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always reckoned positive, considering the eastward reckoning as negative.

(104.) DEF. 21. The altitude of a heavenly body is its apparent angular elevation above the horizon. It is the complement to 90°, therefore, of its zenith distance. The altitude and azimuth of an object being known, its place in the visible heavens is determined.

(105.) DEF. 22. The declination of a heavenly body is its angular distance from the equinoctial or celestial equator, or the complement to 90° of its angular distance from the nearest pole, which latter distance is called its Polar distance. Declinations are reckoned plus or minus, according as the object is situated in the northern or southern celestial hemisphere. Polar distances are always reckoned from the North Pole, from 0° up to 180°, by which all doubt or ambiguity of expression with respect to sign is avoided.

(106.) DEF. 23. Hour circles of the sphere, or circles of declination, are great circles passing through the poles, and of course perpendicular to the equinoctial. The hour circle, passing through any particular heavenly body, serves to refer it to a point in the equinoctial, as a vertical circle does to a point in the horizon.

(107.) DEF. 24. The hour angle of a heavenly body is the angle at the pole included between the hour circle passing through the body, and the celestial meridian of the place of observation. We shall always reckon it positively from the upper culmination (art. 125.) westwards, or in conformity with the apparent diurnal motion, completely round the circle from 0° to 360°. Hour angles, generally, are angles included at the pole between different hour circles.

(108.) DEF. 25. The right ascension of a heavenly body is the arc of the equinoctial included between a certain point in that circle called the Vernal Equinox, and the point in the same circle to which it is referred by the circle of declination passing through it. Or it is the angle included between two hour circles, one of which passes through the vernal equinox (and is called the equinoctial colure), the other through the body. How the place of this initial point on the equinoctial is determined, will be explained further on.

(109.) The right ascensions of celestial objects are always reckoned eastwards from the equinox, and are estimated either in degrees, minutes, and seconds, as in the case of terrestrial longitudes, from 0° to 360°, which completes the circle ; or, in time, in hours, minutes, and seconds, from Oh. to 24h. The apparent diurnal motion of the heavens being contrary to the real motion of the earth, this is in conformity with the westward reckoning of longitudes. (Art. 91.)

(110.) Sidereal time is reckoned by the diurnal motion of the stars, or rather of that point in the equinoctial from which right ascensions are reckoned. This point may be considered as a star, though no star is, in fact, there; and, moreover, the point itself is liable to a certain slow variation,

-so slow however, as not to affect, perceptibly, the interval, of any two of its successive returns to the meridian. This interval is called a sidereal day, and is divided into 24 sidereal hours, and these again into minutes and seconds. A clock which marks sidereal time, i. e. which goes at such a rate as always to show Oh. Om. Os. when the equinox comes on the meridian, is called a sidereal clock, and is an indispensable piece of furniture in every observatory. Hence the hour angle of an object reduced to time at the rate of 15° per hour, expresses the interval of sidereal time by which (if its reckoning be positive) it has past the meridian ; or, if negative, the time it wants of arriving at the meridian of the place of observation. So also the right ascension of an object, if converted into time at the same rate (since 360° being described uniformly in 24 hours, 15° must be so described in 1 hour), will express the interval of sidereal time which elapses from the passage of the vernal equinox across the meridian to that of the object next subsequent.

(111.) As a globe or maps may be made of the whole or particular regions of the surface of the earth, so also a globe, or general map of the heavens, as well as charts of particular parts, may be constructed, and the stars laid down in their proper situations relative to each other, and to the poles of the heavens and the celestial equator. Such a representation, once made, will exhibit a true appearance of the stars as they present themselves in succession to every spectator on the surface, or as they may be conceived to be seen at once by one at the centre of the globe. It is, therefore, independent of all geographical localities. There will occur in such a representation neither zenith, nadir, nor horizon — neither east nor west points; and although great circles may be drawn on it from pole to pole, corresponding to terrestrial meridians, they can no longer, in this point of view, be regarded as the celestial meridians of fixed points on the earth's surface, since, in the course of one diurnal revolution, every point in it passes beneath each of them. It is on account of this change of conception, and with a view to establish a complete distinction between the two branches of Geography and Uranography*, that astronomers have adopted different terms, (viz. declination and right ascension) to represent those arcs in the heavens which correspond to latitudes and longitudes on the earth. It is for this reason that they term the equator of the heavens the equinoctial; that what are meridians on the earth are called hour circles in the heavens, and the angles they include between them at the poles are called hour angles. All this is convenient and intelligible ; and had they been content with this nomenclature, no confusion could ever have arisen. Unluckily, the early astronomers have employed also the words latitude and longitude in their uranography, in speaking of arcs of circles not corresponding to those meant by the same words on the earth, but having reference to the motion of the sun and planets among the stars. It is now too late to remedy this confusion, which is ingrafted into every existing work on astronomy: we can only regret, and warn the reader of it, that he may be on his guard when, at a more advanced period of our work, we shall have occasion to define and use the terms in their celestial sense, at the same time urgently recommending to future writers the adoption of others in their places.

I'n, the earth ; ypapeuv, to describe or represent ; ovpavos, the heaven.

(112.) It remains to illustrate these descriptions by reference to a figure. Let C be the centre of the earth, NCS

its axis; then are N and S its poles ; E Q its equator; AB the parallel of latitude of the station A on its surface; AP parallel to SC N, the direction in which an observer at A will see the elevated pole of the heavens; and A Z, the prolongation of the terrestrial radius C A, that of his zenith. NAES will be his meridian ; NGS that of some fixed station, as Greenwich; and G E, or the spherical angle G NE, his longitude, and E A his latitude. Moreover, if ns be a plane touching the surface in A, this will be his sensible horizon; n As marked on that plane by its intersection with his meridian will be his meridian line, and n and s the north and south points of his horizon.

(113.) Again, neglecting the size of the earth, or conceiving him stationed at its centre, and referring every thing to his rational horizon; let the annexed figure represent the sphere of the heavens; C the spectator; Z his zenith; and N his nadir: then will HAO a great circle of the sphere, whose poles are Z N, be his celestial horizon; Pp the elevated and depressed POLES of the heavens; HP the altitude of the pole, and HP ZE O his meridian; E TQ, a great circle perpendicular to P p, will be the equinoctial; and if r represent the equinox, T will be the right ascension, TS the declination,

and P S the polar distance of any star or object S, referred to the equinoctial by the hour circle PSTp; and BSD

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will be the diurnal circle it will appear to describe about the pole. Again, if we refer it to the horizon by the vertical circle Z SM, OM will be its azimuth, M S its altitude, and ZS its zenith distance. H and O are the north and south, ew the east and west points of his horizon, or of the heavens. Moreover, if H h, Oo, be small circles, or parallels of declination, touching the horizon in its north and south points, Hh will be the circle of perpetual apparition, between which and the elevated pole the stars never set ; Oo that of per. petual occultation, between which and the depressed pole they never rise. In all the zone of the heavens between H h and Oo, they rise and set; any one of them, as S, remaining above the horizon in that part of its diurnal circle represented by a B A, and below it throughout all the part represented by A Da. It will exercise the reader to construct this figure for several different elevations of the pole, and for a variety of positions of the star S in each.

(114.) Celestial perspective is that branch of the general science of perspective which teaches us to conclude, from a knowledge of the real situation and forms of objects, lines, angles, motions, &c. with respect to the spectator, their apparent aspects, as seen by him projected on the imaginary concave of the heavens; and, vice versâ, from the apparent configurations and movements of objects so seen projected,

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