Page:Encyclopædia Britannica, Ninth Edition, v. 2.djvu/831

] by PP. Now, if we consider that the straight line AIIB represents a circle seen edgewise, we perceive that All represents two equal arcs of the circum ference of this circle, one arc being that on which a star moving along that circle by the diurnal motion is carried from the hori zon to the meridian at A, and the other being tlie arc on which the star is carried from A to the horizon again. In like manner H A represents two equal arcs of a star s diur nal course, that is Fi to say, the arcs of a star s visible path on the two sides of the meridian are equal to one another. Similarly the meridian divides the invisible part of a star s course into equal parts. In the case of a star within the circle of perpetual apparition we perceive that acb represents two semicircles of such a star s diurnal circuit, one-half lying on the east of the meridian, the other lying on the west; in this case, then, as in the former, the meridian separates the ascending from the descending paths, which are equal, but the ascent is from a point on the meridian below the pole, not from the horizon, and the descent is to the same point of the subpolar meridian. It will be noticed that a in Fig. 3 lies to the north of the zenith Z; but it is also clear from the figure that some of the circum polar stars cross the meridional arc SMP to the south of the zenith. Fig. 3.

We see from fig. 3 that a star is always at its highest above the horizon when on the part PZS of the meridional circle. A star is said to culminate, or to reach its culmina tion, when on the meridian. The arc of the meridian intercepted between the star and the south point is called the star s meridian altitude; and the arc of the meridian between the star and the zenith is called the star s zenith distance, or more correctly, the meridional zenith distance. The arc-distance of a star from the equator is called its declination, and is northern or southern according as the star is in the northern or southern of the two hemispheres into which the equator divides the celestial sphere. The arc-distance of a star from the north pole is called the north polar distance, the supplement of this arc (the arc-distance from the south pole) being called the south polar distance. ft is evident that the north polar distance of a star having northern declination is complementary to the declination,—that is, N.P.D.&#61;90-N. Dec. But when a star has southern declination N.P.D.&#61;90+S. Dec. When we know the declination or polar distance of a star, we know where it will culminate. For we see from fig. 3 that Arc SA&#61;SM+MA. In other words, the altitude of a star culminating at A is equal to the altitude of the equator on the meridian added to the northern declination of the star. (The arc SM is obviously equal to ZP, the zenith distance of the pole, or the complement of the pole s altitude above the horizon.) Again— Arc SA′&#61;SM-MA′, or the altitude of a star culminating at A is equal to the altitude of the equator on the meridian diminished by the southern declination. These relations hold so long as the star culminates on the arc SZ. For a star culminating at a, we have still Sα&#61;MS+Mα. But the altitude of the star, being iu this case measured from the north point N, is the supplement of the arc obtained by thus adding the north declination to the meridional alti tude of the equator. We see then that the declination of a star (or its north polar distance) determines the altitude of its culminating point. To determine the time at which the star culminates it is necessary that another co-ordinate should be known.

As we measure the declination from the equator, or in other words, determine the altitude of culmination by reference to the equator, it is manifestly convenient to measure the time of a star s culmination by referring it to the time of culmination of some selected point on the equator. This is the course adopted by astronomers. The point selected for the purpose is one of the two points in which a great circle on the celestial sphere, called the ecliptic, and presently to be more particularly described, cuts the equator. This point is called the first point of Aries, and is indicated by the sign T. At present it is only necessary to note that this point is in reality affected by a slow motion on the star-sphere, due to the fact that the axis on which the star-sphere apparently turns undergoes a slow change of position within the star-sphere itself, so that the equator is not really a fixed circle on the heavens. But for the purpose we have at present in view this slow change may be neglected; and we assume that the observer on earth has the equator as a fixed circle from which to measure the declination of stars, and that he also has a fixed point on the equator by which to time the culmina tion of each star. Knowing the declination of a star, he knows at what altitude it will culminate as viewed from the fixed station at which thus far we have supposed him to be placed. Let him now note the exact moment at which the first point of Aries culminates, and let him observe the precise interval in time between that moment and the moment when a star of known declination cul minates; this interval is constant, and thereafter he will always know not only at what altitude that star will cul minate, but at what time after the culmination of the point Υ. The interval in time between the culmination of Υ and the culmination of a given star is called the right ascension of the star. It may be measured, indeed, as an arc, viz., as the arc on the equator intercepted between Υ and that point in which a meridian circle through the star intersects the equator, the arc being measured in the direc tion opposite to that in which the star-sphere rotates. But the right ascension is more conveniently and now almost always measured in time. The time measurement employed is the rotation of the star-sphere itself. The interval in time between the successive culminations of Υ is called a sidereal day. It is divided into 24 hours (numbered 0, 1, 2, 3 . . . to 24), each hour into 60 minutes, each minute into 60 seconds. If we have a clock showing 24 hours, and so rated as always to show 0 hour 0 min. 0 sec., when Υ is at its culmination, that clock will always show true sidereal time. Such a clock would gain nearly 4 min. a day as compared with an ordinary clock; but we need not at present dwell upon this point. Now the right ascension (or, as it is written, the R.A.) is indicated in sidereal time, and therefore corresponds to the time shown by the sidereal clock when that star is culminating. Thus, if a star s right ascension is 3 h. 2 m. 6 s., then when the sidereal clock shows time 3 h. 2 m. 6 s., that star is culminating. Whether it be day or night the astronomer knows this certainly, that is, if his sidereal clock is trustworthy.

It will be manifest that an observer at a fixed station, as we have thus far supposed our observer to be, requires to have the means of determining—(1) the moment at which a star culminates (or is on the meridian), and (2) the star s 