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(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 0h. 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 exbibit 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

*Tn, the earth; ypapav, 10 describe or represent; ovpavos, the heaven.

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.

(112.) It remains to illustrate these descriptions by reference to a figure. Let C be the centre of the earth, N C S its axis; then are N

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and S its poles; E Q its equator; A B the parallel of latitude of the station A on its surface; A P 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. NA ES will be his meridian; N GS that of some fixed station, as Greenwich; and G E, or the spherical angle G N E, his longitude, and E A his latitude. Moreover, if n s be a plane touching the surface in A, this will

be bis 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 H A 0, a great circle of the sphere, whose poles are Z N, be his celestial horizon; P p the elevated and depressed POLES of the heavens; H P the altitude of the pole, and H P ZE O his meridian ; E T Q, a great circle perpendicular to P p, will be the equinoctial; and if r represent the equinox, r T will be the right ascension, TS the declination, and PS the polar distance of any star or object S, referred to the equinoctial by the hour circle P STP; and B S D will be the diurnal circle it will appear to describe

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about the pole. Again, if we refer it to the horizon by the vertical circle ZSM, O M will be its azimuth, M S its altitude, and Z S its zenith distance. H and O are the north and south, e w the east and west points of his horizon, or of the heavens. Moreover, if H h, O o, be small circles, or parallels of declination, touching the horizon in its north and south points, H h will be the circle of perpetual apparition, between which and the elevated pole the stars never set; 0 o that of perpetual occultation, between which and the depressed pole they never rise. In all the zone of the heavens between H h and O o, 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 repre. sented by A D a. 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, to conclude, so far as they can be thence concluded, their real geometrical relations to each other and to the spectator. It agrees with ordinary perspective when only a small visual area is contemplated, because the concave ground of the celestial sphere, for a small extent, may be regarded as a plane surface, on which objects are seen projected or depicted as in common perspective. But when large amplitudes of the visual area are considered, or when the whole contents of space are regarded as projected on the whole interior surface of the sphere, it becomes necessary to use a different phraseology, and to resort to a different form of conception. In common perspective there is a single “ point of sight,” or “ centre of the picture,” the visual line from the eye to which is perpendicular to the “plane of the picture," and all straight lines are represented by straight lines. In celestial perspective, every point to which the view is for the moment directed, is equally entitled to be considered as the "centre of the picture,” every portion of the surface of the sphere being similarly related to the eye. Moreover, every straight line (supposed to be indefinitely prolonged) is projected into a semicircle of the sphere, that, namely, in which a plane passing through the line and the eye cuts its surface. And every system of parallel straight lines, in whatever direction, is projected into a system of semicircles of the sphere, meeting in two common apexes, or vanishing points, diametrically opposite to each other, one of which corresponds to the vanishing point of parallels in ordinary perspective; the other, in such perspective has no existence. In other words, every point in the sphere to which the eye is directed may be regarded as one of the vanishing points, or one apex of a system of straight lines, parallel to that radius of the sphere which passes through it, or to the direction of the line of sight, seen in perspective from the earth, and the points diametrically opposite, or that from which he is looking, as the other. And any great circle of the sphere may similarly be regarded as the vanishing circle of a system of planes, parallel to its own.

(115.) A familiar illustration of this is often to be had by attending to the lines of light seen in the air, when the sun's rays are darted through apertures in clouds, the sun itself being at the time obscured behind them. These lines which, marking the course of rays emanating from a point almost infinitely distant, are to be considered as parallel straight lines, are thrown into great circles of the sphere, having two apexes or points of common intersection one in the place where the sun itself (if not obscured) would be seen. The other diametrically opposite. The first only is most commonly suggested when the spectator's view is towards the sun. But in mountainous countries, the phenomenon of sunbeams converging towards a point diametrically opposite to the sun, and as much depressed below the horizon as the sun is elevated above it, is not unfrequently noticed, the back of the spectator being turned to the sun's place. Occasionally, but much more rarely, the whole course of such a system of sunbeams, stretching in semicircles across the hemisphere from horizon to horizon (the sun being near setting), may be seen.' Thus again, the streamers of the Aurora Borealis, which are doubtless electrical rays, parallel, or nearly parallel to each other, and to the dipping needle, usually appear to diverge from the point towards which the needle, freely suspended, would dip northwards (i. e. about 70° below the horizon and 23° west of north from London), and in their upward progress pursue the course of great circles till they again converge (in appearance) towards the point diametrically opposite (i. e. 70° above the horizon, and 23° to the eastward of south), forming a sort of canopy over-head, having that point for its centre. So also in the phenomenon of shooting stars, the lines of direction which they appear to take on certain remarkable occasions of periodical recurrence, are observed, if prolonged backwards, apparently to meet nearly in one point of the sphere; a certain indication of a general near approach to parallelism in the real directions of their motions on those occasions. On which subject more hereafter.

(116.) In relation to this idea of celestial perspective, we may conceive the north and south poles of the sphere as the two vanishing points of a system of lines parallel to the axis of the earth; and the zenith and nadir of those of a system of perpendiculars to its surface at the place of observation, &c. It will be shown that the direction of a plumb-line, at every place is perpendicular to the surface of still water at that place

* It is in such cases only that we conceive them as circles, the ordinary conventions of plane perspective becoming untenable. The author had the good fortune to witness on one occasion the phenomenon described in the text under circumstances of more than usual grandeur. Approaching Lyons from the south on Sept. 30, 1826, about 54 h. P. 2., the sun was seen nearly setting behind broken masses of stormy cloud, from whose apertures streamed forth beams of rose-coloured light, traceable all across the hemisphere almost to their opposite point of convergence behind the snowy précipices of Mont Blanc, conspicuously visible at nearly 100 miles to the eastward. The im. pression produced was that of another but feebler sun about to rise from behind the mountain, and darting forth precursory beams to meet those of the real one opposite.

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