DETERMINING THE PLACE OF HEAVENLY BODIES. 45

viz., 5b, b5; 2d, d2, &c. At the north pole, NP, the horizon takes the direction of the line E'Q', the north pole of the heavens, N'P', is in his zenith, and all the stars in the hemisphere, E'N'P'Q', revolve in circles parallel to the horizon: E'C' is at once the radius of the circle of perpetual apparition and occultation, since all the stars above the horizon never set, and those below it never rise above it. If the observer moves toward the south pole of the earth, it is clearly seen that these appearances are exactly reversed.

57. LATITUDE OF ANY PLACE EQUAL TO THE ELEVATION OF THE POLE OF THE HEAVENS. From what has been just stated, it is evident that the latitude of any place is equal to the altitude of the pole of the heavens above the horizon. For we have seen that at the equator, where the latitude is nothing, the elevation of the pole is nothing; at latitude forty degrees the elevation of the pole is forty degrees, and at the poles of the earth, or latitude ninety degrees, the pole of the heavens is ninety degrees from the horizon, and is in the zenith. And the same is true for every latitude, either north or south of the equator.

CHAPTER III.

ON THE MODE OF DETERMINING THE PLACE OF A HEAVENLY BODY.

58. THE first object of the geographer in describing the earth with its kingdoms, cities, mountains, oceans, seas, islands, &c., is to determine their exact position on the surface of the globe. This he obtains in the case of a city, for instance, by finding first, how many degrees, minutes, and seconds, it is situated east or west from a great circle, called a meridian,1 passing through the poles of the earth and some assumed point on its surface, as a

1. See Art. 63 for the meaning of the term meridian.

What is the latitude of any place equal to? What is the subject of Chapter III? What is the first object of the geographer? In what manner does he determine the position of a city? Give an instance.

celebrated observatory; and secondly, its distance in degrees, minutes, and seconds, north or south of the great circle called the equator, passing through the centre of the earth at right angles to its axis of rotation. Thus, for instance, the position of New York City Hall is fixed by finding first, that it is situated seventy-four degrees, and three seconds (74° 00′ 03′′) west of the meridian passing through Greenwich Observatory. This is its longitude. Next, that it is distant north of the equator forty degrees, forty-two minutes, and forty-three seconds (40° 42′ 43′′). This is its latitude. These two measurements are sufficient to mark with precision its situation upon the globe, for no other spot on its surface can have this latitude and longitude.

59. In a similar way the astronomer determines the position of stars in the concave sphere of the heavens, by measuring their angular distances from the planes of two great circles, at right angles to each other. But in order to understand intelligibly the method pursued, we must first give our attention to the manner in which both the globe and the sky have been intersected by imaginary lines and circles, and to the relations existing between them; bearing constantly in mind that these lines and circles all are pure fictions, not one of them really existing in nature, but that they have been invented by astronomers and geographers simply for the purpose of arriving at certain results. Some of these we have already described, but shall refer to a few of them again, in this connection, since it is highly important that the scholar should always have in his mind a clear idea respecting these imaginary circles and lines.

60. CELESTIAL SPHERE, POLES, AXES, AND MERIDIANS. The celestial sphere is the concave sphere of the heavens, in which the stars appear to be set. The poles of the earth are the extremities of that imaginary line upon which it revolves; the latter is called the axis. If any plane passes through the poles and the axis in any di

How does the astronomer determine the position of a star? What is said respecting the circles and lines employed by astronomers for this purpose? What is meant by the celestial sphere? The poles of the earth? Its axis? Terrestrial meridians. Explain from figure.

CELESTIAL SPHERE, POLES, AXES, &C.

47

rection, its intersection with the surface of the earth is a circle, and is called a terrestrial meridian. Thus, in Fig. 18, which represents the earth and the celestial sphere,

the line NS is the axis of the earth. N, the north pole, S, the south pole, and NES, N1S, N2S, N3S, are terrestrial meridians.

61. The axis of the earth, extended in imagination

What is meant by the axis of the celestial sphere? The poles of the heavens ?

each way until it meets the starry sky, becomes the axis of the heavens, or celestial sphere, around which all the stars appear to revolve. The extremities of this axis are the poles of the heavens. Thus, in the figure, where the outer starred circle represents a section of the celestial sphere, the line N'S' is the axis of the celestial sphere, and N and S' its north and south poles. The axis of the earth is that part of the axis of the heavens, which is intercepted between two opposite points on the earth's surface, and these two intercepting points are the poles of the earth.

62. If any plane passes through the poles and axis of the heavens in any direction, its intersection with the imaginary surface of the celestial sphere is a celestial meridian. A terrestrial and celestial meridian are, therefore, formed by one and the same plane; the first occurring when the plane is intersected by the surface of the earth, the second when it is cut by the concave sphere of the heavens. Thus, N'E'S', N'1S1, N12S', and N13S', are celestial meridians; and NES, N1S, N2S, and N3S, their corresponding terrestrial meridians.

63. The plane of the meridian at any place is perpendicular to its horizon, and consequently passes through its zenith and nadir, dividing the visible heavens into two equal parts towards the east and west. For this reason this circle is called the meridian circle, because when the sun, in his apparent diurnal revolution, comes to the meridian of any place, it is there noon, or midday; the Latin word for mid-day being meridies.

64. EQUATORS. If we suppose a plane passing through the centre of the earth, perpendicular to the axis of rotation, its intersection with the surface of the earth forms a circle called the equator, or terrestrial équator, and if this plane is extended in imagination to the fixed stars, its intersection with the celestial sphere is also a circle, called the celestial equator, or equinoctial. Thus, in Fig. 18, EQ is the equator, and E'Q' the celestial

What is meant by celestial meridians? Explain from figure. What are the relative positions of the plane of the meridian of any place and the plane of its horizon? What is the meaning of the term meridian? What is the terrestrial equator? What the celestial?

VERTICAL CIRCLES.

49

equator. They appear as straight lines in the figure, because we see them in the direction of their planes.

65. VERTICAL CIRCLES. Vertical circles are those which are imagined to be formed by planes passing through the zenith, perpendicular to the horizon, and intersecting the celestial sphere. The vertical circle passing through the east and west points of the horizon is termed the prime vertical, while that which intersects the north and south points becomes a meridian. Thus, in Fig. 19, where A represents the earth, SZWMN the celestial sphere, Z the zenith, and the plane SWNE the horizon-PZHM is a vertical circle, WZEM the prime vertical, and SZNM a meridian.

66. THE POSITION OF A STAR-HOW DETERMINED. The place of a star in the sky may be determined in three ways. First, by referring it to the planes of a celestial meridian and of the horizon. Secondly, by noting its distance from the planes of a given meridian

What are vertical circles? What the prime vertical? Is a meridian a vertical circle? Explain from figure. In how many ways is the position of a star fixed? Describe them