Let us now suppose the spectator viewing the diurnal revolutions from several different positions on the earth. On the equator, his horizon would pass through both poles; for the horizon cuts the celestial vault at ninety degrees in every direction from the zenith of the spectator; but the pole is likewise ninety degrees from his zenith, when he stands on the equator; and consequently, the pole must be in the horizon. Here, also, the celestial equator would coincide with the prime vertical, being a great circle passing through the east and west points. Since all the diurnal circles are parallel to the equator, consequently, they would all, like the equator be perpendicular to the horizon. Such a view of the heavenly bodies is called a right sphere, which may be thus defined: a right sphere is one in which all the daily revolutions of the stars are in circles perpendicular to the horizon.
Fig. 14.
A right sphere is seen only at the equator. Any star situated in the celestial equator would appear to rise directly in the east, at midnight to be in the zenith of the spectator, and to set directly in the west. In proportion as stars are at a greater distance from the equator towards the pole, they describe smaller and smaller circles, until, near the pole, their motion is hardly perceptible.
If the spectator advances one degree from the equator towards the north pole, his horizon reaches one degree beyond the pole of the earth, and cuts the starry sphere one degree below the pole of the heavens, or below the north star, if that be taken as the place of the pole. As he moves onward towards the pole, his horizon continually reaches further and further beyond it, until, when he comes to the pole of the earth, and under the pole of the heavens, his horizon reaches on all sides to the equator, and coincides with it. Moreover, since all the circles of daily motion are parallel to the equator, they become, to the spectator at the pole, parallel to the horizon. Or, a parallel sphere is that in which all the circles of daily motion are parallel to the horizon.
To render this view of the heavens familiar, I would advise you to follow round in mind a number of separate stars, in their diurnal revolution, one near the horizon, one a few degrees above it, and a third near the zenith. To one who stood upon the north pole, the stars of the northern hemisphere would all be perpetually in view when not obscured by clouds, or lost in the sun's light, and none of those of the southern hemisphere would ever be seen. The sun would be constantly above the horizon for six months in the year, and the remaining six continually out of sight. That is, at the pole, the days and nights are each six months long. The appearances at the south pole are similar to those at the north.
A perfect parallel sphere can never be seen, except at one of the poles,—a point which has never been actually reached by man; yet the British discovery ships penetrated within a few degrees of the north pole, and of course enjoyed the view of a sphere nearly parallel.
As the circles of daily motion are parallel to the horizon of the pole, and perpendicular to that of the equator, so at all places between the two, the diurnal motions are oblique to the horizon. This aspect of the heavens constitutes an oblique sphere, which is thus defined: an oblique sphere is that in which the circles of daily motion are oblique to the horizon.
Suppose, for example, that the spectator is at the latitude of fifty degrees. His horizon reaches fifty degrees beyond the pole of the earth, and gives the same apparent elevation to the pole of the heavens. It cuts the equator and all the circles of daily motion, at an angle of forty degrees,—being always equal to what the altitude of the pole lacks of ninety degrees: that is, it is always equal to the co-altitude of the pole. Thus, let H O, Fig. 15, represent the horizon, E Q the equator, and P P the axis of the earth. Also, l l, m m, n n, parallels of latitude. Then the horizon of a spectator at Z, in latitude fifty degrees, reaches to fifty degrees beyond the pole; and the angle E C H, which the equator makes with the horizon, is forty degrees,—the complement of the latitude. As we advance still further north, the elevation of the diurnal circle above the horizon grows less and less, and consequently, the motions of the heavenly bodies more and more oblique to the horizon, until finally, at the pole, where the latitude is ninety degrees, the angle of elevation of the equator vanishes, and the horizon and the equator coincide with each other, as before stated.
