Astronomy in a nutshell

1. Nature, Shape, and Size of the Earth. The situation of the earth in the universe has been briefly described in Part I; it remains now to see what the earth is in itself, and what are some of the principal phenomena connected with it as a celestial body inhabited by observant and reasoning beings.

We know by ordinary experience that the earth is composed of rock, sand, soil, etc., and generally covered, where there is no running or standing water in the form of rivers, lakes, or seas, with vegetation, such as trees and grass. Further experience teaches us that the earth is very large, and that its surface is divided into wide areas of land and of water. The largest bodies of water, the oceans, taken all together, cover about 72 per cent., or nearly three-quarters of the entire surface of the earth. Investigations carried as far down as we can go show that the interior of the earth consists of various kinds of rock, in which are contained many different kinds of metals. While there is reason for thinking that a high degree of temperature prevails deep in the earth, yet it appears evident, for other reasons, that, taken as a whole, it is solid and very rigid throughout. By methods, the history and description of which we have not here sufficient space to give, it has been proved that the earth is, in form, a globe, or more strictly an ellipsoid, slightly drawn in at the poles and swollen round the equator. The polar diameter is 7899 miles, and the equatorial diameter 7926 miles, the difference amounting to only 27 miles. Thus, for ordinary purposes, we may regard the earth as being a true sphere. The level of its surface, however, is varied by hills and mountains, which, though insignificant in comparison with the size of the whole earth, are enormous when compared with the structures of human hands. The loftiest known mountain on the earth, Mt. Everest in the Himalayas, has an elevation of 29,000 feet above sea-level, and the deepest known depression of the ocean bottom, near the island of Guam in the Pacific, sinks 31,614 feet below sea-level. Thus, the apex of the highest mountain is about eleven and a half miles in vertical elevation above the bottom of the deepest pit of the sea—a distance very considerably less than half the difference between the equatorial and polar diameters of the earth.

It is believed that at the beginning of its history the earth was a molten mass, or perhaps a mass of hot gases and vapours like the sun, and that it assumed its present shape in obedience to mechanical laws, as it cooled off. The rotation caused it to swell round the equator and draw in at the poles.

The outer part of the earth is called its crust, and geology shows that this has been subject to violent changes, such as upheavals and subsidences, and that in many places sea and land have interchanged places, probably more than once. Geology also shows that the rocks of the earth's crust are filled with the remains, or fossils, of plants and animals differing from those now existing, though related to them, and that many of these must have lived millions of years ago. Thus we see that the earth bears marks of an immense antiquity, and that it was probably inhabited during vast ages before the race of man had been developed. The origin of life upon the earth is unknown.

2. The Attraction of Gravitation. Among the phenomena of life upon the earth, which are so familiar that only thoughtful persons see anything to wonder at in them, is what we call the “weight” of bodies. Every person feels that he is held down to the ground by his weight, and he knows that if he drops a heavy body it will fall straight toward the ground. But what is this weight which causes everything either to rest upon the earth or to fall back to it if lifted up and dropped? The answer to this question involves a principle, or “law,” which affects the whole universe, and makes it what we see it. This principle is one of the great foundation stones of astronomy. It is called the law of gravitation, the word gravitation being derived from the Latin gravis, “heavy.” Briefly stated, the law is that every body, or every particle of matter, attracts, or strives to draw to itself, every other body, or particle of matter. This force is called the attraction of gravitation. A large body possesses more attractive force than a small one, in proportion to the mass, or quantity of matter, that it contains. The earth, being extremely large, holds all bodies on its surface with a force proportionate to its great mass. This explains why we possess what we call weight, which is simply the effect of the attraction of the earth upon our bodies. A large body is heavier, or drawn with more force by the earth, than a small one (composed of the same kind of matter), because it has a greater mass. The body really attracts the earth as much as the earth attracts the body, but the amount of motion caused by the attraction is proportional to the respective masses of the attracting bodies, and since the mass of the earth is almost infinitely great in comparison with that of any body that we can handle, the motion which the latter imparts to the earth is imperceptible, and it is the small body only that is seen to move under the force of the attraction.

Now we are going to see how vastly important in its effects is the fact that the earth is spherical in form. Sir Isaac Newton, who first worked out mathematically the law of gravitation, proved that a spherical body attracts, and is attracted, as if its entire mass were concentrated in a point at its centre. From this it follows that the attraction of the earth is exercised just as if the whole attractive force emanated from a middle point, and, that being so, the effect of the attraction is to draw bodies from all sides toward the centre of the earth. This explains why people on the opposite side of the earth, or under our feet, as we say, experience the same attractive force, or have the same weight, that we do. All round the earth, no matter where they may be situated, objects are drawn toward the centre. If at any point on the earth you suspend a plumb-line, and then, going one quarter way round, suspend another plumb-line, each of the lines will be vertical at the place where it hangs, and yet, the directions of the two lines will be at right angles to one another, since both point toward the centre of the earth.

Knowing the manner in which the earth attracts, we have the means of determining its entire mass, or, as it is sometimes called, the weight of the earth. The principle on which this is done is easily understood, Suppose, for instance, that a small ball of lead, of known weight, is brought near a large ball, and delicately suspended in such a way that, by microscopic observation, the movement imparted by the attraction of the large ball can be measured. The force required to produce this movement can be compared with the force of the earth's attraction which produces the weight of the ball, and thus the ratio of the mass of the earth to that of the ball is determined. The total mass of the earth has been found to be equivalent to a “weight” of about 6,500,000,000,000,000,000,000 tons. The mean density of the earth compared with that of water is found to be about 5½, that is to say, the earth weighs 5½ times as much as a globe of water of equal size.

Newton did not stop with showing the manner of the earth's attraction upon bodies on or near its surface; he proved that the earth attracted the moon also, and thus retained it in its orbit. To understand this we must notice another fact concerning the manner in which gravitation acts. Its force varies with distance. Experiment followed by mathematical demonstration, has proved that the variation of the attraction is inversely proportional to the square of the distance. This simply means that if the distance between the two bodies concerned is doubled, the force of attraction will be diminished four times, 4 being the square of 2; and that if the distance is halved, the force will be increased fourfold. Increase the distance three times, and the force diminishes nine times; diminish the distance three times, and the force increases nine times, because 9 is the square of 3, and, as we have said, the force varies inversely, or contrarily, to the change of distance. Knowing this, Newton computed what the force of the earth's attraction must be on the moon, and he found that it was just sufficient to keep the latter moving round and round the earth. But why does not the moon fall directly to the earth? Because the moon had originally another motion across the direction of the earth's attraction. How it got this motion is a question into which we cannot here enter, but, if it were not attracted by the earth (or by the sun), the moon would travel in a straight line through space, like a stone escaping from a sling. The force of the attraction is just sufficient to make the moon move in an orbital path about the earth.

The same principle was extended by Newton to explain the motion of the earth around the sun. The force of the sun's attraction, calculated in the same way, can be shown to be just sufficient to retain the earth in its orbit and prevent it from travelling away into space. And so with all the other planets which revolve round the sun. And this applies throughout the universe. There are certain so-called double, or binary, stars, which are so close together that their attraction upon one another causes them to revolve in orbits about their common centre. In truth, all the stars attract the earth and the sun, but the force of this attraction is so slight on account of their immense distance that we cannot observe its effects. The reader who wishes to pursue this subject of gravitational attraction should consult more extensive works, such as Prof. Young's General Astronomy, or Sir George Airy's Gravitation.

3. The Tides. The tides in the ocean are a direct result of the attraction of gravitation. They also involve in an interesting way the principle that a spherical body, like the earth, attracts and is attracted as if its entire mass were concentrated at its centre. The cause of the tides is the difference in the attraction of the sun and moon upon the body of the earth as a rigid sphere, and upon the water of the oceans, as a fluid envelope whose particles, while not free to escape from the earth, are free to move, or slide, among one another in obedience to varying forces. The difference of the force of attraction arises from the difference of distance. Since the moon, because of her relative nearness, is the chief agent in producing tides we shall, at first, consider her tidal influence alone. The diameter of the earth is, in round numbers, 8000 miles; therefore, its radius is 4000 miles. From this it follows that the centre of the earth is 4000 miles farther from the moon than that side of the earth which is toward her at any time, and 4000 miles nearer than the side which is away from her. Consequently, her attraction must be stronger upon the water of the ocean lying just under her than upon the centre of the earth, and it must also be stronger upon the centre of the earth than upon the water of the ocean lying upon the side which is farthest from her. The result of these differences in the force of the moon's attraction is that the water directly under her tends away from the centre of the earth, while, on the other hand, the earth, considered as a solid sphere, tends away from the water on the side opposite to that where the moon is, and these combined tendencies cause the water to rise, with regard to its general level, in two protuberances, situated on opposite sides of the earth. These we call tides.

Some persons, when this statement is made, inquire: “Why, then, does not the moon take the water entirely away from the earth?” The answer is, that the effect of the tidal force is simply to diminish very slightly the weight of the water, or its tendency towards the earth's centre, but not to destroy, or overmaster, the gravitational control of the earth. The water retains nearly all its weight, for the tidal force of the moon diminishes it less than one part in 8,000,000. Still, this slight diminution is sufficient to cause the water to swell a little above its general level, at the points where it feels the effect of the tidal force. On the other hand, around that part of the earth which is situated half-way between the two tides, or along a diameter at right angles to the direction of the moon, the latter's attraction increases the weight of the water, i. e., its tendency toward the earth's centre (see Fig. 6). Perhaps this can better be understood, if we imagine the earth to be entirely liquid. In that case the difference in the force of the moon's attraction with difference of distance would be manifested in varying degrees throughout the earth's whole frame, and the result would be to draw the watery globe out into an ellipsoidal figure, having its greatest diameter in the line of the moon's attraction, and its smallest diameter at right angles to that line. The proportions of the ellipsoid would be such that the forces would be in equilibrium.

Owing to a variety of causes, such as the rotation of the earth on its axis, which carries the water rapidly round with it; the inertia of the water, preventing it from instantly responding to the tidal force; the irregular shape of the oceans, interrupted on all sides by great areas of land; their varying depth, producing differences of friction, and so on, the tidal waves do not appear directly under, or directly opposite to, the moon, and the calculation of the course and height of the actual tides, at particular points on the earth, becomes one of the most difficult problems in astronomical physics.

We now turn to consider the effects of the sun's tidal force in connection with that of the moon. This introduces further complications. The solar tides are only about two-fifths as high as the lunar tides, but they suffice to produce notable effects when they are either combined with, or act in opposition to, the others. They are combined twice a month—once when the moon is between the earth and the sun, at the time of new moon; and again when the moon is in opposition to the sun, at the time of full moon. In these two positions the attractions of the sun and the moon must, so to speak, act together, with the result that the tides produced by them blend into a single greater wave. This combination produces what are called spring tides, the highest of the month. When, on the other hand, the moon is in a position at right angles to the direction of the sun, which happens at the lunar phases named first and last quarters, the solar and the lunar tides have their crests 90° apart, and, in a sense, act against one another, and then we have the neap tides, which are the lowest of the month.

Without entering into a demonstration, it may here be stated as a fact to be memorised, that the tidal force exerted by any celestial body varies inversely as the cube of the distance. This is the reason why the sun, although it exceeds the moon in mass more than 25,000,000 times, and is situated only about 400 times as far away from the earth, exercises comparatively so slight a tidal force on the water of the ocean. If the tidal force varied as the square of the distance, like the ordinary effects of gravitation, the tides produced by the sun would be more than 150 times as high as those produced by the moon, and would sweep New York, London, and all the seaports of the world to destruction. In that case it might be possible, by delicate observations, to detect a tidal effect produced upon the oceans of the earth by the planet Jupiter.

4. The Atmosphere. The solid globe of the earth is enveloped in a mixture of gases, principally oxygen and nitrogen, which we call the air, or the atmosphere, and upon whose presence our life and most other forms of life depend. The atmosphere is retained by the attraction of the earth, and it rotates together with the earth. If this were not so—if the atmosphere stood fast while the earth continued to spin within it—a terrific wind would constantly blow from the east, having a velocity at the equator of more than a thousand miles an hour.

Exactly how high the atmosphere extends we do not know—it may not have any definite limits—but we do know that its density rapidly diminishes with increase of height above the ground, so that above an elevation of a few miles it becomes so rare that it would not support human life. The phenomena of meteors, set afire by the friction of their swift rush through the upper air, prove, however, that there is a perceptible atmosphere at an elevation of more than a hundred miles.

From an astronomical point of view, the most important effect of the presence of the atmosphere is its power of refracting light. By refraction is meant the property possessed by every transparent medium of bending, under particular circumstances, the rays of light which enter it out of their original course. The science of physics teaches us that if a ray of light passes from any transparent medium into another which is denser, and if the path of this ray is not perpendicular to the surface of the second medium, it will be turned from its original course in such a way as to make it more nearly perpendicular. Thus, if a ray of light passes from air into water at a certain slope to the surface, it will, upon entering the water, be so changed in direction that the slope will become steeper. Only if it falls perpendicularly upon the water will it continue on without change of direction. Conversely a ray passing from a denser into a rarer medium is bent away from a perpendicular to the surface of the first medium, or its slope becomes less. This explains why, if we put a coin in a bowl, with the eye in such a position that it cannot see the coin over the edge, and then fill the bowl with water, the coin seems to be lifted up into sight. Moreover, if any transparent medium increases in density with depth, the amount of refraction will increase as the ray goes deeper, and the direction of the ray will be changed from a straight line into a curve, tending to become more and more perpendicular.

Now all this applies to the atmosphere. If a star is seen in the zenith, its light falls perpendicularly into the atmosphere and its course is not deviated, or in other words there is no refraction. But if the star is somewhere between the zenith and the horizon, its light falls slopingly into the atmosphere, and is subject to refraction, the amount of bending increasing with approach to the horizon. Observation shows that the refraction of the atmosphere, which is zero at the zenith, increases to about half a degree (and sometimes much more, depending upon the state of the air), near the horizon. It follows that a celestial object seen near the horizon will ordinarily appear about half a degree above its true place. Since the apparent diameters of the sun and the moon are about half a degree, when they are rising or setting they can be seen on the horizon before they have really risen above it, or after they have really sunk below it. Tables of refraction at various altitudes have been prepared, and they have to be consulted in all exact observations of the celestial bodies.

5. Dip of the Horizon. Another correction which has to be applied in many observations depends upon the sphericity of the earth. We have described the rational horizon, and pointed out how it differs from the sensible horizon. We have also said that at sea the sensible horizon nearly accords with the rational horizon (see Part I, Sect. 3). But the accord is not complete, owing to what is called the dip of the horizon. In fact, the sea horizon lies below the rational horizon by an amount varying with the elevation of the eye above the surface. Geometry enables us to determine just what the dip of the horizon must be for any given elevation of the eye. A rough and ready rule, which may serve for many purposes, is that the square root of the elevation of the eye in feet equals the dip of the horizon in minutes of arc, or of angular measure. The reader will readily see that the dip of the horizon is a necessary consequence of the rotundity of the earth. It is because of this that, as a ship recedes at sea her hull first disappears below the horizon, and then her lower sails, and finally her top-sails. The use of a telescope does not help the matter, because a telescope only sees straight, and cannot bend the line of sight over the rim of the horizon. Atmospheric refraction, however, enables us to see an object which would be hidden by the horizon if there were no air. In navigation, which, as a science, is an outgrowth of astronomy, these things have to be carefully taken into account.

6. Aberration. A few words must be said about the phenomenon known as aberration of light. This is an apparent displacement of a celestial object due to the motion of the earth in its orbit. It is customary to illustrate it by imagining oneself to be in a shower of rain, whose drops are falling vertically. In such a case, if a person stands fast the rain will descend perpendicularly upon his head, but if he advances rapidly in any direction he will feel the drops striking him in the face, because his own forward motion is compounded with the downward motion of the rain so that the latter seems to be descending slantingly toward him. The same thing happens with the light falling from the stars. As the earth advances in its orbit it seems to meet the light rays, and they appear to come from a direction ahead of the flying earth. The result is that, since we see a star in the direction from which its light seems to come, the star appears in advance of its real position, or of the position in which we would see it if the earth stood fast. The amount by which the position of a star is shifted by aberration depends upon the ratio of the earth's velocity to the velocity of light. In round numbers this ratio is as 1 to 10,000. The motion of the earth being in a slightly eccentric ellipse, the stars describe corresponding, but very tiny, ellipses once every year upon the background of the sky. But the precise shape of the ellipse depends upon the position of the star on the celestial sphere. If it is near one of the poles of the ecliptic, it will describe an annual ellipse which will be almost a circle, its greater diameter being 41″ of arc. If it is near the plane of the ecliptic, it will describe a very eccentric ellipse, but the greater diameter will always be 41″, although the shorter diameter may be immeasurably small. The effects of aberration have to be allowed for in all careful astronomical observation either of the sun or the stars. This is done by reducing the apparent place of the object to the place it would have if it were seen at the centre of its annual ellipse.

7. Time. Without astronomical observations we could have no accurate knowledge of time. The basis of the measurement of time is furnished by the rotation of the earth on its axis. We divide the period which the earth occupies in making one complete turn into twenty-four equal parts, or hours. The ascertainment of this period, called a day, depends upon observations of the stars. Suppose we see a certain star exactly on the meridian at some moment; just twenty-four hours later that star will have gone entirely round the sky, and will again appear on the meridian. The revolving heavens constitute the great clock of clocks, by whose movements all other clocks are regulated. We know that it is not the heavens which revolve, but the earth which rotates, but for convenience we accept the appearance as a substitute for the fact. The rotation of the earth is so regular that no measurable variation has been found in two thousand years. We have reasons for thinking that there must be a very slow and gradual retardation, owing principally to the braking action of the tides, but it is so slight that we cannot detect it with any means at present within our command.

In Part I it was shown how the passage across the meridian of the point in the sky called the vernal equinox serves to indicate the beginning of the astronomical “day,” but the position of the vernal equinox itself has to be determined by observations on the stars. By means of a telescope, so mounted that it can only move up or down, round a horizontal axis, and with the axis pointing exactly east and west so that the up and down movements of the telescope tube follow the line of the meridian, the moment of passage across the meridian of a star at any altitude can be observed. Observations of this nature are continually made at all great government observatories, such as the observatory at Washington or that at Greenwich, and at many others, and by their means clocks and chronometers are corrected, and a standard of time is furnished to the whole world.

There are, however, three different ways of reckoning time, or, as it is usually said, three kinds of time. One is sidereal time, which is indicated by the passage of stars across the meridian, and which measures the true period of the earth's rotation; another is apparent solar time, which is indicated by the passage of the sun across the meridian; and a third is mean solar time, which is indicated by a carefully regulated clock, whose errors are corrected by star observations. This last kind of time is that which is universally used in ordinary life (the use of sidereal time being confined to astronomy), so it is necessary to explain what it is and how it differs from apparent solar time.

In the first place, the reason why sidereal time is not universally and exclusively used is because, although it measures the true period of the earth's rotation by the apparent motion of the stars, it does not exactly accord with the apparent motion of the sun; and, naturally, the sun, since it is the source of light for the earth, and the cause of the difference between day and night, is taken for all ordinary purposes, as the standard indicator of the progress of the hours. The fact that it is mid-day, or noon, at any place when the sun crosses the meridian of that place, is a fact of common knowledge, which cannot be ignored. On the other hand, the vernal equinox, which is the “noon mark” for sidereal time, is independent of the alternation of day and night, and may be on the meridian as well at midnight as at mid-day. Before clocks and watches were perfected, the moment of the sun's passage over the meridian was determined by means of a gnomon, which shows the instant of noon by the length of a shadow cast by an upright rod. Since the apparent course of the sun through the sky is a curve, rising from the eastern horizon, attaining its greatest elevation where it meets the meridian, and thence declining to the western horizon, it is evident that the length of the shadow must be least when the sun is on the meridian, or at its maximum altitude. The gnomon, or the sun-dial, gives us apparent solar time. But this differs from sidereal time because, as we saw in Part I, the sun, in consequence of the earth's motion round it, moves about one degree eastward every twenty-four hours, and, since one degree is equal to four minutes of time, the sun rises about four minutes later, with reference to the stars, every morning. Consequently it comes four minutes later to the meridian day after day. Or, to put it in another way, suppose that the sun and a certain star are upon the meridian at the same instant. The star is fixed in its place in the sky, but the sun is not fixed; on the contrary it moves about one degree eastward (the same direction as that of the earth's rotation) in twenty-four hours. Then, when the rotation of the earth has brought the star back to the meridian at the end of twenty-four sidereal hours, the sun, in consequence of its motion, will still be one degree east of the meridian, and the earth must turn through the space of another degree, which will take four minutes, before it can have the sun again upon the meridian. The true distance moved by the sun in twenty-four hours is a little less than one degree, and the exact time required for the meridian to overtake it is 3 min. 56.555 sec. Thus, the sidereal day (period of 24 hours) is nearly four minutes shorter than the solar day.

It would seem, then, that by taking the sun for a guide, and dividing the period between two of its successive passages over the meridian into twenty-four hours, we should have a perfect measure of time, without regard to the stars; in other words, that apparent solar time would be entirely satisfactory for ordinary use. But, unfortunately, the apparent eastward motion of the sun is not regular. It is sometimes greater than the average and sometimes less. This variation is due almost entirely: first, to the fact that its orbit not being a perfect circle the earth moves faster when it is near perihelion, and slower when it is near aphelion; and, second, to the effects of the inclination of the ecliptic to the equator. In consequence, another measure of solar time is used, called mean solar time, in which, by imagining a fictitious sun, moving with perfect regularity through the ecliptic, the discrepancies are avoided. All ordinary clocks are set to follow this fictitious, or mean, sun. The result is that clock time does not agree exactly with sun-dial time, or, what is the same thing, apparent solar time. The clock is ahead of the real sun at some times of the year, and behind it at other times. This difference is called the equation of time. Four times in the year the equation is zero, i.e., there is no difference between the clock and the sun. These times are April 15, June 14, Sept. 1, and Dec. 24. At four other times of the year the difference is at a maximum, viz. Feb. 11, sun 14 min. 27 sec. behind clock; May 14, sun 3 min. 49 sec. ahead of clock; July 26, sun 6 min. 16 sec. behind clock; Nov. 2, sun 16 min. 18 sec. ahead of clock. These dates and differences vary very slightly from year to year.

But, whatever measures of time we may use, it is observation of the stars that furnishes the means of correcting them.

8. Day and Night. The period of twenty-four hours required for one turn of the earth on its axis is called a day, and in astronomical reckoning it is treated as an undivided whole, the hours being counted uninterruptedly from 0 to 24; but nature has divided the period into two very distinct portions, one characterised by the presence and the other by the absence of the sun. Popularly we speak of the sunlighted portion as day and of the other as night, and there are no two associated phenomena in nature more completely in contrast one to the other. The cause of the contrast between day and night must have been evident to the earliest human beings who were capable of any thought at all. They saw that day inevitably began whenever the sun rose above the horizon, and as inevitably ceased whenever it sank beneath it. In all literatures, imaginative writers have pictured the despair of primeval man when he first saw the sun disappear and night come on, and his joy when he first beheld the sun rise, bringing day back with it. Even his uninstructed mind could not have been in doubt about the causal connection of the sun with daylight.

We now know that the cause of the alternate rising and setting of the sun, and of its apparent motion through the sky, is the rotation of the earth. Making in our minds a picture of the earth as a turning globe exposed to the sunbeams, we are able to see that one half of it must necessarily be illuminated, while the other half is in darkness. We also see that its rotation causes these two halves gradually to interchange places so that daylight progresses completely round the earth once in the course of twenty-four hours. If the earth were not surrounded by an atmosphere, exactly one half of it would lie in the sunlight and exactly one half in darkness, but the atmosphere causes the illuminated part slightly to exceed the unilluminated part. The reason for this is twofold: first, because the atmosphere, being transparent and extending to a considerable height above the solid globe, receives rays from the sun after the latter has sunk below the horizon, and these rays cause a faint illumination in the sky after the sun as viewed from the surface of the ground has disappeared; and, second, because the air has the property of refracting the rays of light, in consequence of which the sun appears above the horizon both a little time before it has actually risen and a little time after it has actually set. The faint illumination at the beginning and the end of the day is called twilight. Its cause is the reflection of light from the air at a considerable elevation above the ground. Observation shows that evening twilight lasts until the sun has sunk about 18° below the western horizon, while morning twilight begins when the sun is still 18° below the nearest horizon. The length of time occupied by twilight, or its duration, depends upon the observer's place on the earth and increases with distance from the equator. The length of twilight at any particular place also varies with the seasons.

It will probably have occurred to the reader that, since day and night are ceaselessly chasing each other round the globe, it must be necessary to choose some point of beginning, in order to keep the regular succession of the days of the week. The necessity for this is evident as soon as we reflect that what is sunrise at one place on the earth, is sunset for a place situated half-way round, on the other side. To understand this it will be better, perhaps, to consider the phenomena of noon at various places. It is noon at any place when the sun is on the meridian of that place. But we have seen that every place has its own meridian; consequently, since the sun cannot be on the meridian of more than one place at a time, each different place (reckoning east and west, for, of course, all places lying exactly north or south of one another have the same meridian), must have its own local noontime. Since the sun appears to move round the earth from east to west, it will arrive at the meridian of a place lying east of us sooner than at our meridian, and it will arrive at our meridian sooner than at that of a place lying west of us. Thus, when it is noon at Greenwich, it is about 7 o'clock A.M., or five hours before noon, at New York, because the angular distance westward round the earth's surface from Greenwich to New York is, in round numbers, 75°, which corresponds with five hours of time, there being 150 to every hour. At the same moment it will be 5 o'clock P.M., or five hours after noon, at Cashmere, because Cashmere lies 75° east of Greenwich. That is to say, the sun crosses the meridian of Cashmere five hours before it reaches the meridian of Greenwich, and it crosses the meridian of Greenwich five hours before it reaches that of New York. At a place half-way round the circumference of the globe, i.e. 180° either east or west of Greenwich, it will be midnight at the same instant when it will be mid-day, or noon, at Greenwich. Now let us consider this for a moment.

It is customary to change the name of the day at midnight. Thus at the stroke of midnight, anywhere, Sunday gives place to Monday. Suppose, then, that the day when we see the sun on the meridian at Greenwich happens to be Sunday. Sunday will then be, so to speak, twelve hours old at Greenwich, because it began there at the preceding midnight. Sunday will be only seven hours old at New York, where it also began at the preceding midnight. In California, 45°, or three hours, still farther west than New York, Sunday will be only four hours old, since the local time there is only four hours after midnight. Go on over the Pacific Ocean, until we arrive at a point 180°, or twelve hours, west of Greenwich. There, evidently, Sunday will just have been born, the preceding day, Saturday, having expired at the stroke of midnight. Now if we just step over that line of 180° in what day shall we be? It cannot be Sunday, because Sunday has just begun on the line itself. It cannot be Saturday, because that would be counting backward. Evidently it can be no other than Monday. Let us examine this a little more closely. It is Sunday noon at Greenwich. We now go round the earth eastward instead of westward. At 90°, or six hours, east of Greenwich, we find that it is 6 P.M. Sunday and at 180°, or twelve hours, east of Greenwich we find that it is Sunday midnight, or in other words Monday morning. But the line of 180° east of Greenwich coincides with the line of 180° west of Greenwich, which we formerly approached from the opposite direction. So we see that we were right in concluding that in stepping over that line from the east to the west side, we were passing from Sunday into Monday. It is on that line that each day vanishes and its successor takes its place. It is the “date-line” for the whole earth, chosen by the common consent of every civilised nation, just as we have seen that the meridian of Greenwich is the common reference line for reckoning longitude. It lies entirely in the Pacific Ocean, hardly touching any island, and it was chosen for this very reason, because if it ran over inhabited lands, like Europe or America, it would cause endless confusion. Situated as it is, it causes no trouble except to sea captains, and very little to them. If a ship crosses the line going westward the captain jumps his log-book one day forward. If it is, for instance, Wednesday noon, east of the line he calls it Thursday noon, as soon as he has passed over. If he is going eastward he drops back a day on crossing the line, as from Thursday noon to Wednesday noon. The date-line theoretically follows the 180th meridian, but, in fact, in order to avoid certain groups of islands, it bends about a little, while keeping its general direction from north to south.

9. The Seasons. We now recall again what was said in Part I, about the inclination of the ecliptic, or the apparent path of the sun in the heavens, to the equator. Because of this inclination, the sun appears half the year above the equator and the other half below it. When it is above the equator for people living in the northern hemisphere, it is below the equator for those living in the southern hemisphere, and vice versa. This is because observers on opposite sides of the plane of the equator look at it from opposite points of view. For the northern observer the celestial equator appears south of the zenith; for the southern observer it appears north of the zenith, its distance from the zenith, in both cases, increasing with the observer's distance from the equator of the earth. If he is on the earth's equator, the celestial equator passes directly through the zenith. For convenience we shall suppose the observer to be somewhere in the northern hemisphere.