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the circumference of a circle into the same number of equal parts, which they called degrees. - The meridian of any place is a semicircle passing through that place, and terminating at the poles of the equator. The other half of this circle is called the opposite meridian. The latitude of any place is that portion of the meridian of that place which is contained between the equator and the given place; and is either south or north, according as the given place is in the northern or southern hemisphere, and therefore cannot exceed 90°. The parallel of latitude of any place is a circle passing through that place parallel to the equator. The difference of latitude between any two places is an arch of a meridian intercepted between the corresponding parallels of latitude of those places. Hence, if the places lie between the equator and the same pole, their difference of latitude is found by subtracting the less latitude from the greater; but if they are on opposite sides of the equator, the difference of latitude is equal to the sum of the latitudes of both places. The first meridian is an imaginary semicircle, passing through any remarkable place, and is therefore arbitrary. Thus, the British esteem that to be the first meridian which passes through the royal observatory at Greenwich; and the French reckon for their first meridian that which passes through the royal observatory at Paris.-Formerly many French geographers reckoned the meridian of the island of Ferro to be their first meridian; and others, that which was exactly 20 degrees to the west of the Paris observatory. The Germans, again, considered the meridian of the Peak of Teneriffe to be the first meridian. By this mode of reckoning, Europe, Asia, and Africa are in east longitude, and North and South America in west longitude. At present the first meridian of any country is generally esteemed to be that which passes through the ... principal observatory, or chief city, of that country. The longitude of any place is that portion of the equator which is contained between the first meridian and the meridian of that place; and is usually reckoned either east or west, according as the given place is on the east or west side of the first meridian; and, therefore, cannot exceed 180°. The difference of longitude between any two places is the intercepted arch of the equator between the meridians of those places, and cannot exceed 180°. * There are three different horizons, the apparent, the sensible, and the true. The apparent or visible horizon is the utmost apparent view of the sea or land; the sensible is a plane

passing through the eye of an observer, perpendicular to a plumb-line hanging freely; and the true or rational horizon is a plane passing through the centre of the earth, parallel to the sensible horizon. Altitudes observed at sea are measured from the visible horizon. At land, when an astronomical quadrant is used, or when observations are taken with a Hadley's quadrant by the method of reflection, the altitude is measured from the sensible horizon; and in either case the altitude must be reduced to the true horizon. | The zenith of any given place is the point immediately above that place, and is, therefore, the elevated pole of the horizon. The nadir is the other pole, or point diametrically opposite. A vertical is a great circle passing through the zenith and nadir ; and therefore intersecting the horizon at right angles. The altitude of any celestial body is that portion of a vertical which is contained between its centre and the true horizon. The meridian altitude is the distance of the object from the true horizon, when on the meridian of the place of observation. When the observed altitude is corrected for the depression of the horizon and the errors arising from the instrument, it is called the apparent altitude; and when reduced to the true horizon, by applying the parallax in altitude, it is called the true altitude. Altitudes are expressed in degrees and parts of a degree. The zenith distance of any object is its distance from the zenith, or the complement of its altitude. | The declination of any object is that portion of its meridian which is contained between the equinoctial and the centre of the object; and is either north or south according as the star is between the equinoctial and the north or south pole. The ecliptic is that great circle in which the annual revolution of the earth round the sun is performed. It is so named because eclipses cannot happen but when the moon is in or near that circle. The inclination of the ecliptic and equinoctial is at present about 23°28'; and by comparing ancient with modern observations, the obliquity of the ecliptic is found to be diminishing—which diminution, in the present century, is about half a second yearly. The ecliptic, like all other great circles of the sphere, is divided into 360°; and is further divided into twelve equal parts, called signs: each sign, therefore, contains 30°. The names and characters of these signs are as follows:

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Since the ecliptic and equinoctial are great circles, they therefore bisect each other in two points, which are called the equinoctial points. The sun is in one of these points in March, and in the other in September; hence, the first is called the vernal, and the other the autumnal equinox—and that sign which begins at the vernal equinox is called Aries. Those points of the ecliptic which are equidistant from the equinoctial points are called the solstitial points; the first the summer, and the second the winter solstice. That great circle which passes through the equinoctial points and the poles of the earth is called the equinoctial colure; and the great circle which passes through the solstitial points and the poles of the earth is called the solstitial colure. o - When the sun enters Aries it is in the equinoctial, and therefore has no declination. From thence it moves forward in the ecliptic, according to the order of the signs, and advances towards the north pole, by a kind of retarded motion, till it enters Cancer, and is then most distant from the equinoctial; and moving forward in the ecliptic, the sun apparently recedes from the north pole with an accelerated motion till it enters Libra, and, being again in the equinoctial, has no declination; the sun, moving through the signs Libra, Scorpio, and Sagittarius, enters Capricorn; and then its south declination is greatest, and is, therefore most distant from the north pole; and moving forward through the signs Capricorn, Aquarius, and Pisces, again enters Aries: hence a period of the seasons is completed, and this period is called a solar year. The signs Aries, Taurus, Gemini, Cancer, Leo, and Virgo are called northern signs, because they are contained in that part of the ecliptic which is between the equinoctial and north pole; and, therefore, while the sun is in these signs, its declination is north : the other six signs are called southern signs. The signs in the first and fourth quarters of the ecliptic are called ascending signs, because while the sun is in these signs it approaches the north pole; and, therefore, in the northern, temperate, and frigid zones, the sun's meridian altitude daily increases; or, which is the same, the sun ascends to a greater height above the horizon every day. The signs in the second and third quarters of the ecliptic are called descending signs. The tropics are circles parallel to the equinoctial, whose distance therefrom is equal to the obliquity of the ecliptic,

The northern tropic touches the ecliptic at the beginning of Cancer, and is therefore called the tropic of Cancer; and the southern tropic touches the ecliptic at the beginning of Capricorn, and is hence called the tropic of Capricorn. Circles about the poles of the equinoctial, and passing through the poles of the ecliptic, are called polar circles; the distance, therefore, of each polar circle from its respective pole is equal to the inclination of the ecliptic and equinoctial. That circle which circumscribes the north pole is called the arctic or north polar circle; and that towards the south pole, the antarctic or south polar circle. That semicircle which passes through a star, or any given point of the heavens, and the poles of the ecliptic, is called a circle of latitude. The reduced place of a star is that point of the ecliptic which is intersected by the circle of latitude passing through that star. The latitude of a star is that portion of the circle of latitude contained between the star and its reduced place; and is either north or south, according as the star is between the ecliptic and the north or south pole thereof. w The longitude of a star is that portion of the ecliptic contained between the vernal equinox and the reduced place of the star.

SECTION II. Description of the instruments requisite in astronomical observations.

THE QUADRANT.

It is generally allowed that we are indebted to John Hadley, Esq. for the invention, or at least for the first public account, of that admirable instrument commonly called Hadley's quadrant, who in the year 1731 first communicated its principles to the Royal Society, which were by them published soon after in their Philosophical Transactions; before this period the cross-staff and Davis’s quadrant were the only instruments used for measuring altitudes at sea, both very imperfect, and liable to considerable error in rough weather; the superior excellence, however, of Hadley's quadrant soon obtained its general use among seamen, and the many improvements this instrument has received from ingenious men at various times have rendered it so correct, that it is now applied, with the greatest success, to the important purposes of ascertaining both the latitude and longitude at sea or land. Figure 2, Frontispiece, represents a quadrant of reflection, the principal parts of which are, the octant or frame ABC (which is generally made of ebony, or other hard wood, and consists of an arch firmly attached to two radii or bars, which are strengthened and bound by the two braces in order to prevent it from warping), the graduated arch BC, the index D, the nonius or vernier scale E, the index glass F, the horizon glasses G and H, the dark glasses or screens I, and the sight vanes K and L. The arch, or limb BC, although only the eighth part of a circle, is, on account of the double reflection, divided into 90 degrees, numbered 0, 10, 20, 30, &c., from the right towards the left: these are subdivided into three parts, containing each 20 minutes, which are again subdivided into single minutes, by means of a scale at the end of the index. The arch extending from 0 towards the right-hand is called the arch of excess. The index D is a flat brass bar, that turns on the centre of the instrument; at the lower end of the index there is an oblong opening; to one side of this opening a nonius scale is fixed, to subdivide the divisions of the arch ; at the bottom or end of the index there is a piece of brass which bends under the arch, carrying a spring to make the nonius scale lie close to the divisions; it is also furnished with a screw to fix the index in any desired position. Some instruments have an adjusting or tangent-screw, fitted to the index, that it may be moved more slowly, and with greater regularity and accuracy than by the hand; it is proper, however, to observe, that the index must be previously fixed near its right position by the above-mentioned screw, before the adjusting screw is put in motion. The nonius is a scale fixed to the end of the index, for the purpose, as before observed, of dividing the subdivisions on the arch into minutes; it sometimes contains a space of 7 degrees, or 21 subdivisions of the limb, and is divided into 20 equal parts; hence each division on the nonius will be one-twentieth part greater, that is, one minute longer, than the divisions on the arch; consequently, if the first division of the nonius, marked 0, be set precisely opposite to any degree, the relative position of the nonius and the arch must be altered one minute, before the next division on the nonius will coincide

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