SECTION IV. 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 ef 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 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 compass-box, 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. I 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 vanes; 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 Amfilitude. 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 nonius, 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 wane. 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. Tofind the variation of the Compassby 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. 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 right hand 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 Variation - 10 38 west, because the true amplitude is the left of the magnetis. EXAMPLE II. September 24, 1812, in latitude 26° 32' N. and longitude 78° W.the Sun's centre was observed to set W. 6° 15' S, about 6h, P. M. required the variation of the compass. ~ * Sun’s declination 0° 30' S. Corr. for long. 78° W. + 3 * Corr. for time 6h. P. M. + 6 Reduced declination 0 41 Sine 8.07650 • Latitude - 26 32 Secant 0.04834 True amplitude W. 04: S. Sine 81.2484 Mag. amplitude W. 6 5 S. Variation 5 29 east, because the true amplitude is to the right hand of the magnetic, To find the Variation of the Comfass 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 place, and the altitude of the Sun; take the difference between half their sum and the polar distance, and note the remainder. 4. Then add together the log secant of the altitude rejecting their the log. secant of the latitude } indices, 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 recköned from the south in north latitude, and from the north in south lati |