Then another set of circles is drawn perpendicular to the horizon, and all intersecting at the zenith and the nadir. These are called vertical circles, from the fact that they are upright to the horizon. That one of the vertical circles which cuts the horizon at the north-and-south points coincides with the meridian, which we have already described. The vertical circle at right angles to the meridian is called the prime vertical. It cuts the horizon at the east and west points, dividing the visible sky into a northern and a southern half. Like the altitude circles, vertical circles may be drawn anywhere we please so as to pass through a star in any quarter of the sky—but the meridian and the prime vertical are fixed.
With the two sets of circles that have just been described, it is possible to indicate accurately the location of any heavenly body, at any particular moment. Its altitude is ascertained by measuring, along the vertical circle passing through it, its distance from the horizon. (Sometimes it is convenient to measure, instead of the altitude of a star, its zenith distance, which is also reckoned on the vertical circle.)
To ascertain the azimuth, we must first choose a point of beginning on the horizon. Any of the cardinal points, i.e., east, west, north, or south, may be employed for this purpose, but in astronomy it is customary to use only the south point, and to carry the measure westward all round the circle of the horizon, and so back to the point of beginning in the south. This involves circular, or degree, measure, to which a few words must now be devoted.
Every circle, no matter how large or how small, is divided into 360 equal parts, called degrees, usually indicated by the sign (°); each degree is subdivided into 60 equal parts called minutes, indicated by the sign (′); and each minute is subdivided into 60 equal parts called seconds, indicated by the sign (″). Thus there are 360°, or 21,600′, or 1,296,000″ in every complete circle. The actual length of a degree in inches, yards, or miles, depends upon the size of the circle, but no circle ever has more than 360°, and a degree of any particular circle is precisely equal to any other degree of that same circle. Thus, if a circle is 360 miles in circumference, every one of its degrees will be one mile long. In mathematics, a degree usually means not a distance measured along the circumference of a circle, but an angle formed at the centre of the circle between two lines called radii (radius in the singular), which lines, where they intersect the circumference, are separated by a distance equal to one 360th of the entire circle. But, for ordinary purposes, it is simpler to think of a degree as an arc equal in length to one 360th of the circle. Now, since the horizon, and the other imaginary lines drawn in the sky, are all circles, it is evident that the principle of circular measure may be applied to them, and indeed must be so applied in order that they shall be of use to us in indicating the position of a star.
To return, then, to the measurement of the azimuth of a star. Since the south point is the place of beginning, we mark it 0°, and we divide the circle of the horizon into 360°, counting round westward. Suppose we see a star somewhere in the south-western quarter of the sky; then the point where the vertical circle passing through that star intersects the horizon will indicate its azimuth. Suppose that this point is found to be 25° west of south; then 25° will be the star's azimuth. Suppose it is 90°; then the azimuth is 90°, and the star must be on the prime vertical in the west, because west, being one quarter of the way round the horizon from south, is 90° in angular distance from the south point. Suppose the azimuth is 180°; then the star must be on the meridian north of the zenith, because north is exactly half-way, or 180° round the horizon from the south point. Suppose the azimuth is 270°; then the star must be on the prime vertical in the east, because east is 270°, or three quarters of the way round from the south point. If the star is on the meridian in the south its azimuth may be called either 0° or 360°, because on any graduated circle the mark indicating 360° coincides in position with 0°, that being at the same time the point of beginning and the point of ending.
The same system of angular measure is applied in ascertaining a star's altitude. Since the horizon is half-way between the zenith and the nadir it must be just 90° from either. If a star is in the zenith, then its altitude is 90°, and if it is below the zenith its altitude lies somewhere between 0° and 90°. In any case it cannot be less than 0° nor more than 90°. Having measured the altitude and the azimuth we have the two co-ordinates which are needed to indicate accurately the place of a star in the sky. But, as we shall see in a moment, other co-ordinates beside altitude and azimuth are needed for a complete description of the places of the stars on the celestial sphere. Owing to the apparent revolution of the heavens round the earth, the altitudes and azimuths of the celestial bodies are continually changing. We shall now study the causes of these changes.
5. The Apparent Motion of the Heavens. We have likened the earth to a rotating school globe. As such a globe turns, any particular spot on it is presented in succession toward the various sides of the room. In precisely the same way any spot on the earth is turned by its rotation successively toward various parts of the surrounding sky. To understand the effect of this, a little patient watching of the actual heavens will be required, but this has the charm of all out-of-doors observation of nature, and it will be found of fascinating interest as the facts begin to unfold themselves.
The Moon Near the “Crater” Tycho
Photographed at the Lick Observatory under the direction of E. S. Holden.
Tycho is the regular oval depression a little below the centre of the view. The vast depression, 140 miles across, with a row of smaller craters within, below the centre of the view at the top, is Clavius. The photograph was made when sundown was approaching on that part of the moon. Observe the jagged line of advancing night lying across the rugged surface on the western (left-hand) side.
It is best to begin by finding the North Star, or pole star. If you are living not far from latitude 40° north, which is the median latitude of the United States, you must, after determining as closely as you can the situation of the north point, look upward along the meridian in the north until your eyes are directed to a point about 40° above the horizon. Forty degrees is somewhat less than half-way from the horizon to the zenith, which, as we have seen, are separated by an arc of 90°. At that point you will notice a lone star of what astronomers call the second magnitude. This is the celebrated North Star. It is the most useful to man of all the stars, except the sun, and it differs from all the others in a way presently to be explained. But first it is essential that you should make no mistake in identifying it. There are certain landmarks in the sky which make such identification certain. In the first place, it is always so close to the meridian in the north, that by naked-eye observation you would probably never suspect that it was not exactly on the meridian. Then, its altitude is always equal, or very nearly equal, to the latitude of the place where you happen to be on the earth, so that if you know your latitude you know how high to carry your eye above the northern horizon. If you are in latitude 50°, the star will be at 50° altitude, and if your latitude is 30°, the altitude of the star will be 30°. Next you will notice that the North Star is situated at the end of the handle of a kind of dipper-shaped figure formed by stars, the handle being bent the wrong way. All of the stars forming this “dipper” are faint, except the two which are farthest from the North Star, in the outer edge of the bowl, one of which is about as bright as the North Star itself. Again, if you carry your eye along the handle to the bowl, and then continue onward about as much farther, you will be led to another, larger, more conspicuous, and more perfect, dipper-shaped figure, which is in the famous constellation of Ursa Major, or the Great Bear. This striking figure is called the Great Dipper (known in England as The Wain). It contains seven conspicuous stars, all of which, with one exception, are equal in brightness to the North Star. Now, look particularly at the two stars which indicate the outer side of the bowl of this dipper, and you will find that if you draw an imaginary line through them toward the meridian in the north, it will lead your eye directly back to the North Star. These two significant stars are often called The Pointers. With their aid you can make sure that you have really found the North Star.