PART I.. The Celestial Sphere.

THE CELESTIAL SPHERE.

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PART I.

THE CELESTIAL SPHERE.

=1. Definition of Astronomy.= Astronomy has to do with the earth, sun, moon, planets, comets, meteors, stars, and nebulæ; in other words, with the universe, or “the aggregate of existing things.” It is the most ancient of all sciences. The derivation of the name from two Greek words, aster, “star,” and nomos, “law,” indicates its nature. It deals with the law of the stars—the word “star” being understood, in its widest signification, as including every heavenly body of whatever kind. The earth itself is such a body. Since we happen to live on the earth, it becomes our standpoint in space, from which we look out at the others. But, if we lived on some other planet, we would see the earth as a distant body in the sky, just as we now see Jupiter or Mars.

Astronomy teaches us that everything in the universe, from the sun and the moon to the most remote star or the most extraordinary nebula, is related to the earth. All are made of similar elementary substances and all obey similar physical laws. The same substance which is a solid upon the earth may be a gas or a vapour in the sun, but that does not alter its essential nature. Iron appears in the sun in the form of a hot vapour, but fundamentally it is the same substance which exists on the earth as a hard, tough, and heavy metal. Its different states depend upon the temperature to which it is subjected. The earth is a cool body, while the sun is an intensely hot one; consequently iron is solid on the earth and vaporous in the sun, just as in winter water is solid ice on the surface of a pond and steamy vapour over the boiler in the kitchen. Even on the earth we can make iron liquid in a blast furnace, and with the still greater temperatures obtainable in a laboratory we can turn it into vapour, thus reducing it to something like the state in which it regularly exists in the sun.

This fact, that the entire universe is made up of similar substances, differing only in state according to the local circumstances affecting them, is the greatest thing that astronomy has to tell us. It may be regarded as the fundamental law of the stars.

=2. The Situation of the Earth in the Heavens.= One of the greatest triumphs of human intelligence is the discovery of the real place which the earth occupies in the universe. This discovery has been made in spite of the most deceptive appearances. If we accepted the sole evidence of our eyes, as men once did, we could only conclude that the earth was the centre of the universe. In the daytime we see the sun apparently moving through the sky from east to west, as if it were travelling in a circle round the earth, overhead by day and underfoot at night. In the night-time, we see the stars apparently travelling round the earth in the same way as the sun. The fact is, that all of them are virtually motionless with regard to the earth, and their apparent movements through the sky are produced by the earth's rotation on its axis. The earth turns round on itself once every twenty-four hours, like a spinning ball. Imagine a fly on a rotating school globe; the whole room would appear to the fly to be revolving round it as the heavens appear to revolve round the earth. It would have to be a very intelligent insect to correct the deceptive evidence of its eyes.

The actual facts, revealed by many centuries of observation and reasoning, are that the earth is a rotating globe, turning once on its axis every twenty-four hours and revolving once round the sun every three hundred and sixty-five days. The sun is also a globe, 1,300,000 times larger than the earth, but so hot that it glows with intense brilliance, while the substances of which it consists are kept in a gaseous or vaporous state. Besides the earth there are seven other principal globes, or planets, which revolve round the sun, at various distances and in various periods, and, in addition to these, there are hundreds of smaller bodies, called asteroids or small planets. There are also many singular bodies called comets, and swarms of still smaller ones called meteors, which likewise revolve round the sun.

The earth and the other bodies of which we have just spoken are not only cooler than the sun, but most of them are in a solid state and do not shine with light of their own. The sun furnishes both heat and light to the smaller and cooler bodies revolving round it. In fact, the sun is simply a star, resembling the thousands of other stars which surround us in the sky, and its apparent superiority to them is due only to the fact that it is relatively near-by while they are far away. It is probable that all, or most, of the stars also have planets, comets, and meteors revolving round them, but invisible owing to their immense distance.

The “paths” in which the earth and the other planets and bodies travel in their revolutions round the sun are called their orbits. These orbits are all elliptical in shape, but those of the earth and the other large planets are not very different from circles. Some of the asteroids, and all of the comets, however, travel in elliptical orbits of considerable eccentricity, i. e., which differ markedly from circles. The orbit of the earth differs so slightly from a circle that the eccentricity amounts to only about one-sixtieth. The distance of the earth from the sun being, on the average, 93,000,000 miles, the eccentricity of its orbit causes it to approach to within about 91,500,000 miles in winter (of the northern hemisphere) and to recede to about 94,500,000 miles in summer. The point in its orbit where the earth is nearest the sun is called perihelion, and the point where it is farthest from the sun, aphelion. The earth is at perihelion about Jan. 1, and at aphelion about July 4.

Now, in order to make a general picture in the mind of the earth's situation, let the reader suppose himself to be placed out in space as far from the sun as from the other stars. Then, if he could see it, he would observe the earth as a little speck, shining like a mote in the sunlight, and circling in its orbit close around the sun. The universe would appear to him to be somewhat like an immense spherical room filled with scattered electric-light bulbs, suspended above, below, and all around him, each of these bulbs representing a sun, and if there were minute insects flying around each light, these insects would represent the planets belonging to the various suns. One of the glowing bulbs among the multitude would stand for our sun, and one of the insects circling round it would be the earth.

=Photograph of the South Polar Region of the Moon=

Made by G. W. Ritchey with the forty-inch refractor of the Yerkes Observatory. ]

We have already remarked that the rotation of the earth on its axis causes all the other heavenly bodies to appear to revolve round it once every twenty-four hours, and we must now add that the earth's revolution round the sun causes the same bodies to appear to make another, slower revolution round it once every year. This introduces a complication of apparent motions which it is the business of astronomy to deal with, and which we shall endeavour to explain.

=3. The Horizon, the Zenith, and the Meridian.= First, let us consider what is the ordinary appearance of the sky. When we go out of doors on a clear night we see the heavens in the shape of a great dome arched above us and filled with stars. What we thus see is one half of the spherical shell of the heavens which surrounds us on all sides, the earth being apparently placed at its centre. The other half is concealed from our sight behind, or below, the earth. This spherical shell, of which only one half is visible to us at a time, is called the celestial sphere. Now, the surface of the earth seems to us (for this is another of the deceptive appearances which astronomy has to correct) to be a vast flat expanse, whose level is broken by hills and mountains, and the visible half of the celestial sphere seems to bend down on all sides and to rest upon the earth in a circle which extends all around us. This circle, where the heavens and the earth appear to meet, is called the horizon. As we ordinarily see it, the horizon appears irregular and broken on account of the unevenness of the earth's surface, but if we are at sea, or in the midst of a great level prairie, the horizon appears as a smooth circle, everywhere equally distant from the eye. This circle is called the sensible horizon. But there is another, ideal, horizon, used in astronomy, which is called the rational horizon. It is of the utmost importance that we should clearly understand what is meant by the rational horizon, and for this purpose we must consider another fact concerning the dome of the sky.

We now turn our attention to the centre of that dome, which, of course, is the point directly overhead. This point, which is of primary importance, is called the zenith. The position of the zenith is indicated by the direction of a plumb-line. If we imagine a plumb-line to be suspended from the centre of the sky overhead, and to pass into the earth at our feet, it would run through the centre of the earth, and, if it were continued onward in the same direction, it would, after emerging from the other side of the earth, reach the centre of the invisible half of the sky-dome at a point diametrically opposite to the zenith. This central point of the invisible half of the celestial sphere, lying under our feet, is called the nadir.

Keeping in mind the definitions of zenith and nadir that have just been given, we are in a position to understand what the rational horizon is. It is a great circle whose plane cuts through the centre of the earth, and which is situated exactly half-way between the zenith and the nadir. This plane is necessarily perpendicular, or at right angles, to the plumb-line joining the zenith and the nadir. In other words, the rational horizon divides the celestial sphere into two precisely equal halves, an upper and a lower half. In a hilly or mountainous country the sensible or visible horizon differs widely from the rational, or true horizon, but at sea the two are nearly identical. This arises from the fact, that the earth is so excessively small in comparison with the distances of most of the heavenly bodies that it may be regarded as a mere point in the midst of the celestial sphere.

Fig. 1. The Rational and the Sensible Horizon.

Let C be the earth's centre, O the place of the observer, and H D the rational horizon passing through the centre of the earth. For an object situated near the earth, as at A, the sensible horizon makes a large angle with the rational horizon. If the object is farther away, as at B, the angle becomes less; and still less, again, if the object is at D. It is evident that if the object be immensely distant, like a star, the sensible horizon O S will be practically parallel with the rational horizon, and will blend with it, because the radius, or semi-diameter, of the earth, O C, is virtually nothing in comparison with the distance of the star. ]

Besides the horizon and the zenith there is one other thing of fundamental importance which we must learn about before proceeding further,—the meridian. The meridian is an imaginary line, or semicircle, beginning at the north point on the horizon, running up through the zenith, and then curving down to the south point. It thus divides the visible sky into two exactly equal halves, an eastern and a western half. In the ordinary affairs of life we usually think only of that part of the meridian which extends from the zenith to the south point on the horizon (which is sometimes called the "noon-line” because the sun crosses it at noon), but in astronomy the northern half of the meridian is as important as the southern.

=4. Altitude and Azimuth.= Now, suppose that we wish to indicate the location of a star, or other object, in the sky. To do so, we must have some fixed basis of reference, and such a basis is furnished by the horizon and the zenith. If we tried to describe the position of a star, the most natural thing would be, first, to estimate, or measure, its height above the horizon, and, second, to indicate the direction in which it was situated with regard to the points of the compass. These two measures, if they were accurately made, would enable another person to find the star in the sky. And this is precisely what is done in astronomy. The height above the horizon is called altitude, and the bearing with reference to the points of the compass is called azimuth. Together these are known as co-ordinates. In order to systematise this method of measuring the location of a star, the astronomer uses imaginary circles drawn on the celestial sphere. The horizon and the meridian are two of these circles. In addition to these, other imaginary circles are drawn parallel to the horizon and becoming smaller and smaller until the uppermost one may run close round the zenith, which is the common centre of the entire set. These are called altitude circles, because each one throughout its whole extent is at an unvarying height, or altitude, above the horizon. Such circles may be drawn anywhere we please, so as to pass through any chosen star or stars. If two stars in different quarters of the sky are found to lie on the same circle, then we know that both have the same altitude.

Fig. 2. Altitude and Azimuth.

C is the place of the observer. N C S, a north-and-south line drawn in the plane of the horizon. E C W, an east-and-west line in the plane of the horizon. N E S W, the circle of the horizon. Z, the observer's zenith. N Z S, vertically above N C S, the meridian. E Z W, the prime vertical. Z s s′, part of a vertical circle drawn through the star s. The circle through s parallel to the horizon is an altitude circle. The angle s C s′, or the arc s′ s, represents the star's altitude. The angle s C Z, or the arc Z s, is the star's zenith distance. To find the azimuth, the angular distance round the horizon from S (0°), through W, N, E, to the point where the star's vertical circle meets the horizon, is measured. In this case it is 315°. But if we measured it eastward from the south point it would be—45°. ]

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.

Having found it, begin by noting the various groups of stars, or constellations, in the northern part of the sky, and, as the night wears on, observe whether any change takes place in their position. To make our description more definite, we will suppose that the observations begin at nine o'clock P.M. about the 1st of July. At that hour and date, and from the middle latitudes of the United States, the Great Dipper is seen in a south-westerly direction from the North Star, with its handle pointing overhead. At the same time, on the opposite side of the North Star, and low in the north-east, appears the remarkable constellation of Cassiopeia, easily recognisable by a zigzag figure, roughly resembling the letter W, formed by its five principal stars. Fix the relative positions of these constellations in the memory, and an hour later, at 10 P.M., look at them again. You will find that they have moved, the Great Dipper sinking, while Cassiopeia rises. Make a third observation at 11 P.M., and you will perceive that the motion has continued, The Pointers having descended in the north-west, until they are on a level with the North Star, while Cassiopeia has risen to nearly the same level in the north-east. In the meantime, the North Star has remained apparently motionless in its original position. If you repeat the observation at midnight, you will find that the Great Dipper has descended so far that its centre is on a level with the North Star, and that Cassiopeia has proportionally risen in the north-east. It is just as if the two constellations were attached to the ends of a rod pivoted at the centre upon the North Star and twirling about it.

In the meantime you will have noticed that the figure of the “Little Dipper,” attached to the North Star, which had its bowl toward the zenith at 9 P.M., has swung round so that at midnight it is extended toward the south-west. Thus, you will perceive that the North Star is like a hub round which the heavens appear to turn, carrying the other stars with them.

To convince yourself that this motion is common to the stars in all parts of the sky, you should also watch the conduct of those which pass overhead, and those which are in the southern quarter of the heavens. For instance, at 9 P.M. (same date), you will see near the zenith a beautiful coronet which makes a striking appearance although all but one of its stars are relatively faint. This is the constellation Corona Borealis, or the Northern Crown. As the hours pass you will see the Crown swing slowly westward, descending gradually toward the horizon, and if you persevere in your observations until about 5 A.M., you will see it set in the north-west. The curve that it describes is concentric with those followed by the Great Dipper and Cassiopeia, but, being farther from the North Star than they are, and at a distance greater than the altitude of the North Star, it sinks below the horizon before it can arrive at a point directly underneath that star. Then take a star far in the south. At 9 o'clock, you will perceive the bright reddish star Antares, in the constellation Scorpio, rather low in the south and considerably east of the meridian. Hour after hour it will move westward, in a curve larger than that of the Northern Crown, but still concentric with it. A little before 10 P.M., it will cross the meridian, and between 1 and 2 A.M., it will sink beneath the horizon at a point south of west.

So, no matter in what part of the heavens you watch the stars, you will see not only that they move from east to west, but that this motion is performed in curves concentric round the North Star, which alone appears to maintain its place unchanged. Along the eastern horizon you will perceive stars continually rising; in the middle of the sky you will see others continually crossing the meridian—a majestic march of constellations,—and along the western horizon you will find still others continually setting. If you could watch the stars uninterruptedly throughout the twenty-four hours (if daylight did not hide them from sight during half that period), you would perceive that they go entirely round the celestial sphere, or rather that it goes round with them, and that at the end of twenty-four hours they return to their original positions. But you can do this just as well by looking at them on two successive nights, when you will find that at the same hour on the second night they are back again, practically in the places where you saw them on the first night.

Of course, what happens on a July night happens on any other night of the year. We have taken a particular date merely in order to make the description clearer. It is only necessary to find the North Star, the Great Dipper, and Cassiopeia, and you can observe the apparent revolution of the heavens at any time of the year. These constellations, being so near the North Star that they never go entirely below the horizon in middle northern latitudes, are always visible on one side or another of the North Star.

Now, call upon your imagination to deal with what you have been observing, and you will have no difficulty in explaining what all this apparent motion of the stars means. You already know that the heavens form a sphere surrounding the earth. You have simply to suppose the North Star to be situated at, or close to, the north end, or north pole, of an imaginary axle, or axis, round which the celestial sphere seems to turn, and instantly the whole series of phenomena will fall into order, and the explanation will stare you in the face. That explanation is that the motion of all the stars in concentric circles round the North Star is due to an apparent revolution of the whole celestial sphere, like a huge hollow ball, about an axis, the position of one of whose poles is graphically indicated in the sky by the North Star. The circles in which the stars seem to move are perpendicular to this axis, and inclined to the horizon at an angle depending upon the altitude of the North Star at the place on the earth where the observations are made.

Another important fact demands our attention, although the thoughtful reader will already have guessed it—the north pole of the celestial sphere, whose position in the sky is closely indicated by the North Star, is situated directly over the north pole of the earth. This follows from the fact that the apparent revolution of the celestial sphere is due to the real rotation of the earth. You can see that the two poles, that of the earth and that of the heavens, must necessarily coincide, by taking a school globe and imagining that you are an intelligent little being dwelling on its surface. As the globe turned on its axis you would see the walls of the room revolving round you, and the poles of the apparent axis round which the room turned, would, evidently, be directly over the corresponding poles of the globe itself. Another thing which you could make clear by this experiment is that, as the poles of the celestial sphere are over the earth's poles, so the celestial equator, or equator of the heavens, must be directly over the equator of the earth.

We can determine the location of the poles of the heavens by watching the revolution of the stars around them, and we can fix the position of the circle of the equator of the heavens, by drawing an imaginary line round the celestial sphere, half-way between the two poles. We have spoken specifically only of the north pole, but, of course, there is a corresponding south pole situated over the south pole of the earth, but whose position is invisible from the northern hemisphere. It happens that the place of the south celestial pole is not indicated to the eye, like that of the northern, by a conspicuous star.

=Drawing of Jupiter= ]

=Drawing of Jupiter=

Note the change of details between the two drawings, made at different times. Similar changes are continually occurring. ]

=6. Locating the Stars on the Celestial Sphere.= Having found the poles and the equator of the celestial sphere, we begin to see how it is possible to make a map, or globe, of the heavens just as we do of the earth, on which the objects that they contain may be represented in their proper positions. When we wish to describe the location of an object on the earth, a city for instance, we have to refer to a system of imaginary circles, drawn round the earth and based upon the equator and the poles. These circles enable us to fix the place of any point on the earth with accuracy. One set of circles called parallels of latitude are drawn east and west round the globe parallel to the equator, and becoming smaller and smaller until the smallest runs close round their common central point, which is one of the poles. Each pole of the earth is the centre of such a set of circles all parallel to the equator. Since each circle is unvarying in its distance from the equator, all places which are situated anywhere on that circle have the same latitude, or distance from the equator, either north or south.

But to know the latitude of any place on the earth is not sufficient; we must also know what is called its longitude, or its angular distance east or west of some chosen point on the equator. This knowledge is obtained with the aid of another set of circles drawn north-and-south round the earth, and all meeting and crossing at the poles. These are called meridians of longitude. In order to make use of them we must, as already intimated, select some particular meridian whose crossing point on the equator will serve as a place of beginning. By common consent of the civilised world, the meridian which passes through the observatory at Greenwich, near London, has been chosen for this purpose. It is, like all the meridians, perpendicular to the equator, and it is called the prime meridian of the earth.

In locating any place on the earth, then, we ascertain by means of the parallel of latitude passing through it how far in degrees, it is north or south of the equator, and by means of its meridian of longitude how far it is east or west of the prime meridian, or meridian of Greenwich. These two things being known, we have the exact location of the place on the earth. Let us now see how a similar system is applied to ascertain the location of a heavenly body on the celestial sphere.

We have observed that the poles of the heavens correspond in position, or direction, with those of the earth, and that the equator of the heavens runs round the sky directly over the earth's equator. It follows that we can divide the celestial sphere just as we do the surface of the earth by means of parallels and meridians, corresponding to the similar circles of the earth. On the earth, distance from the equator is called latitude, and distance from the prime meridian, longitude. In the heavens, distance from the equator is called declination, and distance from the prime meridian, right ascension; but they are essentially the same things as latitude and longitude, and are measured virtually in the same way. In place of parallels of latitude, we have on the celestial sphere circles drawn parallel to the equator and centring about the celestial poles, which are called parallels of declination, and in place of meridians of longitude, we have circles perpendicular to the equator, and drawn through the celestial poles, which are called hour circles. The origin of this name will be explained in a moment. For the present it is only necessary to fix firmly in the mind the fact that these two systems of circles, one on the earth and the other in the heavens, are fundamentally identical.

Just as on the earth geographers have chosen a particular place, viz. Greenwich, to fix the location of the terrestrial prime meridian, so astronomers have agreed upon a particular point in the heavens which serves to determine the location of the celestial prime meridian. This point, which lies on the celestial equator, is known as the vernal equinox. We shall explain its origin after having indicated its use. The hour circle which passes through the vernal equinox is the prime meridian of the heavens, and the vernal equinox itself is sometimes called the “Greenwich of the Sky.”

If, now, we wish to ascertain the exact location of a star on the celestial sphere, as we would that of New York, London, or Paris, on the earth, we measure along the hour circle running through it, its declination, or distance from the celestial equator, and then, along its parallel of declination, we measure its right ascension, or distance from the vernal equinox. Having these two co-ordinates, we possess all that is necessary to enable us to describe the position of the star, so that someone else looking for it, may find it in the sky, as a navigator finds some lone island in the sea by knowing its latitude and longitude.

Declination, as we have seen, is simply another name for latitude, but right ascension, which corresponds to longitude, needs a little additional explanation. It differs from longitude, first, in that, instead of being reckoned both east and west from the prime meridian, it is reckoned only toward the east, the reckoning being continued uninterruptedly entirely round the circle of the equator; and, second, in that it is usually counted not in degrees, minutes, and seconds of arc, but in hours, minutes, and seconds of time. The reason for this is that, since the celestial sphere makes one complete revolution in twenty-four hours, it is convenient to divide the circuit into twenty-four equal parts, each corresponding to the distance through which the heavens appear to turn in one hour. This explains the origin of the term hour circles applied to the celestial meridians, which, by intersecting the equator, divide it into twenty-four equal parts, each part corresponding to an hour of time. In expressing right ascension in time, the Roman numerals—I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII, XIII, XIV, XV, XVI, XVII, XVIII, XIX, XX, XXI, XXII, XXIII, XXIV—are employed for the hours, and the letters m and s respectively for the minutes and seconds. Since there are 360° in every circle, it is plain that one hour of right ascension corresponds to 15°. So, too, one minute of right ascension corresponds to 15′, and one second to 15″. It will be found useful to memorise these relations.

Fig. 3. Right Ascension and Declination.

The plane of the horizon, with the north, south, east, and west points, and the zenith, are represented as in Fig. 2. P and P′ are the poles of the celestial sphere, the dotted line connecting them representing the direction of the axis, both of celestial sphere and the earth. The circle Eq Eq′ is the equator. V is the vernal equinox, or the point on the equator whence right ascension is reckoned round toward the east. The circle passing through s, parallel to the equator, is a declination circle. The circle P s P′ is the hour circle of the star s. The arc of this hour circle contained between s and the point where it meets the equator is the star's declination. Its right ascension is measured by the arc of the equator contained between V and the point where its hour circle meets the equator, or by the angle V P s. The hour circle P V P′, passing through the vernal equinox, is the equinoctial colure. When this has moved up to coincidence with the meridian, N Z S, it will be astronomical noon. ]

=7. Effects Produced by Changing the Observer's Place on the Earth.= The reader will recall that in Sect. 4 we described another system of circles for determining the places of stars, a system based on the horizon and the zenith. This horizon-zenith system takes no account of the changes produced by the apparent motion of the heavens, and consequently it is not applicable to determining the absolute positions of the stars on the celestial sphere. It simply shows their positions in the visible half of the sky, as seen at some particular time from some definite point on the earth. In order to show the changing relations of this system to that which we have just been describing, let us consider the effects produced by shifting our place of observation on the earth. Since the zenith is the point overhead and the nadir the point underfoot, and the horizon is a great circle drawn exactly half-way between the zenith and the nadir, it is evident, upon a moment's consideration, that every place on the earth has its own zenith and its own horizon. It is also clear that every place must have its own meridian, because the meridian is a north-and-south line running directly over the observer's head. You can see how this is, if you reflect that for an observer situated on the other side of the earth what is overhead for you will be underfoot for him, and vice versa. Thus the direction of our zenith is the direction of the nadir for our antipodes, and the direction of their zenith is the direction of our nadir. They see the half of the sky which is invisible to us, and we the half which is invisible to them.

Now, suppose that we should go to the north pole. The celestial north pole would then be in our zenith, and the equator would correspond with the horizon. Thus, for an observer at the north pole the two systems of circles that we have described would fall into coincidence. The zenith would correspond with the pole of the heavens; the horizon would correspond with the celestial equator; the vertical circles would correspond with the hour circles; and the altitude circles would correspond with the circles of declination. The North Star, being close to the pole of the heavens, would appear directly overhead. Being at the zenith, its altitude would be 90° (see Sect. 4). Peary, if he had visited the pole during the polar night, would have seen the North Star overhead, and it would have enabled him with relatively little trouble to determine his exact place on the earth, or, in other words, the exact location of the north terrestrial pole. With the pole star in the zenith, it is evident that the other stars would be seen revolving round it in circles parallel to the horizon. All the stars situated north of the celestial equator would be simultaneously and continuously visible. None of them would either rise or set, but all, in the course of twenty-four hours, would appear to make a complete circuit horizontally round the sky. This polar presentation of the celestial sphere is called the parallel sphere, because the stars appear to move parallel to the horizon. No man has yet beheld the nocturnal phenomena of the parallel sphere, but if in the future some explorer should visit one of the earth's poles during the polar night, he would behold the spectacle in all its strange splendour.

=Jupiter=

Photographed at the Lick Observatory. Observe on the left the Great Red Spot, which first appeared in 1878. ]

Next, suppose that you are somewhere on the earth's equator. Since the equator is everywhere 90°, or one quarter of a circle, from each pole, it is evident that looking at the sky from the equator you would see the two poles (if there was anything to mark their places) lying on the horizon one exactly in the north and the other exactly in the south. The celestial equator would correspond with the prime vertical, passing east and west directly over your head, and all the stars would rise and set perpendicularly to the horizon, each describing a semicircle in the sky in the course of twelve hours. During the other twelve hours, the same stars would be below the horizon. Stars situated near either of the poles would describe little semi-circles near the north or the south point; those farther away would describe larger semi-circles; those close to the celestial equator would describe semi-circles passing overhead. But all, no matter where situated, would describe their visible courses in the same period of time. This equatorial presentation of the celestial sphere is called the right sphere, because the stars rise and set at a right angle to the plane of the horizon. Comparing it with the system of circles on which right ascension and declination are based, we see that, as the prime vertical corresponds with the celestial equator, so the horizon must represent an hour circle. The meridian also represents an hour circle. It may require a little thought to make this clear, but it will be a good exercise.

Finally, if you are somewhere between the equator and one of the poles, which is the actual situation of the vast majority of mankind, you see either the north or the south pole of the heavens elevated to an altitude corresponding with your latitude, and the stars apparently revolving round it in circles inclined to the horizon at an angle depending upon the latitude. The nearer you are to the equator, the steeper this angle will be. This ordinary presentation of the celestial sphere is called the oblique sphere. Its horizon does not correspond with either the equator or the prime vertical, and its zenith and nadir lie at points situated between the celestial poles and the celestial equator.

=8. The Astronomical Clock and the Ecliptic.= It will be remembered that the meridian of any place on the earth is a straight north and south line running through the zenith and perpendicular to the horizon. More strictly speaking, the meridian is a circle passing from north to south directly overhead and corresponding exactly with the meridian of longitude of the place of observation. Now, let us consider the hour circles on the celestial sphere. They are drawn in the same way as the meridians on the earth. But the celestial sphere appears to revolve round the earth, and as it does so it must carry the hour circles with it, since they are fixed in position upon its surface. Fix your attention upon the first of these hour circles, i. e., the one which runs through the vernal equinox. Its right ascension is called 0 hours, because it is the starting point. Suppose that at some time we find the vernal equinox exactly in the south; then the 0 hour circle, or the prime meridian of the heavens, will, at that instant, coincide with the meridian of the place of observation. But one hour later, in consequence of the motion of the heavens, the vernal equinox, together with the circle of 0 hours, will be 15°, or one hour of right ascension, west of the meridian, and the hour circle marked I will have come up to, and for an instant will be blended with, the meridian. An hour later still, the circle of II hours right ascension will have taken its place on the meridian, while the vernal equinox and the circle of 0 hours will be II hours, or 30°, west of the meridian. And so on, throughout the entire circuit of the sky.

What has just been said makes it evident that the apparent motion of the heavens resembles the movement of a clock, the vernal equinox, or the circle of 0 hours, serving as a hand, or pointer, on the dial. Astronomers use it in exactly that way, for astronomical clocks are made with dials divided into twenty-four hour spaces, and the time reckoning runs continuously from 0 hours to XXIV hours. The “astronomical day” begins when the vernal equinox is on the meridian. At that instant the hands of the astronomical clock mark 0 hours, 0 minutes, 0 seconds. Thus the clock follows the motion of the heavens, and the astronomer can tell by simply glancing at the dial, and without looking at the sky, where the vernal equinox is, and what is the right ascension of any body which may at that moment be on the meridian.

We must now explain a little more fully what the vernal equinox is, and why it has been chosen as the “Greenwich of the Sky.” Its position is not marked by any star, but is determined by means of the intersecting circles that we have described. There is one other such circle, that we have not yet mentioned, which bears a peculiar relation to the vernal equinox. This is the ecliptic. Just as the daily, or diurnal, rotation of the earth on its axis causes the whole celestial sphere to appear to make one revolution every day, so the yearly or annual revolution of the earth in its orbit about the sun causes the sun to appear to make one revolution through the sky every year. As the earth moves onward in its orbit, the sun seems to move in the opposite direction. Inasmuch as there are 360° in a complete circle and 365 days in a year, the apparent motion of the sun amounts to nearly 1° per day, or 30° per month. In twelve months, then, the sun comes back again to the place in the sky which it occupied at the beginning of the year. Since the motion of the earth in its orbit is from west to east (the same as that of its rotation on its axis), it follows that the direction of the sun's apparent annual motion in the sky is from east to west (like its daily motion). Thus, while in fact the earth pursues a path, or orbit, round the sun, the sun seems to pursue a path round the earth. This apparent path of the sun, projected against the background of the sky, is called the ecliptic. The name arises from the fact that eclipses only occur when the moon is in or near the plane of the sun's apparent path.

As the apparent motion of the sun round the ecliptic is caused by the real motion of the earth round the sun, we may regard the ecliptic as a circle marking the intersection of the plane of the earth's orbit with the celestial sphere. In other words, if we were situated on the sun instead of on the earth, we would see the earth travelling round the sky in the circle of the ecliptic. We must keep this fact, that the ecliptic indicates the plane of the earth's orbit, firmly in mind, in order to understand what follows.

The ecliptic is not coincident with the celestial equator, for the following reason: The axis of the earth's daily rotation is not parallel to, or does not point in the same direction as, the axis of its yearly revolution round the sun. As the axis of rotation is perpendicular to the equator, so the axis of the yearly revolution is perpendicular to the ecliptic, and since these two axes are inclined to one another, it results that the equator and the ecliptic must lie in different planes. The inclination of the plane of the ecliptic to that of the equator amounts to about 23½°.

As it is very important to have a clear conception of this subject, we may illustrate it in this way: Take a ball to represent the earth, and around it draw a circle to represent the equator. Then, through the centre of the ball, and at right angles to its equator, put a long pin to represent the axis. Set it afloat in a tub of water, weighting it so that it will be half submerged, and placing it in such a position that the pin will be not upright but inclined at a considerable angle from the vertical. Now, imagine that the sun is situated in the centre of the tub, and cause the ball to circle slowly round it, while maintaining the pin always in the same position. Then the surface of the water will represent the plane of the ecliptic, or plane of the earth's orbit, and you will see that, in consequence of the inclination of the pin, the plane of the equator does not coincide with that of the ecliptic (or the surface of the water), but is tipped with regard to it in such a manner that one half of the equator is below and the other half above it. Instead of actually trying this experiment, it will be a useful exercise of the imagination to represent it to the mind's eye just as if it were tried.

We have said that the inclination of the equator to the ecliptic amounts to 23½°, and this angle should be memorised. Now, since both the ecliptic and the equator are great circles of the celestial sphere, i. e., circles whose planes cut through the centre of the sphere, they must intersect one another at two opposite points. In the experiment just described, these two points lie on opposite sides of the ball, where the equator cuts the level of the water. These points of intersection of the equator and the ecliptic on the celestial sphere are called the equinoxes, or equinoctial points, because when the sun appears at either of those points it is perpendicular over the equator, and when it is in that position day and night are of equal length all over the earth. (Equinox is from two Latin words meaning “equal night.”)

=Saturn=

From a drawing by Trouvelot. ]

=Saturn=

Photographed at the Lick Observatory. ]

We shall have more to say about the equinoxes later, but for the present it is sufficient to remark that one of these points—that one where the sun is about the 21st of March, which is the beginning of astronomical spring—is the “Greenwich of the Sky,” or the vernal equinox. The other, opposite, point is called the autumnal equinox, because the sun arrives there about the 23d of September, the beginning of astronomical autumn. The vernal equinox, as we have already seen, serves as a pointer on the dial of the sky. When it crosses the meridian of any place it is astronomical noon at that place. Its position in the sky is not marked by any particular star, but it is situated in the constellation Pisces, and lies exactly at the crossing point of the celestial equator and the ecliptic. The hour circle, running through this point, and through its opposite, the autumnal equinox, is the prime meridian of the heavens, called the equinoctial colure. The hour circle at right angles to the equinoctial colure, i. e., bearing to it the same relation that the prime vertical does to the meridian (see Sect. 4), is called the solstitial colure. This latter circle cuts the ecliptic at two opposite points, called the solstices, which lie half-way between the equinoxes. Since the ecliptic is inclined 23½° to the plane of the equator, and since the solstices lie half-way between the two crossing points of the ecliptic and the equator, it is evident that the solstices must be situated 23½° from the equator, one above and the other below, or one north and the other south. The northern one is called the summer solstice, because the sun arrives there at the beginning of astronomical summer, about the 22d of June, and the southern one is called the winter solstice, because the sun arrives there at the beginning of the astronomical winter, about the 22d of December. The name solstice comes from two Latin words meaning “the standing still of the sun,” because when it is at the solstitial points its apparent course through the sky is for several days nearly horizontal and its declination changes very slowly.

Now, just as there are two opposite points in the sky at equal distances from the equator, which mark the poles of the imaginary axis about which the celestial sphere makes its diurnal revolution, so there are two opposite points at equal distances from the ecliptic which mark the poles of the imaginary axis about which the yearly revolution of the sun takes place. These are called the poles of the ecliptic, and they are situated 23½° from the celestial poles—a distance necessarily corresponding with the inclination of the ecliptic to the equator. The northern pole of the ecliptic is in the constellation Draco, which you may see any night circling round the North Star, together with the Great Dipper and Cassiopeia.

=9. Celestial Latitude and Longitude.= We have seen that the celestial sphere is marked with imaginary circles resembling the circles of latitude and longitude on the earth, and that in both cases the circles are used for a similar purpose, viz., to determine the location of objects, in one case on the globe of the earth and in the other on the sphere of the heavens. It has also been explained that what corresponds to latitude on the celestial sphere is called declination, and what corresponds to longitude is called right ascension. It happens, however, that these same terms, latitude and longitude, are also employed in astronomy. But, unfortunately, they are based upon a different set of circles from that which has been described, and they do not correspond in the way that right ascension and declination do to terrestrial longitude and latitude. A few words must therefore be devoted to celestial latitude and longitude, as distinguished from declination and right ascension.

Celestial latitude and longitude then, instead of being based upon the equator and the poles, are based upon the ecliptic and the poles of the ecliptic. Celestial latitude means distance north or south of the ecliptic (not of the equator), and celestial longitude means distance from the vernal equinox reckoned along the ecliptic (not along the equator). Celestial longitude runs, the same as right ascension, from west toward east, but it is reckoned in degrees instead of hours. Celestial latitude is measured the same as declination, but along circles running through the poles of the ecliptic instead of the celestial poles, and drawn perpendicular to the ecliptic instead of to the equator. Circles of celestial latitude are drawn parallel to the ecliptic and centring round the poles of the ecliptic, and meridians of celestial longitude are drawn through the poles of the ecliptic and perpendicular to the ecliptic itself. The meridian of celestial longitude that passes through the two equinoxes is the ecliptic prime meridian. This intersects the equinoctial colure at the equinoctial points, making with it an angle of 23½°. The solstitial colure, which it will be remembered runs round the celestial sphere half-way between the equinoxes, is perpendicular to the ecliptic as well as to the equator, and so is common to the two systems of circles. It passes alike through the celestial poles and the poles of the ecliptic. It will also be observed that the vernal equinox is common to the two systems of co-ordinates, because it lies at one of the intersections of the ecliptic and the equator. In passing from one system to the other, the astronomer employs the methods of spherical trigonometry.

Fig. 4. The Ecliptic and Celestial Latitude and Longitude.

C, as in the other figures, is the place of the observer and Z is the zenith, but to avoid complication of details the circle of the horizon is not drawn, only the north-and-south line, N C S, being shown. Eq Eq′ is the equator. Ec Ec′ is the ecliptic. P and P′ are the celestial poles. p and p′ are the poles of the ecliptic. Na is the nadir. V is the vernal equinox, and A the autumnal equinox. The circle through s, parallel to the ecliptic, is a latitude circle. The circle p s p' is the ecliptic meridian of the star s. The circle P V P′ A is the equinoctial colure. The circle p V p′ A is the prime ecliptic meridian. The arc of the ecliptic meridian contained between the ecliptic and s measures the star's latitude. The arc of the ecliptic contained between V and the point where the ecliptic meridian p s p′ meets the ecliptic (or the angle V p s) measures the star's longitude east from V, the vernal equinox. ]

=10. The Zodiac and the Precession of the Equinoxes.= The next thing with which we must make acquaintance is the zodiac. We have learned that the ecliptic is a great circle of the celestial sphere inclined at an angle of 23½° to the equator, and crossing the latter at two opposite points called the equinoxes, and that the sun in its annual journey round the sky follows the circle of the ecliptic. Consequently, the place which the sun occupies at any time must be somewhere on the course of the ecliptic. The fact has been mentioned that as seen from the sun the earth would appear to travel round the ecliptic, whence the ecliptic may be regarded as the projection of the earth's orbit, or path, against the background of the heavens. But, besides the earth there are seven other large planets, Mercury, Venus, Mars, Jupiter, Saturn, Uranus, and Neptune, which, like it, revolve round the sun, some nearer and some farther away. Now, the orbits of all of these planets lie in planes nearly coincident with that of the earth's orbit. None of them is inclined more than 7° from the ecliptic and most of them are inclined only one or two degrees. Consequently, as we watch these planets moving slowly round in their orbits we find that they are always quite close to the circle of the ecliptic. This fact shows that the solar system, i. e., the sun and its attendant planets, occupies a disk-shaped area in space, the outlines of which would be like those of a very thin round cheese, with the sun in the centre. The ecliptic indicates the median plane of this imaginary disk. The moon, too, travels nearly in this common plane, its orbit round the earth being inclined only a little more than 5° to the ecliptic.

Even the early astronomers noticed these facts, and in ancient times they gave to the apparent road round the sky in which the sun and planets travel, in tracks relatively as close together as the parallel marks of wheels on a highway, the name zodiac. They assigned to it a certain arbitrary width, sufficient to include the orbits of all the planets known to them. This width is 8° on each side of the circle of the ecliptic, or 16° in all. They also divided the ring of the zodiac into twelve equal parts, corresponding with the number of months in a year, and each part was called a sign of the zodiac. Since there are 360° in a circle, each sign of the zodiac has a length of just 30°. To indicate the course of the zodiac to the eye, its inventors observed the constellations lying along it, assigning one constellation to each sign. Beginning at the vernal equinox, and running round eastward, they gave to these zodiacal constellations, as well as to the corresponding signs, names drawn from fancy resemblances of the figures formed by the stars to men, animals, or other objects. The first sign and constellation were called Aries, the Ram, indicated by the symbol ♈︎; the second, Taurus, the Bull, ♉︎; the third, Gemini, the Twins, ♊︎; the fourth, Cancer, the Crab, ♋︎; the fifth, Leo, the Lion, ♌︎; the sixth, Virgo, the Virgin, ♍︎; the seventh, Libra, the Balance, ♎︎; the eighth, Scorpio, the Scorpion, ♏︎; the ninth, Sagittarius, the Archer, ♐︎; the tenth, Capricornus, the Goat, ♑︎; the eleventh, Aquarius, the Water-Bearer, ♒︎; and the twelfth, Pisces, the Fishes, ♓︎. The name zodiac comes from a Greek word for animal, since most of the imaginary figures formed by the stars of the zodiacal constellations are those of animals. The signs and their corresponding constellations being supposed fixed in the sky, the planets, together with the sun and the moon, were observed to run through them in succession from west to east.

When this system was invented, the signs and their constellations coincided in position, but in the course of time it was found that they were drifting apart, the signs, whose starting point remained the vernal equinox, backing westward through the sky until they became disjoined from their proper constellations. At present the sign Aries is found in the constellation next west of its original position, viz., Pisces, and so on round the entire circle. This motion, as already intimated, carries the equinoxes along with the signs, so that the vernal equinox, which was once at the beginning of the constellation Aries (as it still is at the beginning, or “first point,” of the sign Aries), is now found in the constellation Pisces.

To explain the shifting of the signs of the zodiac on the face of the sky we must consider the phenomenon known as the precession of the equinoxes, which is one of the most interesting things in astronomy. Let us refer again to the fact that the axis of the earth's daily rotation is inclined 23½° from a perpendicular to the plane of its yearly revolution round the sun, from which it results that the ecliptic is tipped at the same angle to the plane of the equator. Thus the sun, moving in the ecliptic, appears half the year above (or north of) the equator, and half the year below (or south of) it, the crossing points being the two equinoxes. Now, this inclination of the earth's axis is the key to the explanation we are seeking. The direction in which the axis lies in space is a fixed direction, which can be changed only by some outside force interfering. What we mean by this will become clearer if we think of the earth's axis as resembling the peg of a top, or the axis of a gyroscope. When a top is spinning smoothly, with its peg vertical, the peg will remain vertical as long as the spin is not diminished, and no outside force interferes. So, too, the axis of the spinning-wheel of a gyroscope keeps pointing in the same direction so persistently that the wheel is kept from falling. If it is so mounted that it is free to move in any direction, and if then you take the instrument in your hand and turn round with it, the axis will adjust itself in such a manner as to retain its original direction in space. This tendency of a rotating body to keep its axis of rotation fixed applies equally to the earth, whose axis, also, maintains a constant direction in space, except for a slow change produced by outside forces, which change constitutes the phenomenon of the precession of the equinoxes.

We cannot too often recall the fact that the axis of the earth is coincident in direction with that of the celestial sphere, so that the earth's poles are situated directly under the celestial poles. But the poles of the ecliptic are 23½° aside from the celestial poles. If the direction of the earth's axis and with it that of the celestial sphere, did not change at all, then the celestial poles and the poles of the ecliptic would always retain the same relative positions in the sky; but, in fact, an exterior force, acting upon the earth, causes a gradual change in the direction of its axis, and in consequence of this change the celestial poles, whose position depends upon that of the earth's poles, have a slow motion of revolution about the poles of the ecliptic, in a circle of 23½° radius. The force which produces this effect is the attraction of the sun and the moon upon the protuberant part of the earth round its equator. If the earth were a perfect sphere, this force could not act, or would not exist, but since the earth is an oblate spheroid, slightly flattened at the poles, and bulged round the equator, the attraction acts upon the equatorial protuberance in such a way as to strive to pull the earth's axis into an upright position with respect to the plane of the ecliptic. But, in consequence of its spinning motion, the earth resists this pull, and tries, so to speak, to keep the inclination of its axis unchanged. The result is that the axis swings slowly round while maintaining nearly the same inclination to the plane of the ecliptic.

Here, again, we may employ the illustration of a top. If the peg of the top is tipped a little aside, so that the attraction of gravitation would cause the top to fall flat on the table if it were not spinning, it will, as long as it continues to spin, swing round and round in a circle instead of falling. We cannot enter into a mathematical explanation of this phenomenon here, but the reader will find a clear popular account of the whole matter in Prof. John Perry's little book on Spinning Tops. It is sufficient here to say that the attraction of gravitation, tending to make the top fall, but really causing the peg to turn round and round, resembles, in its effect, the attraction of the sun and the moon upon the equatorial protuberance of the earth, which makes the earth's axis turn round in space.

=The Milky Way about Chi Cygni=

Photographed at the Lick Observatory by E. E. Barnard, with the six-inch Willard lens.

Observe the cloud-like forms. ]

Now, as we have said, this slow swinging round of the axis of the earth produces the so-called precession of the equinoxes. In a period of about 25,800 years, the axis makes one complete swing round, so that in that space of time the celestial poles describe a revolution about the poles of the ecliptic, which remain fixed. But since the equator is a circle situated half-way between the poles, it is evident that it must turn also. To illustrate this, take a round flat disk of tin, or pasteboard, to represent the equator and its plane, and perpendicularly through its centre run a straight rod to represent the axis. Put one end of the axis on the table, and, holding it at a fixed inclination, turn the upper end round in a circle. You will see that as the axis thus revolves, the disk revolves with it, and if you imagine a plane, parallel to the surface of the table, passing through the centre of the disk at the point where the rod pierces it, you will perceive that the two opposite points, where the edge of the disk intersects this imaginary plane, revolve with the disk. In one position of the axis, for instance, these points may lie in the direction of the north-and-south sides of the room. When you have revolved the axis, and with it the disk, one quarter way round, the points will lie toward the east and west sides of the room. When you have produced a half revolution they will once more lie toward the north-and-south, but now the direction of the slope of the disk will be the reverse of that which it had at the beginning. Finally, when the revolution is completed, the two points will again lie north-and-south and the slope of the disk will be in the same direction as at the start. In this illustration the disk stands for the plane of the celestial equator, the rod for the axis of the celestial sphere, the imaginary plane parallel to the surface of the table for the plane of the ecliptic, and the two opposite points where this plane is intersected by the edge of the disk for the equinoxes. The motion of these points as the inclined disk revolves represents the precession of the equinoxes. This term means that the direction of the motion of the equinoxes, as they shift their place on the ecliptic, is such that they seem to precess, or move forward, as if to meet the sun in its annual journey round the ecliptic. The direction is from east to west, and thus the zodiacal signs are carried farther and farther westward from the constellations originally associated with them; for these signs, as we have said, are so arranged that they begin at the vernal equinox, and if the equinox moves, the whole system of signs must move with it. The amount of the motion is about 50″.2 per year, and since there are 1,296,000″ in a circle, simple division shows that the time required for one complete revolution of the equinoxes must be, as already stated in reference to the poles, about 25,800 years. A little over 2000 years ago the signs and the constellations were in accord; it follows, then, that about 23,800 years in the future, they will be in accord again. In the meanwhile the signs will have backed entirely round the circle of the ecliptic.

The attentive reader will perceive that the precession of the equinoxes, with its attendant revolution of the celestial poles round the poles of the ecliptic, must affect the position of the North Star. We have already said that that star only happens to occupy its present commanding position in the sky. The star itself is motionless, or practically so, with regard to the earth, and it is the north pole that changes its place. At the present time the pole is about 1° 10, from the North Star, in the direction of the Great Dipper, and it is slowly drawing nearer so that in about 200 years it will be less than half a degree from the star. After that the precessional motion will carry the pole in a circle departing farther and farther from the star, until the latter will have entirely lost its importance as a guide to the position of the pole. It happens, however, that several other conspicuous stars lie near this circle. One of these is Thuban, or Alpha Draconis (not now as bright as it once was), and this star at the time when it served as an indicator of the place of the pole, some 4600 years ago, was connected with a very romantic chapter in the history of astronomy. In the great pyramid of Cheops in Egypt, there is a long passage leading straight toward the north from a chamber cut deep in the rock under the centre of the pyramid, and the upward slope of this passage is such that it is believed to have been employed by the Egyptian astronomer-priests as a kind of telescope-tube for viewing the then pole star, and observing the times of its passage over the meridian—for even the North Star, since it is not exactly at the pole, revolves every twenty-four hours in a tiny circle about it, and consequently crosses the meridian twice a day, once above and once beneath the true pole.

About 11,500 years in the future, the extremely brilliant star Vega, or Alpha Lyræ, will serve as a pole star, although it will not be as near the pole as the North Star now is. At that time the North Star will be nearly 50° from the pole. In about 21,000 years the pole will have come round again to the neighbourhood of Alpha Draconis, the star of the pyramid, and in about 25,800 years the North Star will have been restored to its present prestige as the apparent hub of the heavens.

One curious irregularity in the motion of the earth's poles must be mentioned in connection with the precession of the equinoxes. This is a kind of “nodding,” known as nutation. It arises from variation in the effect of the attraction of the sun and the moon, due to the varying directions in which the attraction is exercised. As far as the sun is concerned, the precession is slower near the time of the equinoxes than in other parts of the year; in other words, it is most rapid in mid-summer and mid-winter when one or the other of the poles is turned sunward. A similar, but much larger, change takes place in the effect of the moon's attraction owing to the inclination of her orbit to the ecliptic. During about nine and a half years, or half the period of revolution of her nodes (see Part III, Section 4), the moon tends to hasten the precession, and during the next nine and a half years to retard it. The general effect of the combination of these irregularities is to cause the earth's poles to describe a slightly waving curve instead of a smooth circle round the poles of the ecliptic. There are about 1400 of these “waves,” or “nods,” in the motion of the poles in the course of their 26,000-year circuit. In accurate observation the astronomer is compelled to take account of the effects of nutation upon the apparent places of the stars.

A very remarkable general consequence of the change in the direction of the earth's axis will be mentioned when we come to deal with the seasons.

=The Great Southern Star-Cluster ω Centauri=

Photographed by S. I. Bailey at the South American Station of Harvard Observatory.

Note the streaming of small stars around the cluster. The cluster itself is globular and its stars are too numerous to be counted, or even to be separately distinguished in the central part. ]

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