EXAMPLE IV... Sun's bearing at setting is SW. 81°, and the true amplitude is found to be W. 6. 16'N. Required the variation. The true amplitude being to the right of the magnetical, the variation is easterly.. 2. To find the variation by azimuths. 13. The sun's magnetical azimuth is the bearing thereof at any time of the day, taken by the quartered compass; that is, counted from the north or south towards the east or west points of the box. 14. The sun's true azimuth is the point of the compass it would bear from you upon, if there were no variation; or it is the distance intercepted between the north or south points of the horizon, and a vertical circle, or circle drawn from the zenith through the sun to the horizon. Having the latitude of the place, the sun's declina tion, and its altitude given, the true azimuth is ob 1. As the tangent of half the complement of the latitude, Is to the tangent of half the sum of the distance of the sun from the pole, and complement of the altitude, So is the tangent of half the difference between the distance of the sun from the pole, and complement of the altitude, To the tangent of a fourth arc. Add this fourth arc and half the complement of the latitude together, their sum will give a fifth arc; from which if the complement of the latitude be taken, the remainder will give a sixth arc. Then say, As radius Is to the tangent of the altitude, So is the tangent of the sixth arc To the co-sine of the sun's true azimuth. Which is counted from the north or south, to the east or west, according to the sun's situation at the time and place of observation. If the latitude of the place, and the sun's declination be both north or both south, the declination taken from 90°, gives the sun's distance from the pole; but if one be north and the other south, the declination added to 90°, will give the sun's distance from that pole which is nearest the observer. If both azimuths are east or west, their difference is the variation; but if one be east, and the other west, their sum is the variation. EXAMPLE IV. Sun's bearing at setting is SW. 81°, and the true amplitude is found to be W. 6. 16'N. Required the variation. 90°-811-8°1⁄2 the magnetical amplitude from the The true amplitude being to the right of the magnetical, the variation is easterly.. 2. To find the variation by azimuths. 13. The sun's magnetical azimuth is the bearing thereof at any time of the day, taken by the quartered compass; that is, counted from the north or south towards the east or west points of the box. 14. The sun's true azimuth is the point of the compass it would bear from you upon, if there were no variation; or it is the distance intercepted between the north or south points of the horizon, and a vertical circle, or circle drawn from the zenith through the sun to the horizon. Having the latitude of the place, the sun's declination, and its altitude given, the true azimuth is ob 1. As the tangent of half the complement of the latitude, Is to the tangent of half the sum of the distance of the sun from the pole, and complement of the altitude, So is the tangent of half the difference between the distance of the sun from the pole, and complement of the altitude, To the tangent of a fourth arc. Add this fourth arc and half the complement of the latitude together, their sum will give a fifth arc; from which if the complement of the latitude be taken, the remainder will give a sixth arc. Then say, As radius Is to the tangent of the altitude, So is the tangent of the sixth arc To the co-sine of the sun's true azimuth. Which is counted from the north or south, to the east or west, according to the sun's situation at the time and place of observation. If the latitude of the place, and the sun's declination be both north or both south, the declination taken from 90°, gives the sun's distance from the pole; but if one be north and the other south, the declination added to 90°, will give the sun's distance from that pole which is nearest the observer. If both azimuths are east or west, their difference is the variation; but if one be east, and the other west, their sum is the variation. To know whether the variation be easterly or westerly. Just as with the amplitudes, let the observer's face be turned to the sun; then if the true azimuth be to the right hand of the magnetical one, the variation is easterly; but if to the left, westerly. EXAMPLE I. In the latitude 53°. 20' N. the sun's declination being 19°. 03, N. I find by observation the sun's altitude to be 37°. 30′, and its magnetical azimuth te be SE. 51°. Required the variation. 90°-53.20′-36.40, the compt. of the latitude 18.20. the compt. of the latitude 90°—37°.30′=52°30, the compt. of the alti tude. 90°-19°.03'-70°.57', the sun's dist. from the pole 52.30 compt. of the altitude 123.27 sum 61.43 half sum 18.27 difference |