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any heavenly body from the Zenith, when on the Meridian, and its declination, or the number of degrees and minutes it is to the Northward or Southward of the equinoctial, be given, the Latitude may thence be found.
The Altitude of the Sun, observed by a Quadrant or Sextánt, requires four corrections in order to obtain the true altitude; these are the Semidiameter, Dip, Refraction, and Parallax.
By the Semidiameter of the Sun is meant the angle subtended
by the distance from its centre to its apparent circumference. The quantity of this angle is given for every sixth day in the year in table 10.
The Dip of the Horizon is a vertical angle contained between a Horizontal plane passing through the eye of an observer, and a line drawn from his eye to the visible Horizon. This Dip is found in Table 8, when the visible horizon is formed by the apparent junction of the water and sky; but in Table 9, when land intervenes. In this case, the line that separates the land and water is used as the Horizon, and its distance from the observer must be duly estimated.
The Refraction of any celestial body is the difference between its apparent place, and that wherein it would be seen, if the space between the observer and object, was either a void, or of a uniform density. Table 6 contains this Refraction.
That part of the heavens, in which an object appears, when view. ed from the surface of the earth, is called its apparent place; and the point, wherein it would be seen, at the same instant, if viewed from tlie centre of the earth, is called its true place; the difference between the true and apparent places, is called the Parallax. The Sun's Parallax in Altitude is found in Table 7.
For finding the Latilude from the Sun's Meridian
Having observed with the Quadrant or Sextant, the altitude of the Sun's lower limnb above tbe visible horizon,—or the line of separation of the land from the water, when that horizon is obstructed by land-add thereto the semidiameter, taken
from table 10 at the given day of the month, or the one nearest to it, and from this sum subtract the Dip, from table 8 or 9, corresponding to the beight 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 iinage in an artificial 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.
1st. March 10th, 1811, in longi 2d. May 10th, 1811, in long. 80% tude 70° W. the Mer. Alt. of © W. at noon, the angular distance L. L. was observed to be 49° 50' between the 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° 3040'' required the laMer. Alt.O L.L. = 49° 50'00'S. titude. Semidiameter
+ 16 08 98° 30° 40'' 2 = 49° 15' 20" Dip-table 8
49° 15' 20'S.
Correction Ap. Alt.
50 02 49 Correction - 42 True Alt. = 49 14 37
90 True Alt.
50 02 07
Zenith Dist. = 40 45 23 N.
Reduced Dec. 17 30 34 N. Zenith Dist.
39 57 53 N. Reduced Dec. 4 15 29 S. Latitude = 58 15 57 N.
3d. July 24th, 1811, in long. 62° 4th. October 11, 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 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' bearing ing S. the height of the eye being 8.--the distance of that border of 25 feet; required the latitude. the lake beneath the sun being 5 Mer. Alt. OL, L= 47° 13'00'S miles from the observer, and the Semidiameter + 16 06 height of his eye above the sur- Dip from table 8
4 47 face of the water, 8 feet; requirod the latitude.
47 24 19 Mer. Alt. O L.L. = 56° 32° 00'S. Correction
46 Semidiameter = + 15 48 Dip from table 9 -2 36 True Alt.
47 23 33
90 Ap. Alt.
56 45 12 Correction
33 Zenith Dist. 42 36 27 N,
Reduced Dec. 6 58 16 S.
56 44 39
35 38 11 N.
33 15 21 N. N. B. For the various other me. Reduced Dec. 19 59 46 N. thods of finding the latitude by
observation, the surveyor must apLatitude
53 15 07 N. ply to books professedly on prac:
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.
VARIATION 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 hori
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 com pass, 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 ratherfour 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, wbich 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 saine 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 Jimb 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,