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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 ihe 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 instruments

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 have 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 wood 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 froin the air a wooden trough filled with quicksil

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 single 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 flatways, and, with the quicksilver in a bottle, &c. is packed into a portable flat case,




To find the Latitude by the Meridian Altitude of the Sun, The Latitude of a place is its distance from the equator, either North or South ; and is measured by an arch of a Meridian contained between the Zenith and the equinoctial. Hence, if the disay tance of 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 Sextant, requires fonr 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

1 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 whereiti 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 viewed 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 the 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 Latitude from the Sun's Meridian


Having observed with the Quadrant, or Sextant, the altitude of the Sun's lower limb above the vi. sible horizon,ếor 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 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 artificial horizon, balf 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. 1st, March 10th, 1811, in longi- 22. May 10th, 1811, in long. 80% tude 700 W. the Mer. Alt of O L. W. at noon, the angular distauce L. was observed to be 490 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° 30' 10' required the latiMer. Alt. O L.L.=490 50'00" S. tude. Semidiameter

= +16 08 980 30' 40'' 2=490 15' 20" Dip-table 8

-03 19

O Ap. Alt. =490 -15' 20" S.

-43 Ap. Alt.

= 50 02 49 Correction

True Alt.

49 14 37

90 True Alt.

50 02 07 90

Zenith Dist. =40 45 23 N.

Reduced Dec. =17 30 34 N. Zenith Dist. = 39 57 53N. Reduced Dec. - 4 15 298. Latitude.

=58 15 57 N. Latitude.

35 42 24N.

3d. July 24th, 1811, in long. 62° 4th. October 11th, 1812, in loug 30' W. the Mer. Alt of O L.L. 91° W. the Meridian Altitude ot 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 470 13' bearposite shore, to be 56° 32' bear-ing $. 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

. OL.L.=470 13 00'S. being 5 miles from the observer, Semidiaineter + 16 06 and the height of his eye above Dip from tạble 8 = -4 47 the surface of the water, 8 feet; required the latitude.

Ap. Alt

=47 24 19 Mer. Alt. O L.L.=56° 32'00" S. Correction

- 46 Seinidiameter

+ 15 48
True Alt.

47 23 33 Dip from table 9 = - 2 36

90 Ap. Alt.

= 56 45 12 Correction


Zenith Dist. =42 36 37 N.

Reduced Dec. = 6 58 16 S True Alt. = 56 44 39

Latitude 90

= 35 38 11 N.

N. B. For the various other meZenith Dist. = 33 15 21 N. thods of finding the latitude by Reduced Dec. = 19 59 46 N. observation, the surveyor must ap

ply to books professedly on prac. Latitude = 53.15 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 south ward 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.


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 tises 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 råys 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, trecause his centre is really then in the horizon, although it is ap

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