuth is an arch contained between the magnetic meridian and the azimuth circle passing through the centre of the object; or it is the bearing of the object by compass at any time when it is above the horizon. The true amplitude or azimuth is found by calculation, and the magnetic amplitude or azimuth by an azimuth compass. The magnetic amplitude or azimuth of the sun, or any celestial object, may be accurately observed by Mr. M'Culloch's patent compass, of which the following is a description.

DESCRIPTION OF THE AZIMUTH COMPASS.

Frontispiece, fig. 4, contains a perspective view of the azimuth compass ready for observation. The needle and card of this compass are similar to those of the steering compass, with this difference only, that a circular ring of silvered brass, divided into 360°, or rather four times 90°, circumscribes the card: b represents the compass-box, which is of brass, and has a hollow conical bottom ; e is the prop or support of the compassbox, which stands in a brass socket screwed to the bottom of the wooden box, and may be turned round at pleasure; h is one of the guards, the other, being directly opposite, is hid by the box,−each guard has a slit, in which a pin projecting from the side of the box may move freely in a vertical direction; 1 is a brass bar, upon which, at right angles, the side-vanes are fixed,—a line is drawn along the middle of this bar, which line, the lines in the vanes, and the threads joining their tops are in the same plane ; 2 is a coloured glass moveable in the vane 3; 4 is a magnifying glass moveable in the other vane, whose focal distance is nearly equal to the distance between the wanes; 5 is the vernier, which contains six divisions, and as the limb of the card is divided into half-degrees, each division of the vernier is therefore five minutes, the interior surface of the vernier is ground to a sphere, whose radius is equal to that of the card; 6 is a slide or stopper connected with the vernier, which serves to push the vernier close to the card, and thereby prevent it from vibrating as soon as the observation of the amplitude or azimuth is completed, and hence the degrees and parts of a degree may be read off at leisure with certainty; 7 is a convex glass, to assist the eye in reading off the observed amplitude or azimuth.

To observe the sun's amplitude.

Turn the compass-box until the vane containing the magnifying glass is directed towards the sun; and when the bright speck, or rays of the sun collected by the magnifying glass, falls upon the slit in the other vane, stop the card by means of the monius, and read off the amplitude.

Without using the magnifying glass, the sight may be directed through the dark glass towards the sun; and in this case the card is to be stopped when the sun is bisected by the thread in the other vane.

The observation should be made when the sun's lower limb appears somewhat more than his semidiameter above the horizon, because his centre is really then in the horizon, although it is apparently elevated on account of the refraction of the atmosphere : this is particularly to be noticed in high latitudes.

To observe the sun's azimuth.

Raise the magnifying glass to the upper part of the vane, and move the box, as before directed, until the bright speck fall on the other vane or on the line in the horizontal bar; the card is then to be stopped, and the divisions being read off will be the sun's magnetic azimuth.

If the card vibrate considerably at the time of observation, it will be better to observe the extreme vibrations and take their mean as the magnetic azimuth. When the magnetic azimuth is observed, the altitude of the object must be taken in order to obtain the true azimuth.

It will conduce much to accuracy if several azimuths be observed, with the corresponding altitudes, and the mean of the whole taken for the observation.

To find the variation of the compass by an amplitude.

RULE.—1. To the log. secant of the latitude, rejecting the index, add the log, sine of the sun's declination, corrected for the time and place of observation; their sum will be the log. sine of the true amplitude, to be reckoned from the east in the morning or the west in the afternoon, towards the north or south. according to the declination.

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2. Then if the true and magnetic amplitudes be both north or both south their difference is the variation, but if one be north and the other south their sum is the variation ; and to know whether it be easterly or westerly, suppose the observer looking towards that point of the compass representing the magnetic amplitude; then if the true amplitude be to the righthand of the magnetic amplitude the variation is east, but if to the left-hand it is west.

EXAMPLE I.

July 3, 1812, in latitude 9° 36' S. the sun was observed to rise E. 12° 42' N.; required the variation of the compass.

Latitude 9° 36' S. - - Secant 0.00613
Declination 22 59 N. - - Sine 9.59158
True amplitude E. 23 20 N. - - Sine 9,59771

Mag. amplitude E. 12 42 N.

Variation 10 38 W., because the true amplitude is to the left of the magnetic.

EXAMPLE II. September 24, 1812, in latitude 26° 32' N. and longitude 78° W. the sun's centre was observed to set W. 6o 15 S. about 6h. P. M.; required the variation of the compass.

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Reduced declination 0 41 - - - Sine 8.07650
Latitude 26 32 - - - Secant 0.04834
True amplitude W. 0 46 S. - - Sine 8.12484

Mag. amplitude W. 6 15 S.

Variation 5 29 E., because the true amplitude is to the right-hand of the magnetic.

To find the variation of the compass by an azimuth.

RULE.—1. Reduce the sun's declination to the time and place of observation, and compute the true altitude of the sun's centre. 2. Subtract the sun's declination from 90° when the latitude and declination are of the same name, or add it to 90° when they are of contrary names, and the sum or remainder will be the sun's polar distance. 3. Add together the sun's polar distance, the latitude of the lace, and the altitude of the sun; take the difference between alf their sum and the polar distance, and note the remainder.

4. Then add together' the log. secant of the altitude the log. secant of the latitude the log. co-sine of the half-sum, and the log. co-sine of the remainder. 5. Half the sum of these four logarithms will be the sine of an arch, which doubled will be the sun's true azimuth; to be reckoned from the south in north latitude, and from the north in south latitude; towards the east in the morning, and towards the west in the afternoon. 6. Then if the true and observed azimuths be both on the east or both on the west side of the meridian, their difference is the variation; but if one be on the east and the other on the west side of the meridian, their sum is the variation: and to know if it be east or west, suppose the observer looking towards that point of the compass representing the magnetic azimuth; then if the true azimuth be to the right of the magnetic, the variation is east, but if the true be to the left of the magnetic the variation is west.

: rejecting their indices,

EXAMPLE.

November 2, 1812, in latitude 25°32' N. and longitude 75° W. the altitude of the sun's lower limb was observed to be 15° 36', about 4h. 10m. P. M., his magnetic azimuth at that time being S. 58° 32' W., and the height of the eye 18 feet; required the variation of the compass.

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Co. for ti. 4h. 10m. af. m. Dip 4 Reduced declination 14 55 15 48 90 00 Refraction 3 Polar distance 104 55 True altitude 15 45 Altitude 15 45 - - Secant 0.01662 Latitude 25 32 - - Secant 0.04463 Sum 146 12 Half 73 6 - - Co-sine 9,46345 Remainder 31 49 - - Co-sine 9.92929 19,45399 32 14 - - Sine 9,72699 2 True azimuth S. 64 28 W. Mag. azimuth S. 58 32 W. Variation 5 56 east, because the true azimuth is to the

right of the magnetic.

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