Dip, from table 8 or 9, corresponding to the height of the observer's eye above the surface of the water; and this result will be the apparent altitude of the Sun's centre. Then take the refraction from table 6, and the parallax from table 7, corresponding to this altitude, and the difference of these quantities, called the correction, being subtracted from the apparent altitude, the remainder will be the Sun's true altitude ; the complement of which will be its zenith distance, north or south, according as the Sun bears south or north, at the time of observation. When the observation has been made by bringing the Sun's image in the Quadrant, or Sextant, to a just coincidence with its image in an aruficial horizon, half the angle shown on the instrument is the Sun's apparent altitude, which must be corrected by the corresponding refraction and parallax only, in order to obtain the true altitude. Take the Sun's declination from table 13, answering to the given year, month and day, observing whether it be north or south, and reduce it, as there directed, by the help of table 14, to the longitude of the place of observation. Then the sum, or difference of the zenith distance and declination, according as they are of the same, or of a contrary denomination, will be the latitude of the place of observation, of the same name with the greater of those two quantities. EXAMPLES. ist. March 10th, 1811, in longi. 20. May 10th, 1811, in long. 800 tude 70° W. the Mer. Alt of O L W. at noon, the angular distance L. was observed to be 49° 50' between the O bearing south, and bearing south-height of the ob- its reflected image in the artificial server's eye 12 feet, required the horizon was found with a sextant latitude in to be 98° 30' 40" required the lati. Mer. Alt OL L= 49° 50'00" S. tude. Semidiameter +16 08 98° 30' 40" --2=49° 15' 20" Dip-table 8 -03 19 O Ap. Alt. =499 15' 20" S. -43 = 50 02 49 Correction -42 True Alt. -49 14 37 True Alt. 50. 0207 40 45 23 N. Reduced Dec. Zenith Dist. =17 30 34 N. 39 57 53 N. Reduced Dec. 4 15 29 S. Latitude. =58 15 57 N. Latitude. 35 42 24N. _ Correction Ap. Alt. 90 3d. July 24th, 1811, in long. 629 4th. October 11th, 1812, in long 30' W. the Mer. Alt of O L L. 91° W the Meridian Altitude of above the border of a lake was O L. L. above the visible horizon observed, by a person on the op- was observed to be 47° 13' bear. posite shore, to be 56° 32' bear. ing S. the height of the eye being ing S--the distance of that bor- 25 feet; required the latitude. der of the lake beneath the sun Mer Alt. O L L = 47° 134.00" S. being 5 miles from the observer, Semidiameter = +16 06 and the height of his eye above Dip from table 8 = -4 47 the surface of the water, 8 feet; Ap. Alt. -47 24 19 required the latitude. Correction -46 Mer. Alt. O L.L. —560 321 00" S. Semidiameter = +15 48 True Alt. =47 23 33 Dip from table 9 -2 36 90 Ap. Alt. = 56 45 12 Zenith Dist. 42 36 27 N. Correction 33 Reduced Dec. 6 58 16 S. Truc Alt. 56 44 89 Latitude =35 38 11 N. 90 N. B. For the various other me. Zenith Dist. thods of finding the latitude by =38 15 21 N. observation, the surveyor must ap. Keduced Dec. 59 ply to books professedly on pracLatitude =5315 07 N. tical astronomy. He will, however, find a method of observing the latitude by the altitude of the north star, in the explanation of table 12, annexed to this treatise. SECTION IV. VARIATION OF THE COMPASS. The variation of the compass is the deviation of the points of the mariner's compass from the cor responding 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 AZIMUTH COMPASS. From the accounts of the compasses, heretofore given in the description of surveying instruments, it is presumed that the nature and properties of the azimuth compass will be readily conceived by a contemplative inspection; the directions for its uses are as follow: 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 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 he 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 ap parently 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 variationof 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. 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 99 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 Sine 9 59158 Sine 9.59771 True amplitude E. 23 20 N. Variation 10 38 west, 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. 6° 15' S. about 6. P. M. required the variation of the compass. Sun's declination 0° 30' S. Corr for long. 78° W. + 5 Corr. for time 6h. P. M. + 6 Reduced declination 0 41 26 32 Sine 8.07650 True amplitude W. 046 9. Sine 81.2484 Mag. amplitude W. 6 15 S. Variation 5 29 east, because the true amplitude is to the right hand of the magnetic. To find the Variation of the Compass by an Azimuth. Rule.l.- 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 thelog. co. sine of the remainder. Tt |