the horizon-glass, and with the screw S, raise the telescope to the transparent part of the horizon-glass. Having done this, hold the sextant so that its plane may pass through the two objects: if the sun be to the right hand of the moon, the sextant is to be held with its face upwards; but if it be 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 in 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 adjustingscrew; at the same time move the sextant slowly, making the axis of the telescope the centre of motion, by which means the objects will pass each other, and the contact be more accurately discriminated. The index will show the observed distance of the sun and moon's nearest limbs, which you will read off with a magnifying glass.

Second Method.

It will perhaps be more easy for those who are not accustomed to make observations of this kind, to find the distance nearly, and setting the index forward to it, to look directly towards the moon, holding the instrument as before; the sun will then appear nearly in contact with it, and is to be made perfect by the method abovementioned. In the Nautical Ephemeris, the distance of the sun and moon is set down for every three hours of time at Greenwich, on such days as the moon is not more than 120°, nor less than 40o distant from the sun, and may be found for any intermediate time by taking proportional parts; from these distances you may compute roughly their distance at the time of observation, thus: Turn the ship's longitude into time by Tab. XVI. and add it to the time of observation, if the longitude be west, but subtract it if the longitude be east, the sum or difference will give the time at Greenwich; then, by the Ephemeris, find the distance nearly at that time, from which subtract 30 minutes for the sun and moon's semidiameters, and the remainder will give the distance of their nearest limbs at the time of observation.

If a number of observations are to be taken, the following method will not be found unacceptable: Having brought the objects into contact, as before directed, and noted down their apparent angular distance, 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 necessary, using the mean of all the observations to determine the longitude. This method will be found easy and accurate.

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

To observe the Distance between the Moon and a Star. Turn down the lightest screen before the index glass, and direct the telescope to the star, holding the sextant in its proper position,

as before directed; then move the index forward, till the reflected image of the moon is seen in the telescope; by moving the instrument slowly up and down, the moon will appear to rise and fall by the star. The round and well defined limb of the moon, whether it be nearest or farthest 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 vision, the instrument is held with its face upwards; but when the object to be seen by reflection is to the left hand of that seen directly, the instrument is held with its face downwards. Having brought the objects into contact, the nonius will show the observed angular distance.

If the distance between the moon and one of the stars set down in the Ephemeris for finding the longitude, is to be observed, their distance may be roughly calculated as before directed, to which set the index; then look through the telescope, and direct the sight to the star, which is generally a bright one, and lies in a line nearly perpendicular to the horns of the moon, either to the eastward or westward, as denoted in the Ephemeris; then, holding the instrument in the plane of the two objects, give it a slow 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 correspond in distance to it.

After the distance is observed between the sun and moon, by a sextant or quadrant, there still remains to be made some corrections to obtain the true distance; the corrections are those for parallax, refraction, and semi-diameter.

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

PARALLAX.

The parallax of the sun 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 surface of the earth. The parallax of the heavenly bodies is greatest when in the horizon; hence called the orizontal parallax. That of the moon is set down in the Nautical Almanack for every noon and midnight, but may be found for any intermediate time by taking proportional parts. The sun's mean parallax being only 8". 6, is seldom attended to in nautical calculation, except when his altitude is taken to determine the true ime, or the angular distance to determine the longitude. The tars, on account of their great distance from the earth, have no ensible parallax; the parallax of the sun and moon causing them o appear lower than they really are, it is evident this correction must be added to the apparent altitude of the sun and moon, in order to obtain their true altitude. This will be better illustrated by the plate facing page 146. Let C represent the centre of th

U

earth; a, o, e, part of the moon's orbit; b, d, g, part of the sun's orbit; 1, k, part of the starry 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 less, according to the distance 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 same object, it is evident, when it is in the horizon, the parallax is greatest, and that it diminishes as the object.approaches the zenith, where it vanishes. Thus the horizontal parallax of e and g is greater than the parallax in altitude of o and d; but the objects a and b, as seen from m, the surface, or c, the centre, appear in the same place, 1, or the zenith.

Having the earth's semi-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 semi-diameter in miles :: so is radius: to the distance.

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

REFRACTION.

From various experiments it hath been found that the rays of light passing through the atmosphere, are bent out of their straight course 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 so 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 observed, must (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 distance, in order to obtain the true altitude.

Now, since parallax makes all objects appear lower than they really are, and refraction makes them appear higher than they arc, it is evident that the true altitude of an object cannot be obtained without correcting the observed altitude for the difference of these two sumns.

. SEMI-DIAMETER.

The moon's semi-diameter is smallest when in the horizon, and increasing as she approaches the zenith, where it is greatest; as she is then nearer the spectator by the earth's semi-diameter. This augmentation is set down in Table X. Another reason of the apparent augmentation and diminution of the moon's semi-diameter is, that she moves round the earth in an orbit not circular, but