Page:Encyclopædia Britannica, Ninth Edition, v. 2.djvu/830

764 course of a year the star-sphere has gained a complete rotation, and the stars have the same apparent position at any assigned hour of the night as they had when the observations were commenced. Limiting our attention for the present to the stars, though already, in speaking of the common day, we have in fact referred to the sun, the idea suggested by the observed phenomena is that the apparent star-sphere revolves around the earth precisely as it seems to do, turning about an axis, with a perfectly uniform motion, completing one rotation in twenty-four hours, less about four minutes. The natural steps for determining whether this really is the case, are first, a series of careful observa tions at one fixed station ; and, secondly, a study of the effects produced by change of station.

For the former purpose we require to adopt certain fixed points or circles on the concave hemisphere visible above the horizon, in order that we may refer the apparent motions to these points or circles as unmoving standards. Fig. 1. Let, then, NESW (fig. 1) represent the seemingly circular horizon line around the observer at ; N being the north point, S the south, E the east, and W the west, so that tho lines SON and WOE are at right angles to each other. Let Z be the point immediately over head ; and let P, so placed on the quad rant ZPN that PN is an arc of 51 Fig. 2 Next, let EMWM (fig. 2) represent the path of a star which rises due east. Then EMWM is a circle whose plane passes through WOE, and is there fore a great circle of the sphere. The dia meter WOE divides this circle into tho semicircles EM W and WM E, one above, the other below the hori zon circle NESW, that is to say, a star which rises in the east has one-half of its course above the hori zon, and the other half below the horizon. Again, since the circle SZNZ has the points E and W for its poles, the arcs EM, MW, WM, and M E are quadrants, that is to say, when a star rises in the east, one-fourth of a complete rotation brings it to the meridian, another fourth brings it to the west point, the next fourth part brings it again to the meridian at M below the hori zon, and the remaining fourth part brings it to the east point again. The circle EMWM is called the celestial equator. It is the great circle having for its poles the points P and P, which are the poles of the heavens. (It is sometimes, but perhaps not very correctly, called the equinoctial, because when the sun is on this circle, one-half of his course is above and the other below the horizon, and therefore day and night are equal ; but, strictly speaking, the term equinoctial is applied to the geographical equator because there all the year round the nights are of equal length.) A star at N will clearly be carried by the diurnal motion round the circle Nemiv to N again, not passing below the horizon ; and any star on the segment of the sphere PNemiv will be always above the horizon. Hence the circle of ~Nemw is called the circle of perpetual apparition, as limiting the region of the stars which never set. Such stars are called circumpolar stars. There is evidently an equal opposite region, P Sw mV, around the invisible pole, the stars in which are never seen above the plane of the horizon. It is clear that any circle parallel to the equator, between the circle of perpetual apparition and the equator, has more than its half above the horizon, and so much the more as it lies nearer to the circle of perpetual apparition ; that is to say, stars rising in the quadrant EN are above the horizon for more than half the time of a complete rotation of the star-sphere, and the nearer they rise to N the longer they continue above the horizon. In like manner stars rising in the quadrant ES are above the hori zon for less than half the time of a complete rotation, and the nearer they rise to S the shorter is the time during which they are above the horizon. Let us suppose the sphere of fig. 2 so placed (fig. 3) that the horizon plane appears as a straight line SON, O being the place where the east and west points coalesce. Thus the equator appears as the straight line MOM at right angles to the polar axis POP ; the circles mN, S?/t of fig. 2 become the straight lines wtN, Si parallel to MM in fig. 3. And parallel circles intermediate between these two and the equator appear as the parallel straight lines AC1&amp;gt;, A C B ; while parallel circles outside the circles niN ami SOT appear as the parallel straight lines acb and a c b. All these parallels being at right angles to PP are bisected 