Secondaries.

Declination.

Hour circles.

“All angular distances on the surface of the sphere, to an eye at the centre, are measured by arcs of great circles." [B. p. 48.]

5. "Secondaries to a great circle are great circles which pass through its poles, and are consequently perpendicular to it." [B. p. 48.]

6. "If the plane of the terrestrial equator be produced to the celestial sphere, it marks out a circle called the celestial equator; and if the axis of the earth be produced in like manner, it becomes the aris of the celestial sphere; and the points of the heavens, to which it is produced, are called the poles, being the poles of the celestial equator."

"The star nearest to the north pole is called the north pole star." [B. p. 48.]

7. "Secondaries to the celestial equator are called circles of declination; of these 24, which divide the equator into equal parts of 15° each, are called hour circles."

"Small circles, parallel to the celestial equator, are called parallels of declination." [B. p. 48.]

The parallels of declination correspond, therefore, to the terrestrial parallels of latitude, and the circles of declination to the terrestrial meridians. A certain point of the celestial equator has been fixed by astronomers, and is called the vernal equinox. The circle of declination, which passes through the vernal equinox, bears the same relation to other

$ 11.]

CELESTIAL SPHERE AND ITS CIRCLES. 209

Right ascension.

Horizon.

circles of declination, which the first meridian does to other terrestrial meridians.

1

8. "The declination of a star is its angular distance from the celestial equator," measured upon its circle of declination. [B. p. 49.]

9. The right ascension of a star is the arc of the equator intercepted between its circle of declination and the vernal equinox. [B. p. 49.]

Right ascension is either estimated in degrees, minutes, &c. from 0° to 360°; or in hours, minutes, &c. of time, 15 degrees being allowed for each hour, as in Sph. Trig.

3.

The positions of the stars are completely determined upon the celestial sphere, when their right ascensions and declinations are known. Catalogues of the stars have accordingly been given, containing their right ascensions and declinations. [B. Table viii. p. 80.]

10. "The sensible horizon is that circle in the heavens, whose plane touches the earth at the spectator."

"The rational horizon is a great circle of the celestial sphere parallel to the sensible horizon." [B. p. 48.]

11. The radius, which is drawn to the observer, is called the vertical line.

The point, where the vertical line meets the celestial sphere above the observer, is called the zenith; the opposite point, where this line meets the sphere. below the observer, is called the nadir.

Prime vertical.

Cardinal points.

Hence the vertical line is a radius of the celestial sphere perpendicular to the horizon; and the zenith and nadir are the poles of the horizon. [B. p. 48.]

12. Circles whose planes pass through the vertical line are called vertical circles. [B. p. 48.]

The vertical circles are secondaries to the horizon.

13. The vertical circle at any place, which is also a circle of declination, is called the celestial meridian of that place. [B. p. 48.]

The plane of the celestial meridian of a place is the same with that of the terrestrial meridian.

14. The points, where the celestial meridian cuts the horizon, are called the north and south points. [B. p. 48.]

The north point corresponds to the north pole, and the south point to the south pole.

15. The vertical circle, which is perpendicular to the meridian, is called the prime vertical. [B. p. 48.]

16. The points, where the prime vertical cuts the horizon, are called the east and west points. [B. p. 48.]

"To an observer, whose face is directed towards the south, the east point is to his left hand, and the west to his right hand. Hence the east and west points are 90° distant from the north and south. These four are called the cardinal points."

$ 18.]

CELESTIAL SPHERE AND ITS CIRCLES. 211

Altitude.

Azimuth.

"The meridian of any place divides the heavens into two hemispheres, lying to the east and west; that lying to the east is called the eastern hemisphere, and the other the western hemisphere."

17. The altitude of a star is its angular distance from the horizon, measured upon the verticle circle passing through the star. [B. p. 48.]

18. The azimuth of a star is the arc of the horizon intercepted between its vertical circle and the north or south point. [B. p. 48.]

A star may be found without difficulty, when its altitude and azimuth are known. But these elements of position are constantly varying.

Fixed stars.

Planets.

CHAPTER II.

THE DIURNAL MOTION.

Constellations.

19. "Stars are distinguished into two kinds, fixed and wandering." [B. p. 45.]

Most of the stars are fixed, that is, retain constantly almost the same relative position; so that the same celestial globes and maps continue to be accurate representations of the firmament for many years. This is a fact of fundamental importance, and furnishes the fixed points for arriving at a complete knowledge of the celestial motions. Small changes of position have, indeed, been detected even in the fixed stars, as will be shown in the course of this treatise; but these changes are too small to disturb the general fact; they are, indeed, too small ever to have been detected, if the positions of the stars had been subject to great variations.

20. Of the wandering stars there are eleven, which are called planets. They are Mercury (☀ ), Venus ( ? ), the Earth (→), Mars (♂), Vesta (†), Juno ( ☀ ), Pallas (), Ceres (?), Jupiter (4), Saturn (h), and Uranus (). [B. p. 45.]

21. For the sake of remembering the stars with greater ease, they have been divided into groups called constellations; and to give distinctness to the constellations, they have been supposed to be circumscribed by