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 for the adjustment of the index glass of a quadrant, page 129.

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.

Having 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.

After 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 will be additive when the diameter measured to the right of 0 exceeds that measured

the 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° - 19"=99° 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 left to 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 arc appeared by the nonius to be 14, the real 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, and 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.

to the transparent part of the horizon glass; turn down one or more of the dark glasses, according to the brightness of the sun; then hold the sextant so that its plane may pass through the sun and moon; if the sun be to the right hand of the moon, the sextant is to be held with its face upwards; if to the left hand, the face is to be held downwards; with the instrument in this position, look directly at the moon through the telescope, and move the index forward till the sun's image is brought nearly into contact with the moon's nearest limb; then fix the index by the screw under the sextant, and make the contact perfect by means of the tangent screw; at the same time, move the sextant slowly, making the axis of the telescope the centre of motion; by this means the objects will pass each other, and the contact be more accurately made; observing that the point of contact of the limbs must always be observed in the middle between the parallel wires. The observation being thus made, the index will point out the distance of the nearest limbs of the sun and moon.

To measure the distance between the moon and a star.

Turn down one of the screens, if the moon is bright, and direct the plane of the instrument through both objects, with its face upwards, if the moon is to the right of the star; but if to the left, the face is to be held downwards; look at the star through the telescope and transparent part of the horizon glass, and move the index till the moon's image appears nearly in contact with the star; fasten the index, move the sextant round the axis of the telescope, as in measuring the distance of the sun and moon, and turn the tangent screw, till the coincidence of the star, and the enlightened or round limb of the moon is perfect; observing that the point of contact of the limb of the moon and star must always be in the middle between the parallel wires. The observation being thus made, the index will point out the distance of the enlightened limb of the moon from the star, whether it be the farthest or nearest limb.

Verification of the parallelism of the index glass.

This verification is to be made ashore, by observing the angular distance of two well-defined objects, whose distance exceeds 90° or 100° (having previously well adjusted the instrument), then taking out the central mirror, and turning it, so that the edge which was formerly uppermost may now be nearest the plane of the instrument; rectify its position, and again measure the distance of the two objects; half the difference between these two distances will be the error of the observed angle arising from the defect of parallelism of the central mirror. If the first distance exceeds the second, the error is subtractive, otherwise additive, the mirror being in its first position; but the contrary when in its second position. Thus, if the first distance was 119° 59′ 21′′, and the second 120° 0′ 39", the error would be 39, additive when the mirror was in its first position, subtractive for the second. The error for any other angle may be found by means of col. 2d Table XXXIV., when the inclination of the plane of the horizon glass to the axis of the telescope is 80°, by saying, As the tabular correction corresponding to 120° (4' 5") is to the error of the glass 39", so is the tabular error for any other angle, as 85° (= 1′ 15′′), to the corresponding error of the glass 12". In this manner a table of errors may be made for all angles.*

The angle between the plane of the horizon glass and axis of the telescope produced being constant in all observations and adjustments of the sextant, no error can arise from the want of parallelism of its surfaces.

Verification of the parallelism of the surfaces of the colored glasses.

Turn down the glass at D which is to be examined, and another at E to defend the eye from the sun; direct the telescope to the sun, and move the index till its direct and reflected images coincide; then turn the dark glass at D so that the surface which was farthest from the horizon glass may now be nearest to it, and if the contact of the same two limbs be complete, the surfaces of this glass are parallel; but if they lap over or separate, the index must be moved to bring them again in contact; then half the arc passed over by the index will be the error arising from the want of parallelism of the glass at D. If a defect of this kind is found in any one of these colored glasses, it is best to avoid the use of it altogether.

* The method of calculating the above tabular numbers, when the angle of inclination of the telescope