then take it on the extra arch, as it is called; that is, bring the lower limb to coincide with the upper, and note the angle, half the difference of these two angles will be the true correction of the index error.

EXAMPLE.

Suppose the sun's diameter measures 36 on the arch, and 28 on the extra arch. The difference is 8', half which is the error to be subtracted, because the diameter measures more on the arch, or gives the sun's diameter too much; but had the extra arch given the greater angle, the error would have been additive.

To take the Altitude of the Moon.

The moon's altitude may be either taken by the fore or back observation, exactly in the same manner as the sun's altitude, only here you must bring the edge of the moon into contact with the horizon, which is round and well defined, whether that be the upper or under edge: the corrections to be applied to the observed altitude are as follow:

The index error, as before directed, if any; the dip to be sub. tracted in the fore observation, and to be added in the back observation; the semi-diameter to be found in the Nautical Ephemeris for every noon and midnight, at Greenwich, if very great aceu racy is required, this semi-diameter must be corrected for the intermediate time: which being added to, or subtracted from, the observed altitude, will give the apparent altitude of the centre; and the moon's horizontal parallax for every noon and midnight, at Greenwich, is to be found in the Nautical Ephemeris. This must be corrected for the intermediate time; then take the proportional logarithm of the moon's horizontal parallax out of the Nautical Almanack, increase its index by 10, and subtract the log. co-sine of the moon's apparent altitude from the sum; the remainder will be the proportional logarithm of her parallax in altitude; from which take the moon's refraction (Table VII.) and the remainder will be the correction of the moon's altitude, which being added to her apparent altitude, will give the true altitude of her centre.

To take the Altitude of a Star by the Fore Observation.

Set the index at D, and holding the plane of the quadrant vertical, direct the sight to the star, and at the same time look for the reflected image of the star in the silvered part of the horizon glass; move the index a little, which will separate the reflected image from the direct image; the former will be easily distinguished from the latter by its motion, when you stir the index; continue to advance the index, and at the same time follow the reflected image of the star with your eye, directing your sight lower and lower, and changing the position of the quadrant or sextant, as the

image of the star descends, till you have brought it down to the horizon: the index will then show the observed altitude of the star. The corrections to be applied to the observed altitude of the star are the index error, the dip (these two give the apparent altitude); the refraction gives the true altitude; the fixed stars have neither semi-diameter nor parallax worthy notice.

In taking the altitude of a star, or the moon, by night, always get as near the water as possible; in moderate weather a grating may be slung over the ship's side, and an observer sit upon it to take the altitudes; the same may be done to take the altitude of the sun in a hazy horizon; for the nearer the eye is to the surface of the water, the nearer the true horizon will be to the eye. Advice to Seamen in the Choice of their Quadrants and Sextants.

The joints of the frame must be close, without the least opening or looseness, and the ivory on the arch and nonius inlaid and fixed, so as not to rise at the ends, nor above the plane of the instrument; all the divisions on the arch and nonius must be exceeding fine and straight, so that when the index or nonius is set to any division on the arch, the divisions on the line that coincide may appear distinct; for only the first and last line on the nonius will coincide with the other lines upon the arch, if the quadrant is well divided; likewise try in different parts of the arch, if the nonius, or index plate, cuts regularly in order with those on the arch: if they do not, the divisions are bad, and the quadrant ought to be rejected.

Again, look into the great speculum or index glass slant-ways, holding it about ten or twelve inches from the eye, and observe the image of some distant object; if the image appears clear and distinct in every part of the glass, the speculum is good; but if it appears notched, or drawn with small lines, the glass is veiny, and must be rejected; if more images than one of the same object are seen, it shows that the two surfaces are not ground parallel; the other speculum may be examined in the same manner.

Observe the sun, or a candle, through the dark glasses severally, holding the glass about eight or ten inches from the eye; if they are veiny, the object will appear notched at the edges, but if clear and well defined, the glasses are good.

Quadrants, like watches, may appear well to the eye, and yet be good for little; it is therefore much better to give two guineas and a half, or three guineas, for a good one, that will last a man for life, than purchase those wretched instruments, made up at a low price, which cannot be depended on.

The surprising improvements made in Navigation since the year 1767, when the first Nautical Almanack was published by Dr. Maskelyne, the present Astronomer Royal, are beyond the most sanguine expectations; and though several nations have contributed towards this important end, the English have (by the encouragement held out by parliament, and the great improve

ments made in nautical instruments and calculations) surpassed them all; so that by the help of the improved sextant, the Nautical Almanack, and the Tables contained in this book, a skilful and expert observer can determine the longitude to a degree of accuracy that people unacquainted with the operation would scarcely think possible.

Hadley's sextant is constructed on the same principles as the quadrant; but as it is used to measure the angular distance between the sun and moon, or the moon and a star, in order to determine the longitude, the arch is extended to 120°, for the purpose of measuring their distance when greater than 90°; it is also provided with some appendages not generally annexed to a quadrant, in order to take the observation with greater accuracy.

On the adjoining plate is represented a sextant, the frame of which is generally made of brass; the arch BB is divided into 120°, each degree into three parts, of course equal to 20 minutes, which are again subdivided by the nonius into every half minute, or 30 seconds; every second division, or minute, on the nonius, is cut longer than the intermediate ones; the nonius is numbered at every fifth of these longer divisions, from the right towards the left, with 5, 10, 15, and 20, the first division towards the right hand being to be considered as the index division.

This is the general way of graduating sextants; but for obtaining greater accuracy, some are divided as follow: the arch contains 120°; each degree is subdivided into 4, of course equal to 15', which are again subdivided by the nonius into 15; every fourth division or minute of the nonius, is longer than the intermediate ones; the nonius is numbered at every fifth of these long divisions, from the right towards the left, with 5, 10, 15; the first division towards the right hand is to be considered as the index division. The present mode of dividing the nonius of the sextant is thus: (beginning from the right hand towards the left) by taking fifteen divisions on the nonius, equal to fourteen on the arch, consequently one division on the arch will exceed one on the nonius by, that is, by of a minute, where the degrees on the arch are subdivided into, equal to 15 minutes

The nonius, till very lately, was divided as the quadrant.

In order to observe with accuracy the contact of the limbs of any two objects, an adjusting-screw, L, is added to the index, by which it may be moved with greater regularity than it can by the hand; but this screw does not act until the index is fixed by the finger-screw M. Care should be taken not to force the adjustingscrew when it arrives at either extremity of its adjustment. When the index is to be moved any considerable quantity, the screw M, at the back of the sextant, must be loosened; but when the index is brought nearly to the division required, this back screw should be tightened, and the index moved gradually by the adjusting

screw.

N. B. Many quadrants have an adjusting-screw.

In many sextants the lower part of the index glass, or that nearest the frame, is silvered as usual, and the back surface of the upper part painted black; also a screen is fixed at the base of the index glass, turning on its axis, and may be placed over the silver part when the sun's rays are strong, in which case the image is reflected from the polished surface of the upper part, and the error, which might probably arise from the planes of the glasses not being parallel, is thereby avoided.

There are several coloured glasses at H, each of which is set in a different frame, turning on a centre; they are used to screen the eye from the brightness of the solar rays, and the glare of the moon; and may be used separately or together, as occasion requires.

There are other such glasses placed behind the horizon glass at F, to weaken the rays of the sun or moon when they are viewed directly through the horizon glass; the paler glass is sometimes used in observing altitudes at sea, to take off the strong glare of the horizon.

The sextant is furnished with a plain tube, without any glasses; and to render the objects still more distinct, it has two telescopes, one representing the objects erect, or in their natural position, the other showing them inverted; it has a large field of view, and other advantages; a little use will soon accustom the observer to the inverted position, and the instrument will be as readily managed by it as the plain tube alone. By a telescope the contact of the images is more perfectly distinguished; and by the place of the images in the field of the telescope it is easy to perceive whether the sextant is held in the proper plane for observing. By sliding the tube that contains the eye-glasses in the inside of the other tube, the object is suited to different eyes, and made to appear perfectly distinct and well defined.

The telescopes are to be screwed into a circular ring, at K; this ring rests on two points against an exterior ring, and is held thereto by two screws; by turning one and tightening the other, the axis of the telescope may be set parallel to the plane of the sextant. The exterior ring is fixed on a brass stem that slides in a socket, and by means of the screw S, at the back of the sextant, it may be raised or lowered so as to move the centre of the telescope to point to that part of the horizon glass which shall be judged the most fit for observation.

A circular head, containing a plate, in which there are three coloured glasses, and a fourth that is open, sometimes accompanies this 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 moveable by the finger, so that the open ring, or any of the coloured glasses, may be brought between the eye-glasses of the telescope and the

eve.

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 to set the index and horizonglasses perpendicular to the plane of the instrument, and their planes parallel to each other; by the same method as the quadrant, only screwing on the plain tube or telescope; also to set the axis of the telescope parallel to the plane of the instrument; each of these particulars must be examined before an observation is taken, and the adjustments, if requisite, be made.

For correcting the index error, see the rules for adjusting Hadley's Quadrant.

To set the Axis of the Telescope parallel to the Plane of the Sextant.

In measuring angular distances, the line of sight, or axis of the telescope, should be parallel to the plane of the instrument, as a deviation in that respect will occasion a considerable error in the observation; and this is most sensible in large angles. To avoid which, an inverted telescope is used, in whose field there are placed two wires parallel to each other, and equidistant from the centre; to which are sometimes added two others, at right angles to these, but parallel to each other. By means of these wires the adjustment may be made thus: screw on the telescope, and turn the tube containing the eye-glass, till the wires are parallel to the plane of the instrument; then take two objects, as the sun and moon, or the moon and a star, whose angular distance must not be less than 90°, because the error is more easily discovered when the distance is great; bring them exactly into contact on the wire which is nearest the plane of the instrument, and fix the index ; then, by altering a little the position of the sextant, bring them to appear on the wire farthest from the plane of the instrument; if they remain still in contact, the axis of the telescope is parallel to the plane of the sextant; but if the limbs of the two objects appear to separate at the further wire, it shows that the object-end of the telescope inclines towards the plane of the sextant; this must be rectified by tightening the screw nearest the sextant, which is attached to the ring that holds the telescope, having previously slackened the crew farthest from it. If the images over-top each other when brought to the wire farthest from the sextant, the object-end of the telescope is inclined from the plane of the sextant, and must be rectified by slackening the screw nearest the sextant, 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 observe the angular Distance between the Sun and Moon.

Screw on the inverted telescope, placing the wires parallel te the plane of the instrument; then turn down the screens, according to the brightness of the sun; place the index at O on the arch and if the sun's image be very bright, turn up the screen befor