Having received numerous requests for information upon the subject, I have thought it expedient to endeavor to prepare a description of the method of determining the true meridian which should be sufficiently clear and practical to be generally understood by those desiring to make use of such information.
This will involve an elementary treatment of the subject, beginning with the
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_.
An observation may he made upon Polaris at any of these four points, or at any other point of its orbit, but this latter case becomes too complicated for ordinary practice, and is therefore not considered.
If the observation were made upon the star at the time of its upper or lower culmination, it would give the true meridian at once, but this involves a knowledge of the true local time of transit, or the longitude of the place of observation, which is generally an unknown quantity; and moreover, as the star is then moving east or west, or at right angles to the place of the meridian, at the rate of 15° of arc in about one hour, an error of so slight a quantity as only four seconds of time would introduce an error of one minute of arc. If the observation be made, however, upon either elongation, when the star is moving up or down, that is, in the direction of the vertical wire of the instrument, the error of observation in the angle between it and the pole will be inappreciable. This is, therefore, the best position upon which to make the observation, as the precise time of the elongation need not be given. It can be determined with sufficient accuracy by a glance at the relative positions of the star Alioth, in the handle of the Dipper, and Polaris (see Fig. 1). When the line joining these two stars is horizontal or nearly so, and Alioth is to the _west_ of Polaris, the latter is at its _eastern_ elongation, and _vice versa_, thus: