gard to one another, we may regard them as placed in the concave surface of an immense hollow sphere, having its centre at the centre of the earth. This imaginary sphere is called the Celestial Sphere.

15. Diurnal motions of the fixed stars. Each star in its diurnal motion, moves uniformly, in a circle of which the north pole of the heavens is a geometric pole. The method by which the truth of this proposition is established, will be given in a subsequent chapter.

16. Stars during the day. The strong light of the sun overpowering the feebler light of the stars renders them invisible to the naked eye during the day time. But by the aid of a telescope the brighter stars, except those near the sun, may be distinctly seen, and observations may be made on them in the full light of day.

Copernican System. Copernicus, a celebrated Prussian astronomer, who flourished in the early part of the sixteenth century, formed a theory or system to account for the apparent motions of the heavenly bodies. According to this system, the apparent diurnal motion from east to west is produced by a rotation of the earth from west to east, about a line or axis passing through its centre and the north pole of the heavens: the apparent annual motion of the sun is produced by a real motion of the earth, round the sun at rest; the planets also revolve round the sun at different distances and in different times; and the moon revolves round the earth and with it round the sun; the revolutions all being from west to east. The truth of this system, called, from its author, the Copernican System, is confirmed by many astronomical facts; and no fact inconsistent with it is known to exist. Astronomers, therefore, adopt it as the true system. Some confirmations of its truth will be noticed in subsequent parts of the work.

18 Order of the planets. The order of the primary planets with regard to their distances from the sun, including the earth as one, and also those discovered since the time of Copernicus, is Mercury, Venus, the Earth, Mars, the Asteroids in the order given in Article 8, Jupiter, Saturn, Uranus, and Neptune.

Mercury and Venus, having their orbits, or paths which they describe round the sun, within that of the earth, are called inferior planets. The others, whose orbits are without that of the earth, are called superior planets.

B

19. Characters. The following characters, by which the sun, moon, and planets are sometimes designated, should be impressed on the memory of the student.

In the above table the asteroids are arranged in the order of

their discovery.

20. Solar System. This expression simply implies the sun and bodies connected with him, as the planets and satellites, the earth and moon included, and comets, without any reference to their arrangement.

21. Attraction of Gravitation. That force which causes a heavy body to descend to the earth, when left free to move, is called gravity, or the attraction of gravitation. Sir Isaac Newton assuming this force to decrease in intensity in the inverse ratio of the square of the distance from the earth's centre, found that, at the distance of the moon, it would be just sufficient to retain her in her orbit around the earth. Pursuing his investigations he found that the assumption of similar forces in the sun and planets, varying in the direct ratio of the mass of the body and the inverse ratio of the square of the distance, would account, on mechanical principles, for the motions of the latter, and for other known astronomical facts. He therefore inferred that attraction of gravitation is a universal property of matter, and that its intensity, or the force with which it acts, varies in the direct ratio of the mass, and the inverse ratio of the square of the distance.

This theory of universal gravitation is the foundation of Physical Astronomy; which, originating with Newton, has, through his labours and those of many eminent men since his time, as Clairaut, Euler, Lagrange, and especially Laplace, become a science of great extent.

DEFINITIONS OF TERMS.

22. The Axis of the Heavens is an imaginary straight line, joining the north pole of the heavens and centre of the earth, and extending to the southern part of the celestial sphere. It is the line about which the heavens appear to revolve. The point in which it meets the southern part of the celestial sphere is called the South Pole of the Heavens, or simply the South Pole. Thus, if C, Fig. 1, represent the centre of the earth, and P, the north pole of the heavens, then will PP' be the axis of the heavens, and P', the south pole.

23. The North and South Poles of the Earth, are the points in which the axis of the heavens intersects the surface of the earth. Thus p and p' are the north and south poles of the earth.

The line pp', terminated by p and p', is called the axis of the earth.

24. The Celestial Equator, or simply the Equator, is the great circle in which a plane through the earth's centre, and perpendicular to the axis of the heavens, intersects the celestial sphere. The circle EWQO represents the celestial equator.

The north and south poles of the heavens, P and P', are evidently the geometric poles of the equator.

25. The Terrestrial Equator is the circle in which the plane of the celestial equator intersects the earth's surface. The semicircle ewq represents one half of the terrestrial equator.*

26 A Declination Circle is any great circle which passes througn

The celestial equator is sometimes called the Equinoctial. More commonly, however, simply the term equator is applied both to the celestial and terrestrial equator; the context serving to designate which is intended. The same observation applies to the terms, pole of the heavens and terrestrial pole.

the poles of the celestial equator. It intersects the equator at right angles. The circle PQP/E is a declination circle; and PSP', PS'P' are arcs of declination circles.

2 The Declination of a heavenly body, or of any point in the celestial sphere, is the arc of a declination circle, intercepted between the equator and the centre of the body, or the point. The declination is reckoned north or south, according as the body is on the north or south side of the equator. Thus DS is the declination of a body at S; it is north.

The Polar Distance of a body is its distance from the north pole, measured on the arc of a declination circle. Thus PS is the polar distance of a body at S. The declination and polar distance are the complements of each other.

It is also evident that the angle pCS, contained between the earth's axis and a line joining the centres of the earth and body, expresses the polar distance of the body; for this angle is measured by PS.

2. The Vertical Line, at any place, is a straight line in the direction of gravity at that place: that is, in the direction of the plumb-line when a plummet freely suspended, is at rest. The line AZ represents the vertical line at the place A.

A plane that passes through the vertical line is called a Vertical Plane; A plane that is perpendicular to the vertical line is called a Horizontal Plane.

Regarding the earth as a sphere, a vertical line produced downwards passes through its centre.

29. The Zenith and Nadir are the points, above and below, in which the vertical line at a place meets the celestial sphere. Thus Z is the zenith and N the nadir, of the place A.

30 The Horizon of a place, or, as it is sometimes called, the Sensible Horizon, is the circle in which a plane passing through the place, and perpendicular to the vertical line at the place, cuts the celestial sphere. The plane itself is also frequently called the horizon.

The Rational Horizon is the circle in which a plane through the earth's centre, and parallel to the sensible horizon, cuts the celes

tial sphere. The circle HORW represents the rational horizon of the place A.*

With reference to the fixed stars, the sensible horizon may be regarded as being the same with the rational horizon (13).

31. The Meridian of a place is the declination circle which passes through the zenith of the place. It cuts the horizon at right angles in two opposite points, called the north and south points of the horizon. The circle HPZRN is the meridian of the place A; and H and R are the north and south points of the horizon.

32. A Vertical Circle is any great circle which passes through the zenith and nadir of a place. It cuts the horizon at right angles. The meridian ZRNH is a vertical circle, and ZSB, ZS'B' and ZS"B" are arcs of vertical circles.

The Prime Vertical is that vertical circle which is at right angles to the meridian of a place. It cuts the horizon in two opposite points, called the east and west points of the horizon. The straight line ZN represents the prime vertical, seen edgewise; and O and W, the east and west points of the horizon.

The Altitude of a heavenly body is the arc of a vertical circle, intercepted between the horizon and the centre of the body. Thus BS is the altitude of a body at S; and RM is the altitude of a body on the meridian at M. The latter is called the meridian altitude.

The Zenith Distance of a body is its distance from the zenith, and is equal to the complement of the altitude of the body. Thus ZS is the zenith distance of a body at S.

36. The Azimuth of a body is the arc of the horizon intercepted between the north or south point of the horizon, and a vertical circle through the centre of the body. Thus BR is the azimuth of a body at S; from the south towards the west.

The altitude and azimuth of a heavenly body are the co-ordinates. that determine its position with reference to the horizon and meridian of a place.

* To avoid confusion in the figure, the sensible horizon is not represented