This will involve an elementary treatment of the subject, beginning with the
DEFINITIONS.
The celestial sphere is that imaginary surface upon which all celestial objects are projected. Its radius is infinite.
The earth's axis is the imaginary line about which it revolves.
The poles are the points in which the axis pierces the surface of the earth, or of the celestial sphere.
A meridian is a great circle of the earth cut out by a plane passing through the axis. All meridians are therefore north and south lines passing through the poles.
From these definitions it follows that if there were a star exactly at the pole it would only be necessary to set up an instrument and take a bearing to it for the meridian. Such not being the case, however, we are obliged to take some one of the near circumpolar stars as our object, and correct the observation according to its angular distance from the meridian at the time of observation.
For convenience, the bright star known as Ursæ Minoris or Polaris, is generally selected. This star apparently revolves about the north pole, in an orbit whose mean radius is 1° 19' 13",[1] making the revolution in 23 hours 56 minutes.
[Footnote 1: This is the codeclination as given in the Nautical Almanac. The mean value decreases by about 20 seconds each year.]
During this time it must therefore cross the meridian twice, once above the pole and once below; the former is called the upper, and the latter the lower meridian transit or culmination. It must also pass through the points farthest east and west from the meridian. The former is called the eastern elongation, the latter the western.