manner as an observation of the sun. If the image is so faint as not to be seen in the transparent part of the horizon glass, you must set the index to 0; hold the plane of the quadrant in a vertical position; direct the sight to the moon, and, at the same time, look for her reflected image in the silvered part of the horizon glass; move the index forward till the moon's image (which will appear to descend) just touches the horizon; then sweep the quadrant as in observing the sun, and bring her round limb in contact with the horizon, whether it be her upper or lower. The degrees and minutes pointed out by the index, will be the observed altitude of that limb which was brought in contact with the horizon.

To take an altitude of a star by a fore observation.

This is done exactly in the same manner as in observing the moon's altitude, when her image is so faint as not to be seen in the transparent part of the horizon glass.

To take the sun's altitude by a back observation.

Put the dark glasses in the hole O, and turn one or more of them down, according to the brightness of the sun; then, holding the instrument in a vertical position, look through the back sight vane towards that part of the horizon opposite the sun; move the index till the sun's image is seen in the silvered part of the glass; give the quadrant a slow vibratory notion, and the sun will appear to describe an arc with its convex side upward; bring the upper limb, when in the upper part of this are, in contact with that part of the horizon seen through the transparent slit, and the degrees and minutes pointed out by the index will be the altitude of the sun's lower limb. The altitude of the moon, or a star, may be obtained in the same manuer, only observing to bring the round edge of the moon to the horizon.

The back observation is but little used, on account of the difficulty of adjusting and observing. Various remedies have been proposed for these defects, but none have vet Deen generally adopted. The back observation of the altitude of any object, is useful only when there is not an open horizon for the fore observation; but even in that case, the fore observation may often be used, if the distance of the horizon be known, as will be explained hereafter.

To observe the meridian altitude of any celestial object by a fore observation,

When the object rises and sets, it comes to the meridian above the horizon only once in 24 hours, and is then at its greatest altitude; and by observing it, the latitude may be easily determined. The sun comes to the meridian exactly at noon, or 12 o'clock apparent time; the moon and stars at various hours. To observe the meridian altitude, begin a few minutes before the time of passing the meridian; bring the object to sweep the horizon, according to the preceding directions; this operation must be repeated until the object begins to descend below the edge of the sea; the degrees and minutes then shown by the index will be the meridian altitude.

If the object does not set, it comes to the meridian below the pole, and is then at its least altitude; this altitude may be observed as above directed, with this difference, that you must continue sweeping till the object begins to rise above the edge of the sea, instead of descending below it.

The meridian altitude of any object may be taken in a similar manner by a back observation.

Strictly speaking, this method of finding the meridian altitude is not absolutely accurate, except the ship be at rest, and the suns declination constant. For if the ship is sailing towards the sun, the altitude will be increased; but the altitude will be decreased in sailing from the sun. The correction of altitude arising from this source is generally very small, and it may be neglected in most cases, as will be shown hereafter.

Advice to seamen in the choice of a quadrant.

The joints of the frame must be close, without the least opening or looseness, and the ivory on the arc inlaid and fixed, so as not to rise in any place above the plane of the instrument; all the divisions of the arc and vernier must be exceedingly fine and straight, so that no two divisions of the vernier (except the first and last) coincide, at the same time, with the divisions of the arc. All the glasses belonging to the quadrant

should have their surfaces perfectly plane, and their fore and back surfaces exactly paralle.; this may be verified, in the horizon, glass and index glass, by means of two distant objects, in the following manner :-Move the index till both objects are exactly in contact, at the upper edge of the silvered part of the horizon glass; then move the quadrant in its own plane, so as to make the united images move along the line, separating the silvered from the transparent part of the horizon glass; and if, in this motion, the images continue united, the reflecting surfaces are good planes, otherwise the planes are imperfect. To examine the dark glasses, we must bring the image of a distant object to coincide with the object seen directly; then turn the colored glass so that the plane which was next to the index glass may now be next to the horizon glass, and if the direct and reflected images still coincide, the surfaces of the glass are parallel.

DESCRIPTION AND USE OF A SEXTANT OF REFLECTION.

A SEXTANT is constructed on the same principles, and may be used for measuring altitudes in the same manner, as a quadrant.* The arc of a sextant, as its name implies, contains 60°, but, by reason of the double reflection, is divided into 120o. This instrument is particularly intended to measure the distance of the moon from the sun, a planet, or a fixed star; and as that distance is wanted as accurately as possible, to determine the longitude of the place of observation, the instrument is constructed with more care, and is provided with some additional appendages that are not in the quadrant. Plate IX., figure 3, represents a sextant, the frame being generally made of brass, or other hard metal; the handle at its back is made of wood. When observing, the instrument is to be held with one hand, by the handle, while the other hand moves the index. The arc AA is divided into 120°, each degree into 3 parts of 20 minutes each, and the vernier scale is in general so divided as to show half or a quarter of a minute. In some sextants, the degree is divided into six equal parts, of 10 each, and the vernier shows 10''.

In order to observe with accuracy, and make the images come precisely in contact, a tangent screw B is fixed to the index, and by this it can be moved with greater regularity than it can be by hand; but the screw B does not act until the index is fixed by the screw C, at the back of the sextant. Care must be taken not to force the tangent screw, when it arrives at either extremity of its arc. When the index is to be moved any considerable quantity, the screw C must be loosened; and when the index is brought nearly to the division required, the back screw C must be tightened, and then the index moved gradually by the tangent screw.

In many sextants, the lower part of the index glass, or that next the plane of the instrument, is silvered as usual, and the back surface of the upper part painted black; a screen, painted black, is fixed by its axis to the base of the index glass, and may be placed over the silvered part when the rays are strong; in this case, the image is to be reflected from the outer surface of the upper part, and the error which might possibly arise from the planes of the glass not being parallel, is thereby avoided.

In

The colored glasses are similar to those applied to a common quadrant, and are usually four in number, placed at D, to screen the eye from the solar rays, and the glare of the moon; they may be used separately or together, as occasion requires. addition to these, there are three similar glasses, placed behind the horizon glass, to be used in finding the index error by means of the sun, and in observing the sun's altitude, by an artificial horizon on land. The paler glass is sometimes used in observing altitudes at sea, to take off the strong glare of the horizon below the sun, arising from the sun's light, reflected irregularly from the small rippling waves-an appearance which has lately been called kumatage.

A sextant is generally furnished with a tube without glasses, and two telescopes, the one representing the objects erect or in their natural situation, the other inverting them,

There is not, in general, any apparatus for the back observation fixed to a sextant; but if the altitude of any celestial object be greater than 60°, the supplement of the altitude may be obtained by a back observation, with a sextant, with ease and accuracy; and as this method may be often used with advantage, when a fore observation cannot be obtained, we shall here point out the method of taking the observation, and shall hereafter give the calculations for determining the latitude from a meridian observation, taken in this manner:-The back of the observer being turned to the sun, he must move the index till the image of the sun touches the edge of the back horizon, and then move the sextant a little to the right and left (as in a fore observation), and the image will describe an arc with the convex side upward; move the index till the lower limb of the image, when in the upper part of the arc, just touches the horizon, and the observation will be complete; observing that, if the telescope be used, the image must be brought in the middle between the two parallel wires; but if the telescope he not used, the image of the sun must be seen in the horizon glass, at the same distance from the plane of the instrument as the eye of the observer. The altitude thus obtained will be the supplement of the altitude of the sun's upper limb. The corrections to be applied to obtain the true central altitude, will be given

hereafter,

the eye-glass being fixed in a movable tube, in order to adjust the telescope to a proper focus. By means of these telescopes, the line of sight may be rendered parallel to the plane of the instrument, and the contact of the limbs of any two objects more accurately observed. The tube, or either telescope, is to be screwed into a brass ring, which is connected with another brass ring by means of two screws; and by loosening one, and tightening the other, the axis of the tube or telescope may be set parallel to the plane of the instrument. One of these rings is fixed to a brass stem, which slides in a socket; and by means of the screw L, at the back of the sextant, it may be raised or lowered so as to move the axis of the telescope to point to that part of the horizon glass judged the most fit for observation.

A circular head, containing a plate, in which there are three colored glasses, and a part that is open, sometimes accompanies the sextant; this head is to be screwed on the eye end of the tube, or on that of either telescope. The edge of the plate projects a little beyond the head on one side, and is movable by the finger, so that the open ring, or any of the colored glasses, may be brought between the eye-glass of the telescope and the eye; this answers the purpose of the dark glasses placed at E, in adjusting by the sun, or observing by an artificial horizon on land.

To these are added a small screw-driver, to adjust the screws, and a magnifying glass, to read off the observation with greater accuracy.

The adjustments of a sextant are similar to those of a quadrant; the index and horizon glasses must be perpendicular to the plane of the instrument, and their planes parallel to each other when the index stands on 0; also the axis of the telescope must be set parallel to the plane of the instrument; each of these particulars must be examined before an observation is taken and the adjustments, if requisite, made according to the following directions :—

1st. To set the index glass perpendicular to the plane of the instrument.

Move the index forward to about 60°, and proceed exactly in the manner prescribed 129. for the adjustment of the index glass of a quadrant, page

2d.

To make the horizon glass perpendicular to the plane of the sextant. This adjustment is made exactly in the same manner as that of the quadrant, described in page 129, except that, instead of looking through the sight vane, you may use the tube, or a telescope.

To make the horizon glass and index glass parallel when the index is on 0.

made the foregoing adjustments, set the first division on the index at 0 on the limb; fasten the index in this position, and make the coincidence of these divisions as perfect as possible, by means of the tangent screw, the eye being assisted by the magnifying glass; screw the tube, or telescope, into its support, and turn the screw L, at the back of the instrument, till the line which separates the transparent and silvered parts of the horizon glass appears in the middle of the tube or telescope; having done this, hold the plane of the sextant vertically, and direct the sight through the tube or telescope to the horizon; then, if the reflected and true horizons do not coincide, turn the tangent screw at the back of the horizon glass till they are made to appear in the same straight line. Then will the horizon glass be adjusted.

the screw that retains the horizon glass in its place is fastened, it will be proper to re-examine this adjustment; if the coincidence of the horizons is not perfect, the adjustment must be repeated till it is so; but as it is difficult to obtain a perfect coincidence by this means, the horizons may be brought to coincide by turning the tangent screw of the index; and the difference between the 0 on the arc and the 0 on the vernier will be the index error, which is additive to all observations if the 0 of the index stand on the extra arc, otherwise subtractive. The index error may also be found very accurately, by measuring the diameter of the sun twice, with a motion of the index in contrary directions; that is, first bring the upper limb, seen by reflection, to coincide with the lower limb seen directly; then bring the lower limb by reflection to coincide with the upper seen directly. If both these measures are taken either to the right or left of 0 on the limb, half their sum will be the index error; additive if to the right of 0, subtractive if to the left: but if one of the measures be taken to the right, and the other to the left of 0, half their difference will be the index error, which ill be additive when the diameter measured to the right of 0 exceeds that measured to the left, otherwise subtractive. Thus. if the measures were 38' to the left of 0 on

he arc, and 26' to the right on the extra arc, half the difference, or 6', would be the correction, subtractive. In some sextants, the horizon glass cannot be adjusted; the index error must in that case be found, and must be considered as a constant quantity to be applied to all angles measured with the same instrument.

To set the aris of the telescope parallel to the plane of the sextant.

In measuring angular distances, the line of sight, or axis of the telescope, must be parallel to the plane of the instrument, as a deviation in that respect, in measuring large angles, will occasion a considerable error. To avoid this, a telescope is made use of, in which are placed two wires, parallel to each other, and equidistant from the centre of the telescope; by means of these wires, the adjustment may be made in the following manner: Screw on the telescope, and turn the tube containing the eye-glass till the wires are parallel to the plane of the instrument; then select two objects, as the sun and moon, whose angular distance must not be less than 90°, because an error is more easily discovered when the distance is great; bring the reflected image of the sun exactly in contact with the direct image of the moon, at the wire nearest the plane of the sextant, and fix the index; then, by altering a little the position of the instrument, make the objects appear on the other wire; if the contact still remains perfect, the axis of the telescope is in its right situation; but, if the limbs of the two objects appear to separate or lap over, at the wire which is farthest from the plane of the sextant, the telescope is not parallel, and it must be rectified by turning one of the two screws of the ring into which the telescope is screwed and fixed, having previously unturned the other screw; by repeating this operation a few times, the contact will be precisely the same at both wires, and the axis of the telescope will be parallel to the plane of the instrument.†

In order to estimate the error committed in not observing the contact of the objects in the middle, between the two parallel wires of the telescope, it is necessary to know the angular distance of these wires. This may be found as follows:-Turn_round the eye-piece of the telescope, till the wires are perpendicular to the plane of the instrument; hold the instrument in a vertical position, and move the index till the direct and reflected images of the horizon appear in the same line, which will happen when the index is at 0, if the instrument be well adjusted; then move the index till the reflected image of the horizon be at one wire, and the direct image at the other; the angle moved through by the index, as shown by the divisions of the arc, will be the angular distance of the two wires. This angular distance being obtained, the observer may, by means of it, estimate, at each observation, how much the place where the contact is observed is elevated above, or depressed below, the plane passing through the eye and the middle line between the two parallel wires; the correction in Table XXXV., corresponding to this angle, is to be subtracted from the observed angular distance of the objects. Thus, if the distance between the wires be 3°, one of them will be elevated above the plane 1° 30', and the other depressed as much below it; and if, in taking an observation, the point of contact is estimated to be one third part of the distance from the middle towards either wire, the angle of elevation or depression will be one third part of 1° 30', or 30'; and if the observed distance be 100°, the correction in Table XXXV. will be 19", subtractive from the observed angle, which will therefore be 100°. 1999° 59′ 41". In general, it will not be necessary to attend to this correction.

To measure the distance between the sun and moon.

Screw on the telescope, and place the wires parallel to the plane of the instrument; then, if the index glass is half silvered and half blacked, and the sun very bright, raise the plate before the silvered part of the glass, and, with the screw L, raise the telescope

* In reading off the measure on the extra arc, you must reckon the minutes on the vernier from lett ic right, counting 19 as 1', 18' as 2', &c., or else take the difference between the minutes denoted by the vernier and 20. Thus, if the angle on the extra are appeared by the nonius to be 14′, the rea angle would be only 6'.

This adjustment may be made in a manner similar to that by which the graduation on the frame of the telescope of a circular instrument is verified, by using the adjusting tools of a circle or a ruler whose surfaces are perfectly parallel to each other. Thus, lay the sextant horizontally on a table, aud place the ruler on the limb or plane of the instrument, and, at about 12 or 15 feet distance, let a welldefined mark be placed in a range with the telescope, so as to be in the same straight line with the top of the ruler; then raise or lower the telescope, by means of the screw L, till the centre of the eye-piece of the telescope be at the same height as the top of the ruler; then, if the mark be seen in the middle Between the wires of the telescope, it is well adjusted; if not, it must be altered by means of the screws of the ring into which the telescope is screwed.