sidereal clock, and is an indispensable piece of furniture earth, NCS its axis; then are N and S its poles; EQ its equator; A B the parallel of latitude of the station A on its surface; AP parallel to SCN, the direction in which an observer at A will see the elevated pole of the heavens; and AZ, 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 GNE, 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. (94.) 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 HPZEO his meridian; ETQ, a great circle perpendicular to Pp, will be the equinoctial; and if 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 PSTp; and BSD 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 ZSA, HA will be its azimuth, AS its altitude, and Z S its zenith distance. H and O are the north and south, and e w the east and west points of his horizon, or of the heavens. Moreover, if Hh, Oo, 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; Oo that of perpetual occultation, between which and the depressed pole they never rise. In all the zone of the heavens between Hh 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 AD 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. The following consequences result from these definitions, and are propositions which the reader will readily bear in mind: (95.) The altitude of the elevated pole is equal to the latitude of the spectator's geographical station. For, comparing the figures of arts. 93. and 94., it appears that the angle PA Z, between the pole and zenith, in the one figure, which is the co-altitude (complement to 90° of the altitude) of the pole, is equal to the angle NC A in the other; CN and AP being parallels whose vanishing point is the pole. Now, NCA is the co.. latitude of the plane A. (96.) The same stars, in their diurnal revolution, come to the meridian, successively, of every place on the globe once in twenty-four sidereal hours. And, since the diurnal rotation is uniform, the interval, in sidereal time, which elapses between the same star coming upon the meridians of two different places is measured by the difference of longitudes of the places. (97.) Vice versâ — the interval elapsing between two different stars coming on the meridian of one and the same place, expressed in sidereal time, is the measure of the difference of right ascensions of the stars. This explains the reason of the double division of the equator and equinoctial into degrees and hours. (98.) The equinoctial intersects the horizon in the east and west points, and the meridian in a point whose altitude is equal to the co-latitude of the place. Thus, at Greenwich, the altitude of the intersection of the equinoctial and meridian is 38° 31′ 20′′. (99.) All the heavenly bodies culminate (i. e. come to their greatest altitudes) on the meridian; which is, therefore, the best situation to observe them, being least confused by the inequalities and vapours of the atmosphere, as well as least displaced by refraction. (100.) All celestial objects within the circle of perpetual apparition come twice on the meridian, above the horizon, in every diurnal revolution; once above and once below the pole. These are called their upper and lower culminations. (101.) We shall conclude this chapter by calling the reader's attention to a fact, which, if he now learn it for the first time, will not fail to surprise him, viz. that the stars continue visible through telescopes during the day as well as the night; and that, in proportion to the power of the instrument, not only the largest and brightest of them, but even those of inferior lustre, such as scarcely strike the eye at night as at all conspicuous, are readily found and followed even at noonday,—unless in that part of the sky which is very near the sun, by those who possess the means of pointing a telescope accurately to the proper places. Indeed, from the bottoms of deep narrow pits, such as a well, or the shaft of a mine, such bright stars as pass the zenith may even be discerned by the naked eye; and we have ourselves heard it stated by a celebrated optician, that the earliest circumstance which drew his attention to astronomy was the regular appearance, at a certain hour, for several successive days, of a considerable star, through the shaft of a chimney. CHAP. II. OF THE NATURE OF ASTRONOMICAL INSTRUMENTS AND OBSERV- (102.) OUR first chapter has been devoted to the acquisition chiefly of preliminary notions respecting the globe we inhabit, its relation to the celestial objects which surround it, and the physical circumstances under which all astronomical observations must be made, as well as to provide ourselves with a stock of technical words of most frequent and familiar use in the sequel. We might now proceed to a more exact and detailed statement of the facts and theories of astronomy; but, in order to do this with full effect, it will be desirable that the reader be made acquainted with the principal means which astronomers possess, of determining, with the degree of nicety their theories require, the data on which they ground their conclusions; in other words, of ascertaining by measurement the apparent and real magnitudes with which they are conversant. It is only when in possession of this knowledge that he can fully appreciate either the truth of the theories themselves, or the degree of reliance to be placed on any of their conclusions antecedent to trial: since it is only by knowing what amount of error can certainly be perceived and distinctly measured, that he can satisfy himself whether any theory offers so close an approximation, in its nu |