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Before we enter upon the explanation of the contents and uses of the Nautical Almanac, we will give definitions of the most important terms used in Nautical Astronomy.

Astronomical Terms and Definitions.

4. To a spectator on the earth the sun, moon, and stars seem to be placed on the interior surface of a hollow sphere of great but indefinite magnitude. The interior surface of this sphere is called the celestial concave, the centre of which may be supposed to be the same as that of the earth.

5. The heavenly bodies are not in reality thus situated with respect to the spectator; for they are interspersed in infinite space at very different distances from him : the whole is an optical deception, by which an observer, wherever he is placed, is induced to imagine himself to be the centre of

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the universe. For let us suppose that e p q be the earth, PZ M the celestial concave, and m and n heavenly bodies at different distances from a spectator placed at A. Then the spectator not being able to estimate the relative distances of m and n, would imagine both the bodies to be

situated in the celestial con

cave at z and м, at the same distance from him. This figure will enable us to explain the terms true and apparent place of a heavenly body. The body m viewed from the surface of the earth would appear to a spectator a to be at M in the celestial concave: if it were seen from the centre of the earth, the point occupied by m would be м', the ex-. tremity of a line drawn from the centre c of the earth through the heavenly body to the celestial concave. M is called the apparent place, and м' the true place of the heavenly body m.

6. The axis of the earth is that diameter about which it revolves: the poles of the earth are the extremities of the axis.

7. The terrestrial equator is that great circle on the earth that is equidistant from each pole.

8. A spectator on the earth, not being sensible of the motion by which in fact he describes daily a circle from west to east with the spot on which he stands, views in appearance the heavens moving past him in the opposite direction, or from east to west. The sphere of the fixed stars, or as it is more usually called, the celestial concave, thus appears to revolve from east to west round a line which is the axis of the earth produced to the celestial concave: this line is therefore called the axis of the heavens.

9. The poles of the heavens are the extremities of the axis of the heavens.

10. The celestial equator is that great circle in the celestial concave which is perpendicular to the axis of the heavens; or it may be defined to be the terrestrial equator expanded or extended to the celestial concave. The poles of the celestial equator and the poles of the heavens are therefore identical. While the earth thus performs its daily revolution, it is carried with great velocity from west to east round the sun, and describes an elliptic orbit once every year. This annual motion of the earth round the sun, causes the latter body, to a spectator on the earth, insensible of his own change of place, to appear to describe a great circle in the celestial concave

from west to east.
This may
be explained by a figure. Let
Ae, A, be the earth's orbit, s the
sun, and s, m s,, the celestial
concave; then, to a spectator at
e, the sun is seen at a point s,
the celestial concave, a little, we



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will suppose, to the west of a fixed star at m; but when

the earth has arrived at e,,, the spectator (not being sensible of his motion from e, to e,,) imagines the sun to be at s,,, to the east of the star m, and to have described the arc s, s,, in the time the earth moved from e, to ell It appears from this, that when the earth has arrived again at e, the sun will again be at s,, having described one complete circle in the celestial concave among the fixed stars. The great circle thus described by the sun is called the ecliptic.

11. The axis of the earth as it is thus carried round the sun, continues always parallel to itself, and is supposed, on account of the smallness of the earth's orbit (small, when compared with the distance of the heavenly bodies), to be always directed to the same points in the celestial concave, namely, the poles of the heavens.

12. From observation, the celestial equator is found to be inclined to the ecliptic at an angle of about 23° 28'. This inclination of the equator to the ecliptic is called the obliquity of the ecliptic. The axis of the earth, therefore, which is perpendicular to the equator, is inclined to the ecliptic, or, as it is in the same plane, to the earth's orbit, at an angle of 66° 32'.

13. In consequence of the whirling motion of the earth about its axis, the parts near the equator, which have the greatest velocity, acquire thereby a greater distance from the centre than the parts near the poles. By actual measurement of a degree of latitude in different parts of the earth, it is found that the equatorial diameter is longer than the axis or polar diameter by 26 miles: the former being about 7924 miles; the latter


q about 7898 miles,* and that the form of the earth is that of an oblate spheroid resembling the annexed figure, in which pp, is the axis and e q the equator. It is usual, however,

* See the author's Problems in Astronomy, &c., and Solutions, page 56, where the investigation of this problem is given, and the values of the equatorial and polar diameters calculated.

in drawing the figure of the earth to exaggerate very much its ellipticity; this is done for the sake of drawing the lines about the figure with greater clearness; for if it were constructed according to its true dimensions, the line pp. (being only about theth part of itself less than e q) would appear to the eye of the same length as e q, and we should see that the figure that more nearly resembles the earth would be a sphere.

14. If a perpendicular A G be drawn to the earth's surface passing through A, the angle a G q, formed by the line with the plane of the equator is the latitude of the point A.

If a line be drawn from a to c, the centre of the earth, the angle A c q is called the reduced, or central latitude of a. The difference between the true and reduced latitude is not great: it is, however, of importance in some of the problems in Nautical Astronomy. This correction has accordingly been calculated,* and forms one of the Nautical Tables.

Sections of the earth passing through the poles, as p A q, are called meridians of the earth. If the earth is considered as a sphere (which it is very nearly), the meridians will be circles on this supposition, moreover, the perpendicular A G would coincide with A c, and the latitude of a place on the surface of the earth may be, on this supposition, defined to be the arc of the meridian passing

through the place, intercepted be-
tween the place and the equator. If
GA be produced to meet the celestial
concave at z, the point z is the zenith
of the spectator at A.
If c A be pro-
duced to the celestial concave at z',

then z' is called the reduced zenith of


the spectator at A. The point opposite to z in the celestial concave is called the Nadir. In the figure the terrestrial

* See the author's Astronomical Problems and Solutions, page 59, for the investigation of this correction.

equator e

Չ is extended to the celestial concave, and therefore e co is the plane of the celestial equator.

By means of the figure we may define the zenith, reduced zenith, latitude, and reduced latitude, as follows:

The zenith is that point in the celestial equator which is the extremity of the line drawn perpendicular to the place of the spectator, as z.

The reduced zenith is that point in the celestial concavewhich is the extremity of a straight line drawn from the centre of the earth, through the place of the spectator, as z'.

The latitude of a place a on the surface of the earth, is the inclination of the perpendicular A G to the plane of the equator: thus the angle A G Q is the latitude of a. The arc

z Q in the celestial concave measures the angle a GQ; hence z Q, or the distance of the zenith from the celestial equator, is equal to the latitude of the spectator.

The reduced latitude of the place A, is the inclination of z'c or Ac to the plane of the equator: or it is the angle ACQ or arc z'Q, which measures the angle. Since the curvature of the earth diminishes from the equator to the poles, the reduced latitude z' Q must be always less than the true latitude z Q, and therefore the difference z z' must be subtracted from the true latitude to get the reduced latitude.




The visible horizon is that circle in the celestial concave which touches the earth where the spectator stands, as h ▲ r; and a circle parallel to the visible horizon, and passing through the centre of the earth, is called the rational horizon: thus HCR is the rational horizon. These two

circles, however, form one and the same great circle in the celestial concave: thus R and r in the figure must be sup

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