Part 5

4. Rotation of the Celestial Sphere.--It is well known that the sun and the majority of the stars rise in the east, and set in the west. In our latitude there are certain stars in the north which never disappear below the horizon. These stars are called the circumpolar stars. A close watch, however, reveals the fact that these all appear to revolve around one of their number called the pole star, in the direction indicated by the arrows in Fig. 7. In a word, the whole heavens appear to rotate once a day, from east to west, about an axis, which is the prolongation of the axis of the earth. The ends of this axis are called the poles of the heavens; and the great circle of the heavens, midway between these poles, is called the celestial equator, or the equinoctial. This rotation of the heavens is apparent only, being due to the rotation of the earth from west to east.

5. Diurnal Circles.--In this rotation of the heavens, the stars appear to describe circles which are perpendicular to the celestial axis, and parallel with the celestial equator. These circles are called diurnal circles. The position of the poles in the heavens and the direction of the diurnal circles with reference to the horizon, change with the position of the observer on the earth. This is owing to the fact that the horizon changes with the position of the observer.

When the observer is north of the equator, the north pole of the heavens is elevated above the horizon, and the south pole is depressed below it, and the diurnal circles are oblique to the horizon, leaning to the south. This case is represented in Fig. 8, in which PP' represents the celestial axis, EQ the celestial equator, SN the horizon, and ab, cN, de, fg, Sh, kl, diurnal circles. O is the point of observation, Z the zenith, and Z' the nadir.

When the observer is south of the equator, as at O in Fig. 9, the south pole is elevated, the north pole depressed, and the diurnal circles are oblique to the horizon, leaning to the north. When the diurnal circles are oblique to the horizon, as in Figs. 8 and 9, the celestial sphere is called an oblique sphere.

When the observer is at the equator, as in Fig. 10, the poles of the heavens are on the horizon, and the diurnal circles are perpendicular to the horizon.

When the observer is at one of the poles, as in Fig. 11, the poles of the heavens are in the zenith and the nadir, and the diurnal circles are parallel with the horizon.

6. Elevation of the Pole and of the Equinoctial.--At the equator the poles of the heavens lie on the horizon, and the celestial equator passes through the zenith. As a person moves north from the equator, his zenith moves north from the celestial equator, and his horizon moves down from the north pole, and up from the south pole. The distance of the zenith from the equinoctial, and of the horizon from the celestial poles, will always be equal to the distance of the observer from the equator. In other words, the elevation of the pole is equal to the latitude of the place. In Fig. 12, O is the point of observation, Z the zenith, and SN the horizon. NP, the elevation of the pole, is equal to ZE, the distance of the zenith from the equinoctial, and to the distance of O from the equator, or the latitude of the place.

Two angles, or two arcs, which together equal 90°, are said to be complements of each other. ZE and ES in Fig. 12 are together equal to 90°: hence they are complements of each other. ZE is equal to the latitude of the place, and ES is the elevation of the equinoctial above the horizon: hence the elevation of the equinoctial is equal to the complement of the latitude of the place.

Were the observer south of the equator, the zenith would be south of the equinoctial, and the south pole of the heavens would be the elevated pole.

7. Four Sets of Stars.--At most points of observation there are four sets of stars. These four sets are shown in Fig. 13.

(1) The stars in the neighborhood of the elevated pole never set. It will be seen from Fig. 13, that if the distance of a star from the elevated pole does not exceed the elevation of the pole, or the latitude of the place, its diurnal circle will be wholly above the horizon. As the observer approaches the equator, the elevation of the pole becomes less and less, and the belt of circumpolar stars becomes narrower and narrower: at the equator it disappears entirely. As the observer approaches the pole, the elevation of the pole increases, and the belt of circumpolar stars becomes broader and broader, until at the pole it includes half of the heavens. At the poles, no stars rise or set, and only half of the stars are ever seen at all.

(2) The stars in the neighborhood of the depressed pole never rise. The breadth of this belt also increases as the observer approaches the pole, and decreases as he approaches the equator, to vanish entirely when he reaches the equator. The distance from the depressed pole to the margin of this belt is always equal to the latitude of the place.

(3) The stars in the neighborhood of the equinoctial, on the side of the elevated pole, set, but are above the horizon longer than they are below it. This belt of stars extends from the equinoctial to a point whose distance from the elevated pole is equal to the latitude of the place: in other words, the breadth of this third belt of stars is equal to the complement of the latitude of the place. Hence this belt of stars becomes broader and broader as the observer approaches the equator, and narrower and narrower as he approaches the pole. However, as the observer approaches the equator, the horizon comes nearer and nearer the celestial axis, and the time a star is below the horizon becomes more nearly equal to the time it is above it. As the observer approaches the pole, the horizon moves farther and farther from the axis, and the time any star of this belt is below the horizon becomes more and more unequal to the time it is above it. The farther any star of this belt is from the equinoctial, the longer the time it is above the horizon, and the shorter the time it is below it.

(4) The stars which are in the neighborhood of the equinoctial, on the side of the depressed pole, rise, but are below the horizon longer than they are above it. The width of this belt is also equal to the complement of the latitude of the place. The farther any star of this belt is from the equinoctial, the longer time it is below the horizon, and the shorter time it is above it; and, the farther the place from the equator, the longer every star of this belt is below the horizon, and the shorter the time it is above it.

At the equator every star is above the horizon just half of the time; and any star on the equinoctial is above the horizon just half of the time in every part of the earth, since the equinoctial and horizon, being great circles, bisect each other.

8. Vertical Circles.--Great circles perpendicular to the horizon are called vertical circles. All vertical circles pass through the zenith and nadir. A number of these circles are shown in Fig. 14, in which SENW represents the horizon, and Z the zenith.

The vertical circle which passes through the north and south points of the horizon is called the meridian; and the one which passes through the east and west points, the prime vertical. These two circles are shown in Fig. 15; SZN being the meridian, and EZW the prime vertical. These two circles are at right angles to each other, or 90° apart; and consequently they divide the horizon into four quadrants.

9. Altitude and Zenith Distance.--The altitude of a heavenly body is its distance above the horizon, and its zenith distance is its distance from the zenith. Both the altitude and the zenith distance of a body are measured on the vertical circle which passes through the body. The altitude and zenith distance of a heavenly body are complements of each other.

10. Azimuth and Amplitude.--Azimuth is distance measured east or west from the meridian. When a heavenly body lies north of the prime vertical, its azimuth is measured from the meridian on the north; and, when it lies south of the prime vertical, its azimuth is measured from the meridian on the south. The azimuth of a body can, therefore, never exceed 90°. The azimuth of a body is the angle which the plane of the vertical circle passing through it makes with that of the meridian.

The amplitude of a body is its distance measured north or south from the prime vertical. The amplitude and azimuth of a body are complements of each other.

11. Alt-azimuth Instrument.--An instrument for measuring the altitude and azimuth of a heavenly body is called an alt-azimuth instrument. One form of this instrument is shown in Fig. 16. It consists essentially of a telescope mounted on a vertical circle, and capable of turning on a horizontal axis, which, in turn, is mounted on the vertical axis of a horizontal circle. Both the horizontal and the vertical circles are graduated, and the horizontal circle is placed exactly parallel with the plane of the horizon.

When the instrument is properly adjusted, the axis of the telescope will describe a vertical circle when the telescope is turned on the horizontal axis, no matter to what part of the heavens it has been pointed.

The horizontal and vertical axes carry each a pointer. These pointers move over the graduated circles, and mark how far each axis turns.

To find the azimuth of a star, the instrument is turned on its vertical axis till its vertical circle is brought into the plane of the meridian, and the reading of the horizontal circle noted. The telescope is then directed to the star by turning it on both its vertical and horizontal axes. The reading of the horizontal circle is again noted. The difference between these two readings of the horizontal circle will be the azimuth of the star.

To find the altitude of a star, the reading of the vertical circle is first ascertained when the telescope is pointed horizontally, and again when the telescope is pointed at the star. The difference between these two readings of the vertical circle will be the altitude of the star.

12. The Vernier.--To enable the observer to read the fractions of the divisions on the circles, a device called a vernier is often employed. It consists of a short, graduated arc, attached to the end of an arm c (Fig. 17), which is carried by the axis, and turns with the telescope. This arc is of the length of nine divisions on the circle, and it is divided into ten equal parts. If 0 of the vernier coincides with any division, say 6, of the circle, 1 of the vernier will be 1/10 of a division to the left of 7, 2 will be 2/10 of a division to the left of 8, 3 will be 3/10, of a division to the left of 9, etc. Hence, when 1 coincides with 7, 0 will be at 6-1/10; when 2 coincides with 8, 0 will be at 6-2/10; when 3 coincides with 9, 0 will be at 6-3/10, etc.

To ascertain the reading of the circle by means of the vernier, we first notice the zero line. If it exactly coincides with any division of the circle, the number of that division will be the reading of the circle. If there is not an exact coincidence of the zero line with any division of the circle, we run the eye along the vernier, and note which of its divisions does coincide with a division of the circle. The reading of the circle will then be the number of the first division on the circle behind the 0 of the vernier, and a number of tenths equal to the number of the division of the vernier, which coincides with a division of the circle. For instance, suppose 0 of the vernier beyond 6 of the circle, and 7 of the vernier to coincide with 13 of the circle. The reading of the circle will then be 6-7/10.

13. Hour Circles.--Great circles perpendicular to the celestial equator are called hour circles. These circles all pass through the poles of the heavens, as shown in Fig. 18. EQ is the celestial equator, and P and P' are the poles of the heavens.