Astronomy

CHAPTER I.
THE EARTH AND ITS ROTATION.

It is a common remark that we are creatures of circumstances, and in no sense is this truer than in its application to the conditions under which we view the heavenly bodies. At the commencement of a study of astronomy it is accordingly important to first ascertain as far as possible the nature of the earth on which we are situated, and to determine in what way our observations are affected by our local conditions.

The Horizon.—When we look at the sky we see a vast hemispherical vault of which we seem to occupy the centre. If we are at sea, the water and sky appear to meet at a certain distance, in whatever direction we look. Where these meet we have what is called the visible horizon. On land, the horizon is usually broken up by terrestrial objects, such as hills, buildings, or vegetation, but otherwise the appearances are the same as at sea.

Shape of THE Earth.—When we observe the horizon, whether from land or sea, our eyes are at a certain elevation above the level of the ground or water, as the case may be, and the higher we are situated, the greater is the distance of the visible horizon, although the circular outline is retained. No matter where we may be, the same appearances are noted, and we are thus led to infer that the earth is a globe, as no other shape could appear circular from all points of view.

There are other considerations which lead to the same conclusion with regard to the shape of the earth. One of the most familiar proofs that the earth cannot be flat is found in the aspects of a ship putting out to sea or coming into port, when observed from a somewhat elevated position on shore. A ship does not become visible in its entirety, as it would if diminishing distance were the only cause affecting its visibility; the masts are seen first, and then the lower parts of the vessel gradually make their appearance. This finds a simple explanation in the curvature of the surface of the sea, and as similar appearances can be seen in all parts of the world, a globular form is indicated.

The fact that one may continue to travel westward and yet return to the point of starting, is quite in harmony with the supposition that the earth is globular, but it does not furnish a proof. This facility would evidently be equally afforded by a cylindrical earth, or even by a flat earth of which the Pole occupied the centre.

Still another indication of the rotundity of the earth is given by the phenomena of an eclipse of the moon. On these occasions, as will appear later, the moon passes through the shadow of the earth, and as this shadow is always circular, nothing but a spherical, or nearly spherical, body can be in question.

Size of the Earth Roughly Measured.—Granting then that the earth is spherical, a measurement of its curvature will enable us to determine its size. To do this it is necessary to measure the distance of the visible horizon from the eye at a known elevation. Then it can be shown that if the height of the eye is only a small fraction of the diameter of the earth, the diameter is as many times larger than the distance of the horizon as that distance is greater than the height of the eye. Thus, to an observer whose eye is 5 feet above sea level, the horizon is 2¾ miles distant, while from the top of a lighthouse 66 feet high the sky would appear to meet the sea at a distance of 10 miles. One way in which an approximate measurement may be made is illustrated in Fig. 1. Three posts are placed in line, with their tops at the same height above the surface of some calm stretch of water such as is afforded by a canal. A telescope fixed to the first post, so that its centre is at the top, is directed to the upper end of the third post, and it is seen to sight the middle one at some distance from the top. When the posts are a mile apart, the line joining the two extremes turns out to be 8 inches below the top of the middle one.

In our diagram this 8 inches is represented by the distance b d, and if we imagine an arc of a circle d e concentric with the surface of the water, the part which it intersects on the end post, namely a e, will also be 8 inches. This means that to an eye at a, 8 inches above the surface represented by d e, the visible horizon at d would be a mile distant. Applying the proportion named above, it results that the earth is 7,920 miles in diameter.

Owing to various causes, this method only furnishes a rough indication of the dimensions of our globe; but, if we had no other evidence, the result would suffice to explain that the irregularities of the earth’s surface, though seeming so large to us who dwell upon it, are not inconsistent with the idea that the surface forms part of a sphere. The highest mountains with which we are acquainted do not exceed 5½ miles in height, and this is only ¹⁄₁₄₀₀th part of the earth’s diameter. On a globe 14 inches in diameter, representing the earth, the highest mountains would be less than a hundredth of an inch on the same scale; so that, taking the earth generally, it is practically a smooth globe.

Different Horizons at Different Places.—So far then we have learned that the earth is a globe about 8,000 miles in diameter. This enables us to understand that persons in different parts of the earth will see the sky in different ways. At any given place we can see only what is above our horizon, and it results from the spherical form of the earth that no two observers have precisely the same horizon. If we consider a section of the earth, such as is shown in Fig. 2, an observer at the point a will have a horizon represented in section by the line b c, while the horizon of an observer at d will be represented be e f. It is clear then that an external distant object, such as the sun or a star, which may appear on the horizon in the direction a b, as seen from the point a, will be at a considerable angle above the horizon when seen from the point d.

Sensible and Rational Horizon.—Having this conception of the horizon as a thing terrestrial, we may consider its astronomical relationships a little further. If we imagine the plane of the horizon prolonged until it cuts the distant sphere on which the stars and other celestial bodies seem to lie, it will meet that sphere in what is called the sensible horizon. A parallel plane passing through the centre of the earth is called the rational horizon, but as the starry sphere is at an almost infinite distance, the rational and sensible horizons coalesce into one celestial horizon.

Closely associated with the horizon is the point vertically overhead which is called the zenith, and the point vertically below which is called the nadir. As the plane of the horizon is tangential to the earth’s surface at the point of observation, the zenith is simply the prolongation into space of the line joining the centre of the earth with the place of observation; at the point a in Fig. 2, for example, the zenith is in the direction o a z.

The zenith as thus defined, however, is not the astronomical zenith, but what is called the geocentric zenith. As will appear later, the earth is not truly spherical, so that the direction of gravity does not pass exactly through the earth’s centre, and the astronomical zenith is overhead in the direction of gravity.

Diurnal Motion of the Heavens.—In the day-time, when the sky is clear, we see the sun; at night, we sometimes see the moon, always some stars, and occasionally a comet. If we continue our observations, even for a few hours, we begin to recognise that the heavenly bodies have an apparent movement towards the west, very similar to the daily motion of the sun, with which everyone must have been familiar from childhood.

Continuing such observations, it is found that the great majority of the stars do not appear to change their positions relatively to each other, although their apparent places in the sky are different at different times. These have consequently been called the “fixed stars,” but in the light of our present knowledge, the name is not to be taken too strictly. On account of this seeming fixity, the stars have been divided from very remote times into constellations, or groups, which enable us to name and identify individual members of the starry host. Other bright objects having the appearance of stars, when they are viewed merely by the naked eye, may be seen to change their positions with regard to the stars in that part of the sky in which they appear. These are the planets—the “wandering stars” of the ancients, to whom five were known, namely, Mercury, Venus, Mars, Jupiter, and Saturn.

Comets also are seen to share in the general westward movement of the heavenly bodies, but, in addition, they have another movement relative to the stars situated in the same part of the sky.

If we closely observe the stars in Europe, we shall find some of them rising due east, and setting due west; others, again, will be found to rise in the north-east, and to travel nearly overhead; still others will be seen to rise south of east, attain only a small elevation above the horizon, and pass from our view as far south of west as they rise south of east. One point in the heavens appears stationary, and all the stars seem to traverse their daily courses round this as a centre. This stationary point is the north celestial pole. It is marked by no star, but a fairly conspicuous star is at present only about a degree and a half removed from it The name given to this star is the Pole Star, or Polaris. As seen from London, stars within 51½° from the celestial pole never set, and such stars are said to be circumpolar.

When our place of observation is changed from one of middle latitude to one very near the Equator, these appearances are modified. We still see the stars rising and setting daily, but there will be two points which do not seem to move, one on the northern and the other on the southern horizon. One of these stationary points is identical with that seen from higher latitudes, and the other, which is called the south celestial pole, is diametrically opposite to it What is more, stars which were not visible at all at our first place of observation will be seen in the south. All the stars will rise and set, and will alike be above the horizon for twelve hours.

If we could see the stars from the North Pole, the Pole Star, which is on the horizon of places at the Equator, would be found overhead, and all the stars visible to us would be ever above the horizon. Not only this, not one of the glittering stars which adorns the southern heavens would ever be seen at all.

In place of the rising and setting of stars, which lends such a great interest to their observation in other parts of the world, as seen from the poles the stars will simply travel round and round in circles parallel to the horizon.

To produce the apparent daily revolution of the heavens, and the changes in the appearances observed at different places, one of two causes must be at work; either the celestial bodies themselves must be performing a daily majestic movement from east to west round a motionless earth, or the earth itself must be whirling round from west to east, and so changing the situation of the observer’s horizon with regard to external bodies. In the early days of astronomical observations this observed revolution of the heavens was thought to be real, but, with our present knowledge, we are no longer justified in regarding the earth as occupying a place of any such importance as that of the centre of the universe. By the earth’s rotation, an observer, unless situated exactly at the North or South Pole, is carried round in a circle, and his horizon is gradually swept round so that on one side stars are setting and on the other side rising. The appearances at different places find a simple and sufficient explanation in the varying inclination of the observer’s horizon to the earth’s axis of rotation as the place of observation is changed.

A very simple experiment will assist one to comprehend the varying position of the horizon in different latitudes, and its effect upon the apparent diurnal movement of the heavens. Through the middle of an orange pass a knitting-needle, so that the two together may be taken to represent the earth and its axis. A circular piece of thin card pushed on to the needle at one end will represent the polar horizon, and, if the orange be rotated, it will be at once realised that such movement produces no change in the plane of this horizon, although different points on the visible horizon will be successively brought in line with different groups of stars or other external bodies.

Another piece of card should next be fixed on the orange by means of a pin at a point corresponding to the Equator. Again spinning the model earth on its axis, this horizon will be seen to constantly change its plane with regard to outside objects, and in a manner which perfectly accounts for the apparent movement of the heavens as observed from a point on the Equator.

A third piece of card touching the surface of the orange at an intermediate place will have an oblique movement, and as referred to this plane, the stars appear to traverse their daily rounds in oblique circles.

Experimental Proofs of Rotation.—Not only does a supposed rotation of the earth accord perfectly with all that we can glean from observations of the heavens, but actual demonstrations of the reality of this movement are forthcoming. Sir Isaac Newton suggested one experimental method of setting the matter at rest. The further a thing is removed from the centre of the earth, the greater is the circle which it describes in a day, and the greater, consequently, the speed with which it must travel. Thus the top of a high tower moves more quickly than its base, and the surface of a mine than the bottom of the shaft. A stone let fall from the top of a tower thus starts with a greater forward velocity than that of objects at the base, and when it reaches the earth’s surface, it will be a little east of the point where a plumb-line let down from its starting-point reaches the surface. This experiment has been tried, but there are so many disturbing causes affecting the movement of the falling stone that the results are not very satisfactory, although generally confirming the earths rotation from west to east. Evidently this method would fail at the Pole, and would be most effective at the Equator.

A much more beautiful and perfect proof is furnished by the celebrated Foucault’s pendulum experiment. Again fancying ourselves at the North Pole, let us imagine a long and heavy pendulum, suspended in such a manner that the plane in which it swings is not affected by the earth’s rotation. The trace of such a pendulum on a bed of sand placed beneath it would remain in a constant position if the earth were at rest. As the earth rotates, the bed of sand is twisted round, and the path of the pendulum apparently changes. The experiment was first actually carried out by Foucault in 1851, at the Pantheon in Paris, and it created a widespread interest. Since then, pendulums have been erected in various parts of the world, and all agree in essential results. The experiment can be seen in actual operation in the science section of the South Kensington Museum. The pendulum bob is a very heavy one, and before commencing the experiment, it is held out of the vertical by a loose band, which is fixed to the wall by a piece of string. On burning the string, the band falls off, and the pendulum starts its swing with little or no movement out of a plane. The pendulum bob is suspended by a long piano wire which is attached to a bracket carrying a conical pivot. The pivot rests on an agate plate at the end of a beam, and the weight of the bracket is compensated by an adjustable weight (Fig. 3). When swinging, the pendulum has a constant tendency to remain in one plane, and the turning of the beam beneath the pivot has no effect on the absolute direction of the plane of swing. Beneath the pendulum is a table divided into degrees, and the hourly apparent movement of the plane of swing at Kensington is observed to be nearly 12°.

If the experiment could be performed at the North Pole, the pendulum plane would apparently rotate from east to west, making a complete rotation once a day. At the South Pole the direction of movement would be reversed, but the rate would be the same as at the North Pole. The experiment, however, fails altogether at the Equator, while at places between the Poles and Equator the rate of movement varies with the latitude.

A more compact piece of apparatus for demonstrating the earth’s rotation is the gyroscope, which we also owe to Foucault’s ingenuity. The principle is exactly the same as in the case of the pendulum. A heavy disc is set in very rapid rotation, and is suspended in such a way that its points of support may be turned round without disturbing its plane of rotation. The results obtained with this instrument substantiate those derived from pendulums.

These experimental proofs of the rotation of the earth further teach us the same fact that we learn from observations of the stars, namely, that the earth makes a complete turn on its axis once a day.

Latitude and Longitude.—Having thus arrived at the conclusion that the earth is a globe turning on an axis once in twenty-four hours, the North and South Poles may be defined as the points where the axis of rotation meets the surface, while the Equator is the circle passing through places midway between the Poles. Imaginary circles passing round the earth through the Poles are called meridians, while circles parallel to the Equator are called parallels. These conceptions enable us to define very precisely the situation of any particular place upon the terrestrial sphere. We measure its angular distance from the Equator, as seen from the centre of the earth, and call this its latitude; London, for instance, is 51½° north of the Equator, and this is abbreviated to lat. 51½°N. All places on the same parallel have the same latitude, so that another measurement is required to designate the exact location of any one place. For this purpose the meridian passing through some place is agreed upon as a start-point, and we can then say that the place in question is so many degrees east or west; such a measurement represents the longitude of the place. At present there is no universal agreement as to the initial meridian, but in all British maps the meridian passing through the centre of the transit instrument at the Royal Observatory, Greenwich, is taken as the start-point. Longitudes are reckoned up to 180° E. and 180° W. New York, for example, is in long. 73° 58′ W., and Berlin in long. 13° 24′ E.

The Cardinal Points.—For general convenience in expressing the situation of an object, it is usual to say that it is towards the north, south, south-west, etc., as the case may be. A north or south line at any place, or a meridian line, as it is called, is in the direction of the terrestrial meridian passing through the place. The north point of the horizon is thus the point in which the meridian line meets the horizon towards the North Pole. The opposite point is south; while the east and west points lie in the directions at right angles. There are various ways in which a meridian line may be drawn. One of the simplest is to erect a vertical rod and to observe when its shadow thrown by the sun is shortest; at that moment the shadow marks the direction of north and south. This method is not very exact, as it is so difficult to tell when the shadow is shortest. A more accurate result may be obtained by drawing a circle round the stick as centre, and noting the points on this circle reached by the end of the shadow before and after noon; the point midway between these, marks the position of the shadow when shortest. By taking the average result of observations made with more than one circle, a good approximation can be obtained.

For a somewhat rough determination of the direction of the cardinal points, a watch showing the correct time may be utilised. Directing the hour hand to the sun, the south point will lie midway between that and XII. In the case of a watch having a dial marked up to XXIV., and reading XII. at mid-day, the latter figure would always point to the south when the hand indicating the hour was directed towards the sun. This will be easily understood if it be remembered that the sun is in the south at intervals of (approximately) twenty-four hours.

Day and Night.—The succession of days and nights by which our daily arrangements are regulated is at once explained by the fact that the earth is round, and turns on its axis once a day. At any particular instant of time the sun can only shine on that half of the earth which is turned towards it. At all places included in the illuminated part the sun will be above the horizon, and it will be day. One half of the earth will be turned away from the sun, and to all places in that part it will be night. Under the conditions represented in Fig. 4, to a person situated at the point P it will be midnight; he will, however, be carried by the earth’s rotation along the circle P Q R; when he arrives at a point on a b, the sun will be rising to him, and his day will commence. On reaching the point R the sun will be on the spectator’s meridian, and it will be noon. After another interval he will arrive at the boundary of light and shade, and his night will commence.

Atmospheric Refraction.—In common with other substances through which light can pass, the atmosphere by which the earth is surrounded has the effect of bending rays of light out of their courses, and on account of this we do not see the heavenly bodies in their true positions. If the air were of uniform density the effect of this refraction would be as illustrated to the left in Fig. 5. The light from a star S will reach the observer at O after striking the atmospheric shell at a and being refracted along the line a O; consequently the observer will see it in the direction O S′, and not in the direction O S, which it would have if the air were absent. As a matter of fact, the atmosphere becomes less dense in passing upwards, so that the rays of light are subjected to a succession of small deviations; two such refractions are illustrated at the right of Fig. 5. When a star is overhead there is no refraction, and the greatest displacements of a star’s positions are produced on the horizon, where the light has to pass through a great thickness of atmosphere.

Refraction always makes the heavenly bodies appear higher in the sky than they otherwise would be, and some very curious effects can be traced to it. Thus the sun becomes visible on account of refraction some time before it has actually risen, and remains visible for a little while after it has really descended below the horizon. The amount of refraction varies with the temperature and pressure of the air, but the average amounts for different elevations above the horizon are as follows:

Refraction is responsible, among other things, for the curiously distorted appearances of the sun and moon, when they are very near the horizon.

Twilight.—The atmosphere, or rather the solid and liquid particles which it always contains, has the property of reflecting light, and hence it does not suddenly become dark when the sun has set. Even until the sun has descended 18° below the horizon, the upper parts of the air continue to reflect his beams, and this is the origin of twilight. In the tropics the sun sets almost vertically, so that it gets below the twilight limit comparatively quickly, and this explains the short twilight which is remarked by all who have visited a tropical country. In our own country the sun has an apparent oblique motion, and a relatively long period elapses before twilight ends. The increase in the duration of twilight is, indeed, very noticeable in merely travelling from London to the north of Scotland in summer-time.

Within the Arctic Circle, at places where the sun itself is never visible for months together, its reflected beams in the form of twilight may be seen for months.

Apparent Movements of the Sun.—During any day on which we may observe the sun, it will be seen to rise at a certain place on the horizon, gradually ascend into the heavens to a certain point, then as steadily sink towards the west until it disappears at some point on the western horizon. If we watch the sun about the 20th of March, we shall find it to rise due east, and set due west; it will be above the horizon for exactly twelve hours, and below for the same length of time. When this happens, we have the vernal or spring equinox, as the nights are then equal in all parts of the world. From this time to the third week in June, we shall find the sun to rise more and more to the north of east, and to set gradually further north of west. This is accompanied by a daily increase in the apparent height of the sun at noon, and by increasing length of day and reduction of night. For some days before the 21st of June the change of the sun’s place of rising and setting is very slow, and after this day the places of rising and setting begin to recede to the south. We then have the summer solstice, so-called because the sun seems to stand still, in so far as its northward travel is concerned. The point of rising or setting of the sun goes on moving nearer to the south point of the horizon, until about September 22, we again have the sun above the horizon for twelve hours, and below the horizon for an equal period; this is the autumnal equinox. The southward movement is continued until December 21, after which the rising begins to take place further towards the north. When furthest south, we have the winter solstice in the Northern Hemisphere, the sun being above the horizon for only a short time, and reaching only a small altitude at noon. From December 21 to March 20, the sun rises further to the north, at first very gradually, and afterwards more rapidly. These varying amounts of sunshine correspond to the short days of winter, and the long days of summer. A diagrammatic representation of the apparent path of the sun at the solstices and equinoxes for some place, such as London, is given in Fig. 6.

It is clear, then, that our relations to the sun are very different from our relation to the stars, inasmuch as the apparent position of the sun, as projected upon the sky, is constantly changing, but returns to similar conditions at the end of a year. If our place of observation is changed, the apparent diurnal movement of the sun is affected in the same way as that of the stars.

To explain these annual changes of the sun, with regard to an observer’s horizon, it is only necessary to suppose that the sun marches northwards towards the celestial pole from the winter to the summer of the Northern Hemisphere, and southwards from summer to winter. It is not to be imagined, however, that this apparent movement towards or from the north celestial pole is necessarily a real movement of the sun; we shall, in fact, very shortly see that it is only an apparent movement due to the changing situation of the earth with respect to the sun.

The Ecliptic.—A very small amount of actual observation, without the aid of instruments, suffices to show that the changes in the sun’s relation to any observers horizon at different parts of the year are associated with a change in its situation among the stars. If we direct our gaze towards the south at midnight, we are looking towards that part of space which is directly opposite to the sun, as will be evident from Fig. 4, and if the sun’s apparent movement were only in a polar direction, we should always see the same stars in the same part of the sky at the same hour. Such, however, is not the case. The stars are found more and more towards the west at the same hour as the year advances. Sirius, for instance, is due south about midnight on December 31; but at the end of January it will pass through the south point shortly before ten P.M. Similar changes are noted in the case of all the stars, and they indicate either an easterly movement of the sun among the stars, or a westerly motion of the stars with regard to the sun. If it were possible to see the stars in the immediate neighbourhood of the sun, this relative motion could be directly observed; but under the actual circumstances, the apparent track of the sun amongst the stars must be determined indirectly. When we make observations at midnight, we know that the sun is opposite to stars which are due south at that moment; and the height which it reaches above the horizon at noon indicates its angular distance from the celestial pole. It is thus possible to trace the sun’s apparent path on a map of the stars, or upon a celestial globe; this is called the ecliptic, and it is found to be a great circle of the celestial sphere—that is, it is a circle contained in a plane which passes through the centre of the sphere.

The observed movement of the sun among the stars might be produced either by a revolution of the sun round the earth in a year, or by a revolution of the earth round the sun in the same period, the stars being supposed at rest at a greater distance than the sun. There are many phenomena which indicate that it is the earth which moves round the sun, but the most direct proof is found in what is known to astronomers as the aberration of light.

Aberration as a Proof of the Earth’s Revolution.—While engaged on an observation having for its object the determination of the distance of a star, Dr. Bradley made a discovery of very great interest and importance to astronomers. What he found practically amounts to this, that in order to see a star exactly at the centre of the field of view of a telescope we must direct the optical axis of the instrument at a small angle to the line joining the earth and star, irrespective of other deviations, such as that produced by refraction. The direction of this displacement is constantly changing throughout the year, but it is common to all the stars, and the fact that the original apparent position is regained at the end of a year at once associates aberration with a revolution of the earth round the sun.

In Fig. 7 we have a perspective view of the earth’s orbit with the sun at S. A star s would appear in the direction A s when seen from the earth, supposed at rest at the point A; actually it is seen at a, ahead of its place, and in the course of a year it describes the aberrational orbit, a b c d, these points corresponding to positions A B C D of the earth in its annual path.

As a result of aberration, then, each star appears to revolve once a year in a small elliptic path about its average position. The breadths of these ellipses vary according to their angular distances from the ecliptic, but all have precisely the same length of about 41″. Half the length of the ellipses, which amounts to 20″.5, is accordingly called the constant of aberration.

The fact that the earth’s velocity in its orbit forms a sensible fraction of the velocity of light is the cause of aberration. If we let an object fall down the middle of a tube which is at rest, it will fall to the bottom without touching the side if the tube be held vertically. When the tube has a forward movement, however, it must be inclined at an angle in order that the falling body may pass clear to the bottom, and the greater the speed of the tube the more it must be inclined. So it is with light which comes from a star and traverses the tube of a telescope situated on a moving earth; the tube must be inclined to the actual path of the light rays.

Other proofs that it is the earth which moves round the sun are furnished by the parallaxes of the stars, and by spectroscopic measures of the earth’s velocity.

Approximate Scale of Earth’s Orbit.—A very beautiful application of the constant of aberration is in the measurement of the distance of the earth from the sun. We have only to bear in mind that the apparent size of the sun does not change very much, in order to realise that the path of the earth must be very nearly a circle; if the distance changed very much there would be a correspondingly great change in the sun’s apparent diameter. Now the constant of aberration is a measure of the relative velocity of the earth in its orbit and the velocity of light. There are several ways of determining the velocity of light, and it is known to be very nearly 186,300 miles per second. In a right-angled triangle having one angle equal to the constant of aberration, the side opposite to this angle would represent the velocity of the earth, if the longer side represented that of light. In such a triangle the proportion between these sides would be nearly as 1 to 10,000. That is, the velocity of light is about 10,000 times that of the earth in its orbit. The earth’s velocity is thus found to be about 18½ miles per second, so that the distance which it traverses in a year is found by a simple multiplication. In this way the circumference of the earth’s orbit is obtained, and it is easily deduced that the radius of the orbit, which is nothing more than the sun’s distance, is not far from 93,000,000 miles.

The Zodiac.—The space about 8° above and below the ecliptic constitutes what is called the zodiac. The zodiac is of very great antiquity, and marks out the region traversed by the sun and all the planets known to the ancients. It is divided into twelve parts of 30° each, called signs of the zodiac, from the supposed outlines of animals, etc., marked out by the stars. The names of these signs are probably familiar to everyone from the well-known rhyme:

The astronomical names and symbols corresponding to these are as follows:—

The sun enters the sign Aries at the vernal equinox in March, and the others in successive months. On account of the precession of the equinoxes (see p. 69), however, the sun no longer enters the constellation Aries at the vernal equinox, but it is still said to enter the sign Aries.

Inclination of the Earth’s Axis.—The revolution of the earth round the sun provides us with a very satisfactory explanation of the apparent easterly movement of the sun among the stars. There is, however, another very important point. We have seen that during a year the sun has a movement towards and from the Pole, as well as an easterly movement. The plane of the earth’s orbit, therefore, cannot be coincident with the plane of the Equator; if it were, the sun would have the same apparent movement every day—it would always rise due east, and set due west, in all parts of the earth. The ecliptic, moreover, would be coincident with the celestial equator. When the ecliptic is determined by observations in the way already explained (p. 57), it is found to intersect the celestial equator in two points, and the plane containing it is inclined at an angle of very nearly 23½° to the equatorial plane. This inclination of the Equator to the ecliptic, or “obliquity of the ecliptic,” indicates that the earth’s axis of rotation is inclined to the plane in which the revolution round the sun is performed, the actual inclination being about r66½°.

Further, the axis of rotation must remain parallel to itself during the revolution of the earth. Otherwise, the situation of the celestial pole would be seen to change, and the Pole Star would no longer serve to show us which way lies north.

It is precisely this inclination of the earth’s axis which brings about the varying lengths of days and nights which we associate with different seasons.

The Seasons.—Let us in the first place contrast the conditions in summer with those which obtain in winter. Imagine that we can view the sun and earth from a very distant point lying in the plane of the ecliptic, and situated so that a line joining it with the sun is perpendicular to the line joining the sun and earth in summer or winter.

The sun will thus appear in some position represented by O in Fig. 8; in the summer of the Northern Hemisphere the earth will be in the position S, and in winter in the position W, since it travels half way round its orbit in six months’ time. An observer situated at London will be 38½° from the North Pole, and he is represented by the point A in our diagram. The horizon at noon of such an observer is represented by the line H R, tangential to the surface of the sphere at the point A. At noon, then, the altitude of the sun is equal to the angle O A H. When it is winter in the Northern Hemisphere, the earth’s axis is inclined away from the sun, and our observer at London is so situated that at noon his horizon is the line H′ R′, while the sun’s altitude is the angle O A′ R′, which is no less than 47° smaller than in summer. People who dwell in the Southern Hemisphere enjoy the long days of summer at the time when our own days are shortest, and vice versâ, and the reason for this is clearly that when the position of the earth’s axis presents the greatest part of the Northern Hemisphere towards the sun, the greater part of the southern half of our globe is turned away from the sun.

At the equinoxes, which occur very nearly midway between the solstices, the earth’s axis is directed neither towards nor away from the great source of light and heat, so that both hemispheres are presented to the sun under exactly the same conditions. This state of affairs is shown diagrammatically in Fig. 9. The sun’s altitude at noon at the commencement of spring is equal to that at the beginning of autumn, and depends only upon the observer’s latitude. The half of our globe which is then flooded with the sun’s rays comprises both the North and South Poles, and it is evident that as the earth turns round, every place upon it, whether in Arctic or equatorial regions, receives the benefit of twelve hours sunshine, and at the same time has a night of twelve hours duration.

The Midnight Sun.—The facilities which are now offered for foreign travel have induced many people to pay a visit to the north of Norway, one of the objects in view frequently being to witness the so-called “midnight sun.” It seems somewhat paradoxical to speak of night when the sun is above the horizon, but it simply means that in high latitudes the sun may be seen over the northern horizon when it is midnight at places further south which have the same longitude. We have seen that in our own country there are certain stars which never set, and when we get to the Pole itself, all the stars which are there visible will present this peculiarity.

In order to see the sun at midnight, then, what we have to do is to travel towards the Pole until we reach a latitude where the sun itself becomes circumpolar. At the Pole this would be the state of things during the whole of the northern summer, when the sun is north of the Equator, and since the sun never travels northward more than 23½°, it can only be circumpolar at places within that angular distance from the Pole, that is, within the Arctic Circle.