86 ASTRONOMY. 
horizon, and the axis of the heavens is perpendicular to their planes, the 
axis itself will be inclined to the horizon at the angle PSO, or the are PO. 
Their two extremities, P, F, are called the poles, P being the north pole, F 
the south. From the preceding it follows, that for all planes between the 
equator and the poles of the earth, the celestial sphere is oblique (pl. 9, fig. 
3), since the equator, the parallels of declination, and the axis of rotation, 
have ansoblique situation with respect to the horizon. 
If the observer be situated at the north pole (fig. 4). O, then the celestial 
sphere becomes to him parallel, since there the equator and the tropics, as 
seen in fig. 4, are parallel to the horizon. The axis Pp of the horizon coin- 
cides with the axis of the sphere Pp, and the horizon H/ with the equator 
Ee. Should the sun be situated in the plane of the equator, he will describe 
the circle SH, or the horizon, his disk being half above and half below it. 
When, after the expiration of three months, the sun has reached the tropic 
of Cancer at S”, he will describe the circle S’N, 23° 27’ above the horizon. 
He will now be evidently above the horizon, and, in fact, so remain for 
three months longer, gradually returning to the equator. Thus at and 
about the north pole the day is six months long. As a matter of course the 
region about the south pole of the earth must have an equal length of night. 
During the other six months of the year, these conditions are reversed for 
the two poles. The fixed stars, however, of these regions never set, that is, 
those of the northern heavens at the north pole, and those of the southern hea- 
vens at the south pole, since they describe their circles parallel to the horizon. 
Fig. 5, pl. 9, shows the position of the points and circles of the celestial 
sphere to the observer at the equatorial regions of the earth. There the 
two poles, P, p, lie in the horizon, Hh, and consequently the axis, Pp, 
zenith, EK, and nadir, c, in the equator. The planes of the equator and 
tropics are perpendicular to the plane of the horizon, whence the celestial 
globe forms a right sphere. The fixed stars all rise and set perpendicularly 
to the horizon ; each one remaining visible for 12 hours, and invisible for a 
like portion of time. It is very evident that, in the region of the equator, 
al] the fixed stars must gradually come in sight, and that whether the sun 
describe the circles, 8, 8’, or 8’, they will all be divided into two equal 
parts by the horizon. In consequence of this, throughout the whole year at 
the equator, the days and nights will be equal, and of 12 hours each. 
The Geographical Latitude and Longitude of a place; Determination 
of these. 
10. An accurate knowledge of the geographical latitude and longitude of 
a place, that is, its geographical position upon the earth, is of vast import- 
ance to mathematical geography and navigation. The geographical latt- 
tude of a place is the shortest distance of the place from the equator, 
expressed in degrees, minutes, and seconds. It will, therefore, be northern 
or southern, as the place lies north or south of the equator. If, through the 
given place and the axis of the earth, we pass a great circle, cutting the 
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