To adjust things properly we must rectify the globe to the latitude of 25° 40′ N., or, in other words, incline the axis of the globe at that angle to the wooden horizon.
It will be at once seen that the inclination of the axis to the horizon is very much less than in the case of London. Since all the stars which pass between the North Pole and the horizon cannot set, all their apparent movement will take place above the horizon. All the stars between the horizon and the South Pole will never rise. Hence, stars within the distance of 25° from the North Pole will never set at Thebes, and those stars within 25° of the South Pole will never be visible there. At any place the latitude and the elevation of the pole are the same. It so happens that all these places with which archæologists have to do in studying the history of early peoples, Egypt, Babylonia, Assyria, China, Greece, &c., are in middle latitudes, therefore we have to deal with bodies in the skies, which do set, and bodies which do not; and the elevation of the pole is neither very great nor very small. In each different latitude the inclination of the equator to the horizon, as well as the elevation of the pole, will vary, but there will be a strict relationship between the inclination of the equator at each place and the elevation of the pole. Except at the poles themselves the equator will cut the horizon due east and due west. Therefore every celestial body which rises or sets to the north of the equator will cut the horizon between the east or west point and the north point; those bodies which do not set will, of course, not cut the horizon at all.
The sun, and stars near the equator, in such a latitude as that of Thebes, will appear to rise or set at no very considerable angle to the vertical; but when we deal with stars rising or setting near to the north or south points of the horizon they will seem to skim along the horizon instead of rising or setting vertically.
Now it will at once be obvious that there must be a strict law connecting the position of the sun (or a star) with its place of rising or setting. Stars at the same distance from either of the celestial poles will rise or set at the same point of the horizon, and if a star does not change its place in the heavens it will always rise or set in the same place.
Here it will be convenient to introduce one or two technical terms. Every celestial body, whether we deal with the sun, moon, planet, or star, occupies at any moment a certain place in the sky, partly, though not wholly, defined by what we term its declination, i.e., its distance from the celestial equator. This declination is one of the two co-ordinates which are essential for enabling us to state accurately the position of any body on the celestial vault; and we must quite understand that if all these bodies rise and set, and rise and set visibly, the place of their rising or setting must be very closely connected with their declination. Bodies with the same declination will rise at the same points of the horizon. When the declination changes, of course the body will rise and set in different points of the horizon.
Next we define points on the horizon by dividing the whole circumference into four quadrants of 90° each = 360°, so that we can have azimuths of 90° from the north or south points to the east and west points.
Azimuths are not always reckoned in this way, navigators preferring one method, while astronomers prefer another. Thus azimuth may also be taken as the distance measured in degrees from the south point in a direction passing through the west, north, and east points. On this system, a point can have an azimuth varying from 0° to 360°.
SHOWING AMPLITUDES RECKONED FROM THE EAST OR WEST POINTS TO N.P., NORTH POINT OF HORIZON, AND S.P., SOUTH POINT OF HORIZON.
It is next important to define the term amplitude. The amplitude of a body on the horizon is its distance north and south of the east and west points; it is always measured to the nearest of these two latter points, so that its greatest value can never exceed 90°. For instance, the south point itself would have an amplitude of 90° south of west (generally written W. 90° S.), or 90° south of east (E. 90° S.), while a point 2° to the westward of south would have an amplitude of W. 88° S., and not E. 92° S.