An introduction to astronomy: designed as a text-book for the use of students in college. By Denison Olmsted ...

20 THE EARTH.
and less, and consequently the motions of the heavenly bodies
more and more oblique, until finally, at the pole, where the latitude is 90~, the angle of elevation of the equator vanishes, and
the horizon and the equator coincide with each other, as before
stated.
5 4. The CIRCLE OF PERPETUAL APPARITION/ is the boundary
of that space around the elevated pole, where the stars never set.
Its distance from the pole is equal to the latitude of the place.
For, since the altitude of the pole is equal to the latitude, a
star whose polar distance is just equal to the latitude, will,
when at its lowest point, only just reach the horizon; and all
the stars nearer the pole than this will evidently not descend
so far as the horizon.
Thus, mm (Fig. 5), is the circle of perpetual apparition, between which and the north pole, the stars never set, and its
distance from the pole OP is evidently equal to the elevation
of the pole, and of course to the latitude.
55. In the opposite hemisphere, a similar part of the sphere
adjacent to the depressed pole never rises. Hence,
The CIRCLE OF PERPETUAL OCCULTATION, is the boundary of
that space around the depressed pole, within which the stars
never rise. Thus, m'm' (Fig. 5), is the circle of perpetual occultation, between which and the south pole the stars never
rise.
56. In an oblique sphere, the horizon cuts the circles of
daily motion unequally. Towards the elevated pole, more
than half the circle is above the horizon, and a greater and
greater portion as the distance from the equator is increased,
until finally, within the circle of perpetual apparition, the
whole circle is above the horizon. Just the opposite takes
place in the hemisphere next the depressed pole. Accordingly,
when the sun is in the equator, as the equator and horizon, like
all other great circles of the sphere, bisect each other, the days
and nights are equal all over the globe. But when the sun is
north of the equator, our days become longer than our nights,
but shorter when the sun is south of the equator. Mloreover,
the higher the latitude, the greater is the inequality in the