In many fextants the lower prof the index glass, or that nearest the frame, is filvered as ufual ad the back furface of the upper part painted black; alfo a fcreris fixed at the base of the index glafs, turning on its axis, and my be placed over the filver part when the fun's rays are ftrong irwhich cafe the image is reflectedfrom the polished furface of ne pper part, and the error, which might probably arife from the phes of the glaffes not being parallel, is thereby avoided.

There are feveral coloured glas at H, each of which is set in a different frame, turning on a cere; they are used to screen the eye from the brightness of theolar rays, and the glare of the moon, and may be ufed feparaty or together, as occafion requires.

There are other fuch glaffes ced behind the horizon glass at F, to weaken the rays of the funr moon when they are viewed directly through the horizon gla; the paler glafs is fometimes ufed in obferving altitudes at sea, take off the strong glare of the horizon.

The fextant is furnished with lain tube, without any glaffes; and to render the objects ftill me diftinct, it has two telescopes, one reprefenting the objects erecor in their natural pofition, the other fhewing them inverted; ias a large field of view, and other advantages; a little ufe w foon accuftom the observer to the inverted pofition, and the trument will be as readily managed by it as the plain tube alo By a telefcope the contact of the images is more perfectly diftiuifhed; and by the place of the images in the field of the telefco it is easy to perceive whether the fextant is held in the properane for obferving. By fliding the tube that contains the eye-ges in the infide of the other tube, the object is fuited to differ eyes, and made to appear perfectly distinct and well defined.

The telescopes are to be fcred into a circular ring, at K; this ring refts on two points agai an exterior ring, and is held thereto by two fcrews; by turn one and tightening the other, the axis of the telescope may bet parallel to the plane of the fextant. The exterior ring is fil on a brass stem that flides in a focket, and by means of the fcrev, at the back of the fextant, it may be raised or lowered fo as toove the centre of the telescope to point to that part of the horizoglafs which shall be judged the moft fit for obfervation.

A circular head, containing slate, in which there are three coloured glaffes, and a fourth it is open, fometimes accompanies this fextant. This head is be fcrewed on the eye-end of the tube, or on that of either tecope. The edge of the plate projects a little beyond the head, one fide, and is moveable by the finger, fo that the open ringor any of the coloured glaffes, may be brought between the eyelaffes of the telescope and the eye.

To these are added, a fmall fow-driver to adjust the screws,

and a magnifying glafs to read off the obfervation with greater

accuracy.

The Adjustments of a Sextantre to fet the index and horizonglaffes perpendicular to the planof the inftrument, and their planes parallel to each other; by the fne method as the quadrant, only fcrewing on the plain tube or tescope; alfo to fet the axis of the telescope parallel to the plane othe inftrument; each of thefe particulars must be examined befor an obfervation is taken, and the adjustments, if requifite, be mae.

For correcting the index erro, fee the rules for adjufting Hadley's Quadrant.

To fet the Axis of the Telefcopearallel to the Plane of the Sextant.

In measuring angular diftanes, the line of fight, or axis of the telescope, fhould be parallel t the plane of the inftrument, as a deviation in that refpect will ccafion a confiderable error in the observation; and this is most enfible in large angles. To avoid which, an inverted telescope i used, in whofe field there are placed two wires parallel to each oter, and equidiftant from the centre; to which are sometimes adde two others, at right angles to thefe, but parallel to each other. By means of thefe wires the adjuftment may be made thus: ferw on the telescope, and turn the tube containing the eye glass, tillthe wires are parallel to the plane of the inftrument; then take tvo objects, as the fun and moon, or the moon and a star, whofe angilar diftance muft not be lefs than 90°, because the error is more easily discovered when the distance is great; bring them exactly nto contact on the wire which is nearest the plane of the inftrumeit, and fix the index; then, by altering a little the position of the fextant, bring them to appear on the wire fartheft from the plane of the inftrument; if they remain ftill in contact, the axis of tle telescope is parallel to the plane of the fextant; but if the limb of the two objects appear to separate at the further wire, it fhews that the object-end of the telescope inclines towards the plane of the fextant; this must be rectified by tightening the fcrew reareft the fextant, which is attached to the ring that holds the telecope, having previously flackened the fcrew fartheft from it. If the images overtop each other when brought to the wire fartheft from the fextant, the object end of the telescope is inclined from the plane of the fextant, and must be rectified by flackening the fcrew neareft the fextant, and tightening the other. Repeat this operation till the contact be rendered perfect on both wires, the axis of the telescope will then be truly adjusted.

To obferve the angular Distance between the Sun and Moon.

Screw on the inverted telefcope, placing the wires parallel to the plane of the inftrument; then turn down the fcreens, according to the brightness of the fun; place the index at O on the arch, and if the fun's image be very bright, turn up the fcreen before the hori

zon

1

zon glass, and with the screw S, ife the telescope to the tranfparent part of the horizon glafs. hving done this, hold the fextant fo that its plane may pass throgh the two objects: if the fun be to the right hand of the moon, he fextant is to be held with its face upwards; but if it be to the ft hand, the face is to be held downwards. With the inftrumet in this pofition, look directly at the moon through the telescop and move the index forward, till the fun's image is brought nealy in contact with the moon's neareft limb; then fix the index b the fcrew under the fextant, and make the contact perfect by mans of the adjusting-ferew; at the fame time move the fextant flwly, making the axis of the telescope the centre of motion, b which means the objects will pass each other, and the contact benore accurately discriminated. The index will fhew the observed iftance of the fun and moon's nearest limbs, which you will read ff with a magnifying glass.

Second Mhod.

It will perhaps be more eafy for thse who are not accustomed to make obfervations of this kind, tofind the diftance nearly, and fetting the index forward to it, to loc directly towards the moon, holding the inftrument as before; the fun will then appear nearly in contact with it, and is to be made erfect by the method abovementioned. In the Nautical Ephemeris, the diftance of the fun and moon is fet down for every three lours of time at Greenwich, on fuch days as the moon is not more than 120°, nor less than 40° diftant from the fun, and may be found for by taking proportional parts; from thee diftances you may comany intermediate time pute roughly their diftance at the time of obfervation, thus: Turn the fhip's longitude into time by Tab. XVI. and add it to the time of obfervation, if the longitude be weft, but fubtract it if the longitude be eaft, the fum or difference will give the time at Greenwich; then, by the Ephemeris, find the distance nearly at that time, from which fubtract 30 minutes for the fun and moon's femi-diameters, and the remainder will give the diftance of their nearest limbs at the time of obfervation."

If a number of obfervations are to be taker, the following method will not be found unacceptable: Having brought the objects into contact, as before direted, and noted down their apparent angular diftance, advance or draw back your index two or three minutes, according as the objects are receding or approaching, and wait till they again come into contact, repeating the operation as often as judged neceffary, ufing the mean of all the obfervations to determine the longitude. This method will be found eafy and ac

curate.

NOTE.-The contact of the limbs must always be observed in the middle, between the parallel wires,

To obferve the Distance between the Moon and a Star. Turn down the lighteft fcreen before the index glass, and direct the telescope to the ffar, holding the fextant in its proper pofition,

as before directed; then move the index forward, till the reflected image of the moon is seen in the telescope; by moving the inftrument flowly up and down, the moon will appear to rife and fall by the ftar. The round and well defined limb of the moon, whether it be nearest or furtheft from the star, must be brought into contact with it. When the object to be seen by reflection is to the right hand of that to be seen by direct vifion, the inftrument is held with its face upwards; but when the object to be seen by reflection is to the left hand of that feen directly, the inftrument is held with its face downwards. Having brought the objects into contact, the nonius will fhew the obferved angular distance.

If the distance between the moon and one of the stars fet down in the Ephemeris for finding the longitude, is to be observed, their distance may be roughly calculated as before directed, to which fet the index; then look through the telescope, and direct the fight to the ftar, which is generally a bright one, and lies in a line nearly perpendicular to the horns of the moon, either to the eastward or weftward, as denoted in the Ephemeris; then, holding the inftru ment in the plane of the two objects, give it a flow motion up and down, and if the moon's image come in the field of the telescope, it is a proof you have taken the right star, as no other in that direction will correfpond in distance to it.

After the distance is obferved between the fun and moon, by a fextant or quadrant, there ftill remains to be made fome corrections to obtain the true diftance; the corrections are thofe for parallax, refraction, and femi-diameter.

The dip of the horizon is an angle made with the height of the eye of the observer and the vifible horizon, and which makes the angle of celeftial objects appear higher than they really are by the amount of the correction found in Table VIII. and which is to be fubtracted from all altitudes.

PARALLAX.

The parallax of the fun and moon is the difference of the altitude of either object, if observed at the same moment of time from the centre, and from the furface of the earth. The parallax of the heavenly bodies is greatest when in the horizon; hence called the horizontal parallax. That of the moon is fet down in the Nauti cal Almanack for every noon and midnight, but may be found for any intermediate time by taking proportional parts. The fun's mean parallax being only 8".6, is feldom attended to in nautical calculation, except when his altitude is taken to determine the true time, or the angular diftance to determine the longitude. The ftars, on account of their great diftance from the earth, have no fenfible parallax; the parallax of the fun and moon caufing them to appear lower than they really are, it is evident this correction must be added to the apparent altitude of the fun and moon, in order to obtain their true altitude. This will be better illuftrated by the plate facing page 146. Let C reprefent the centre of the

T

earth;

earth; a, o, e, part of the moon's orbit; b, d, g, part of the fun's orbit; 1, k, part of the ftarry heavens. Now, to a spectator at m, upon the surface of the earth, let the moon appear at e, in the horizon of m, and it will be referred to f; but if viewed from the centre c, it will be referred to h. The difference between these places, or the arch f, h, is called the horizontal parallax, and the angle m, e, c, the paralactic angle. The parallax will be greater or lefs, according to the diftance of the objects from the earth; thus, the parallax f, h, of e, is greater than the parallax f, n, of g, and with respect to the fame object, it is evident when it is in the horizon, the parallax is greateft, and that it diminishes as the ob ject approaches the zenith, where it vanifhes. Thus the horizontal parallax of e and g is greater than the parallax in altitude of and d; but the objects a and b, as seen from m, the furface, or c, the centre, appear in the fame place, 1, or the zenith.

Having the earth's femi-diameter, and the parallax of any of the planets, their distance may be found thus: As the tangent of the parallax is to the earth's femi-diameter in miles :: fo is radius: to the distance.

Having the distance, the parallax in altitude is found thus: As the distance is to radius :: fo is the earth's femi-diameter: to the tangent of the parallax.

:

REFRACTION.

From various experiments it hath been found that the rays of light paffing through the atmosphere, are bent out of their trait courfe into an elliptic curve-line, from whence it follows, that all heavenly bodies, except when they are in the zenith, appear higher than they ought to do, and the more fo the nearer they are to the horizon, where they are nearly 33 miles. This apparent elevation of the heavenly bodies above their true height is called the Refraction, therefore all apparent altitudes obferved, muft (after the dip has been allowed for) be reduced to their true altitudes by the correction found in Table VII. which must be subtracted from the apparent altitude, or added to the zenith diftance, in order to obtain the true altitude.

Now, fince parallax makes all objects appear lower than they really are, and refraction makes them appear higher than they are, it is evident that the true altitude of an object cannot be obtained without correcting the obferved altitude for the difference of thefe two fums.

SEMI-DIAMETER.

The moon's femi-diameter is fmallest when in the horizon, and increasing as the approaches the zenith, where it is greatest; as fhe is then nearer the fpectator by the earth's femi-diameter. This augmentation is fet down in Table X. Another reafon of the apparent augmentation and diminution of the moon's femi-diameter is, that he moves round the earth in an orbit not circular, but