I. THEORY OF THE SOLAR SYSTEM.
35. Members of the Solar System.—The solar system is composed of the sun, planets, moons, comets, and meteors. Five planets, besides the earth, are readily distinguished by the naked eye, and were known to the ancients: these are Mercury, Venus, Mars, Jupiter, and Saturn. These, with the sun and moon, made up the seven planets of the ancients, from which the seven days of the week were named.
The Ptolemaic System.
36. The Crystalline Spheres.—We have seen that all the heavenly bodies appear to be situated on the surface of the celestial sphere. The ancients assumed that the stars were really fixed on the surface of a crystalline sphere, and that they were carried around the earth daily by the rotation of this sphere. They had, however, learned to distinguish the planets from the stars, and they had come to the conclusion that some of the planets were nearer the earth than others, and that all of them were nearer the earth than the stars are. This led them to imagine that the heavens were composed of a number of crystalline spheres, one above another, each carrying one of the planets, and all revolving around the earth from east to west, but at different rates. This structure of the heavens is shown in section in Fig. 49.
Fig. 49.
37. Cycles and Epicycles.—The ancients had also noticed that, while all the planets move around the heavens from west to east, their motion is not one of uniform advancement. Mercury and Venus appear to oscillate to and fro across the sun, while Jupiter and Saturn appear to oscillate to and fro across a centre which is moving around the earth, so as to describe a series of loops, as shown in Fig. 50.
Fig. 50.
The ancients assumed that the planets moved in exact circles, and, in fact, that all motion in the heavens was circular, the circle being the simplest and most perfect curve. To account for the loops described by the planets, they imagined that each planet revolved in a circle around a centre, which, in turn, revolved in a circle around the earth. The circle described by this centre around the earth they called the cycle, and the circle described by the planet around this centre they called the epicycle.
38. The Eccentric.—The ancients assumed that the planets moved at a uniform rate in describing the epicycle, and also the centre in describing the cycle. They had, however, discovered that the planets advance eastward more rapidly in some parts of their orbits than in others. To account for this they assumed that the cycles described by the centre, around which the planets revolved, were eccentric; that is to say, that the earth was not at the centre of the cycle, but some distance away from it, as shown in Fig. 51. E is the position of the earth, and C is the centre of the cycle. The lines from E are drawn so as to intercept equal arcs of the cycle. It will be seen at once that the angle between any pair of lines is greatest at P, and least at A; so that, were a planet moving at the same rate at P and A, it would seem to be moving much faster at P. The point P of the planet's cycle was called its perigee, and the point A its apogee.
Fig. 51.
As the apparent motion of the planets became more accurately known, it was found necessary to make the system of cycles, epicycles, and eccentrics exceedingly complicated to represent that motion.
The Copernican System.
39. Copernicus.—Copernicus simplified the Ptolemaic system greatly by assuming that the earth and all the planets revolved about the sun as a centre. He, however, still maintained that all motion in the heavens was circular, and hence he could not rid his system entirely of cycles and epicycles.
Tycho Brahe's System.
40. Tycho Brahe.—Tycho Brahe was the greatest of the early astronomical observers. He, however, rejected the system of Copernicus, and adopted one of his own, which was much more complicated. He held that all the planets but the earth revolved around the sun, while the sun and moon revolved around the earth. This system is shown in Fig. 52.
Fig. 52.
Kepler's System.
41. Kepler.—While Tycho Brahe devoted his life to the observation of the planets. Kepler gave his to the study of Tycho's observations, for the purpose of discovering the true laws of planetary motion. He banished the complicated system of cycles, epicycles, and eccentrics forever from the heavens, and discovered the three laws of planetary motion which have rendered his name immortal.
42. The Ellipse.—An ellipse is a closed curve which has two points within it, the sum of whose distances from every point on the curve is the same. These two points are called the foci of the ellipse.
Fig. 53.
One method of describing an ellipse is shown in Fig. 53. Two tacks, F and F', are stuck into a piece of paper, and to these are fastened the two ends of a string which is longer than the distance between the tacks. A pencil is then placed against the string, and carried around, as shown in the figure. The curve described by the pencil is an ellipse. The two points F and F' are the foci of the ellipse: the sum of the distances of these two points from every point on the curve is equal to the length of the string. When half of the ellipse has been described, the pencil must be held against the other side of the string in the same way, and carried around as before.
The point O, half way between F and F', is called the centre of the ellipse; AA' is the major axis of the ellipse, and CD is the minor axis.
43. The Eccentricity of the Ellipse.—The ratio of the distance between the two foci to the major axis of the ellipse is called the eccentricity of the ellipse. The greater the distance between the two foci, compared with the major axis of the ellipse, the greater is the eccentricity of the ellipse; and the less the distance between the foci, compared with the length of the major axis, the less the eccentricity of the ellipse. The ellipse of Fig. 54 has an eccentricity of 1/8. This ellipse scarcely differs in appearance from a circle. The ellipse of Fig. 55 has an eccentricity of 1/2, and that of Fig. 56 an eccentricity of 7/8.
Fig. 54.
Fig. 55.
Fig. 56.
44. Kepler's First Law.—Kepler first discovered that all the planets move from west to east in ellipses which have the sun as a common focus. This law of planetary motion is known as Kepler's First Law. The planets appear to describe loops, because we view them from a moving point.
The ellipses described by the planets differ in eccentricity; and, though they all have one focus at the sun, their major axes have different directions. The eccentricity of the planetary orbits is comparatively small. The ellipse of Fig. 54 has seven times the eccentricity of the earth's orbit, and twice that of the orbit of any of the larger planets except Mercury; and its eccentricity is more than half of that of the orbit of Mercury. Owing to their small eccentricity, the orbits of the planets are usually represented by circles in astronomical diagrams.
Fig. 57.
45. Kepler's Second Law.—Kepler next discovered that a planet's rate of motion in the various parts of its orbit is such that a line drawn from the planet to the sun would always sweep over equal areas in equal times. Thus, in Fig. 57, suppose the planet would move from P to P1 in the same time that it would move from P2 to P3, or from P4 to P5; then the dark spaces, which would be swept over by a line joining the sun and the planet, in these equal times, would all be equal.
A line drawn from the sun to a planet is called the radius vector of the planet. The radius vector of a planet is shortest when the planet is nearest the sun, or at perihelion, and longest when the planet is farthest from the sun, or at aphelion: hence, in order to have the areas equal, it follows that a planet must move fastest when at perihelion, and slowest at aphelion.
Kepler's Second Law of planetary motion is usually stated as follows: The radius vector of a planet describes equal areas in equal times in every part of the planet's orbit.
46. Kepler's Third Law.—Kepler finally discovered that the periodic times of the planets bear the following relation to the distances of the planets from the sun: The squares of the periodic times of the planets are to each other as the cubes of their mean distances from the sun. This is known as Kepler's Third Law of planetary motion. By periodic time is meant the time it takes a planet to revolve around the sun.
These three laws of Kepler's are the foundation of modern physical astronomy.
The Newtonian System.
47. Newton's Discovery.—Newton followed Kepler, and by means of his three laws of planetary motion made his own immortal discovery of the law of gravitation. This law is as follows: Every portion of matter in the universe attracts every other portion with a force varying directly as the product of the masses acted upon, and inversely as the square of the distances between them.
48. The Conic Sections.—The conic sections are the figures formed by the various plane sections of a right cone. There are four classes of figures formed by these sections, according to the angle which the plane of the section makes with the axis of the cone.
OPQ, Fig. 58, is a right cone, and ON is its axis. Any section, AB, of this cone, whose plane is perpendicular to the axis of the cone, is a circle.
Fig. 58.
Any section, CD, of this cone, whose plane is oblique to the axis, but forms with it an angle greater than NOP, is an ellipse. The less the angle which the plane of the section makes with the axis, the more elongated is the ellipse.
Any section, EF, of this cone, whose plane makes with the axis an angle equal to NOP, is a parabola. It will be seen, that, by changing the obliquity of the plane CD to the axis NO, we may pass uninterruptedly from the circle through ellipses of greater and greater elongation to the parabola.
Any section, GH, of this cone, whose plane makes with the axis ON an angle less than NOP, is a hyperbola.
Fig. 59.
It will be seen from Fig. 59, in which comparative views of the four conic sections are given, that the circle and the ellipse are closed curves, or curves which return into themselves. The parabola and the hyperbola are, on the contrary, open curves, or curves which do not return into themselves.
49. A Revolving Body is continually Falling towards its Centre of Revolution.—In Fig. 60 let M represent the moon, and E the earth around which the moon is revolving in the direction MN. It will be seen that the moon, in moving from M to N, falls towards the earth a distance equal to mN. It is kept from falling into the earth by its orbital motion.
Fig. 60.
The fact that a body might be projected forward fast enough to keep it from falling into the earth is evident from Fig. 61. AB represents the level surface of the ocean, C a mountain from the summit of which a cannon-ball is supposed to be fired in the direction CE. AD is a line parallel with CE; DB is a line equal to the distance between the two parallel lines AD and CE. This distance is equal to that over which gravity would pull a ball towards the centre of the earth in a minute. No matter, then, with what velocity the ball C is fired, at the end of a minute it will be somewhere on the line AD. Suppose it were fired fast enough to reach the point D in a minute: it would be on the line AD at the end of the minute, but still just as far from the surface of the water as when it started. It will be seen, that, although it has all the while been falling towards the earth, it has all the while kept at exactly the same distance from the surface. The same thing would of course be true during each succeeding minute, till the ball came round to C again, and the ball would continue to revolve in a circle around the earth.
Fig. 61.
50. The Form of a Body's Orbit depends upon the Rate of its Forward Motion.—If the ball C were fired fast enough to reach the line AD beyond the point D, it would be farther from the surface at the end of the second than when it started. Its orbit would no longer be circular, but elliptical. If the speed of projection were gradually augmented, the orbit would become a more and more elongated ellipse. At a certain rate of projection, the orbit would become a parabola; at a still greater rate, a hyperbola.
51. The Moon held in her Orbit by Gravity.—Newton compared the distance mN that the moon is drawn to the earth in a given time, with the distance a body near the surface of the earth would be pulled toward the earth in the same time; and he found that these distances are to each other inversely as the squares of the distances of the two bodies from the centre of the earth. He therefore concluded that the moon is drawn to the earth by gravity, and that the intensity of gravity decreases as the square of the distance increases.
Fig. 62.
52. Any Body whose Orbit is a Conic Section, and which moves according to Kepler's Second Law, is acted upon by a Force varying inversely as the Square of the Distance.—Newton compared the distance which any body, moving in an ellipse, according to Kepler's Second Law, is drawn towards the sun in the same time in different parts of its orbit. He found these distances in all cases to vary inversely as the square of the distance of the planet from the sun. Thus, in Fig. 62, suppose a planet would move from K to B in the same time that it would move from k to b in another part of its orbit. In the first instance the planet would be drawn towards the sun the distance AB, and in the second instance the distance ab. Newton found that AB : ab = (SK)2 : (Sk)2. He also found that the same would be true when the body moved in a parabola or a hyperbola: hence he concluded that every body that moves around the sun in an ellipse, a parabola, or a hyperbola, is moving under the influence of gravity.
[Transcriber's Note: In Newton's equation above, (SK)2 means to group S and K together and square their product. In the original book, instead of using parentheses, there was a vinculum, a horizontal bar, drawn over the S and the K to express the same grouping.]
Fig. 63.
53. The Force that draws the Different Planets to the Sun Varies inversely as the Squares of the Distances of the Planets from the Sun.—Newton compared the distances jK and eF, over which two planets are drawn towards the sun in the same time, and found these distances to vary inversely as the squares of the distances of the planets from the sun: hence he concluded that all the planets are held in their orbits by gravity. He also showed that this would be true of any two bodies that were revolving around the sun's centre, according to Kepler's Third Law.
54. The Copernican System.—The theory of the solar system which originated with Copernicus, and which was developed and completed by Kepler and Newton, is commonly known as the Copernican System. This system is shown in Fig. 64.
Fig. 64.
II. THE SUN AND PLANETS.
I. THE EARTH.
Form and Size.
55. Form of the Earth.—In ordinary language the term horizon denotes the line that bounds the portion of the earth's surface that is visible at any point.
(1) It is well known that the horizon of a plain presents the form of a circle surrounding the observer. If the latter moves, the circle moves also; but its form remains the same, and is modified only when mountains or other obstacles limit the view. Out at sea, the circular form of the horizon is still more decided, and changes only near the coasts, the outline of which breaks the regularity.
Here, then, we obtain a first notion of the rotundity of the earth, since a sphere is the only body which is presented always to us under the form of a circle, from whatever point on its surface it is viewed.
(2) Moreover, it cannot be maintained that the horizon is the vanishing point of distinct vision, and that it is this which causes the appearance of a circular boundary, because the horizon is enlarged when we mount above the surface of the plain. This will be evident from Fig. 65, in which a mountain is depicted in the middle of a plain, whose uniform curvature is that of a sphere. From the foot of the mountain the spectator will have but a very limited horizon. Let him ascend half way, his visual radius extends, is inclined below the first horizon, and reveals a more extended circular area. At the summit of the mountain the horizon still increases; and, if the atmosphere is pure, the spectator will see numerous objects where from the lower stations the sky alone was visible.
Fig. 65.
This extension of the horizon would be inexplicable if the earth had the form of an extended plane.
(3) The curvature of the surface of the sea manifests itself in a still more striking manner. If we are on the coast at the summit of a hill, and a vessel appears on the horizon (Fig. 66), we see only the tops of the masts and the highest sails; the lower sails and the hull are invisible. As the vessel approaches, its lower part comes into view above the horizon, and soon it appears entire.
Fig. 66.
In the same manner the sailors from the ship see the different parts of objects on the land appear successively, beginning with the highest. The reason of this will be evident from Fig. 67, where the course of a vessel, seen in profile, is figured on the convex surface of the sea.
Fig. 67.
As the curvature of the ocean is the same in every direction, it follows that the surface of the ocean is spherical. The same is true of the surface of the land, allowance being made for the various inequalities of the surface. From these and various other indications, we conclude that the earth is a sphere.
56. Size of the Earth.—The size of the earth is ascertained by measuring the length of a degree of a meridian, and multiplying this by three hundred and sixty. This gives the circumference of the earth as about twenty-five thousand miles, and its diameter as about eight thousand miles. We know that the two stations between which we measure are one degree apart when the elevation of the pole at one station is one degree greater than at the other.
57. The Earth Flattened at the Poles.—Degrees on the meridian have been measured in various parts of the earth, and it has been found that they invariably increase in length as we proceed from the equator towards the pole: hence the earth must curve less and less rapidly as we approach the poles; for the less the curvature of a circle, the larger the degrees on it.
Fig. 68.
58. The Earth in Space.—In Fig. 68 we have a view of the earth suspended in space. The side of the earth turned towards the sun is illumined, and the other side is in darkness. As the planet rotates on its axis, successive portions of it will be turned towards the sun. As viewed from a point in space between it and the sun, it will present light and dark portions, which will assume different forms according to the portion which is illumined. These different appearances are shown in Fig. 69.
Fig. 69.
59. Day and Night.—The succession of day and night is due to the rotation of the earth on its axis, by which a place on the surface of the earth is carried alternately into the sunshine and out of it. As the sun moves around the heavens on the ecliptic, it will be on the celestial equator when at the equinoxes, and 23-1/2° north of the equator when at the summer solstice, and 23-1/2° south of the equator when at the winter solstice.
60. Day and Night when the Sun is at the Equinoxes.—When the sun is at either equinox, the diurnal circle described by the sun will coincide with the celestial equator; and therefore half of this diurnal circle will be above the horizon at every point on the surface of the globe. At these times day and night will be equal in every part of the earth.
Fig. 70.
Fig. 71.
The equality of days and nights when the sun is on the celestial equator is also evident from the following considerations: one-half of the earth is in sunshine all of the time; when the sun is on the celestial equator, it is directly over the equator of the earth, and the illumination extends from pole to pole, as is evident from Figs. 70 and 71, in the former of which the sun is represented as on the eastern horizon at a place along the central line of the figure, and in the latter as on the meridian along the same line. In each diagram it is seen that the illumination extends from pole to pole: hence, as the earth rotates on its axis, every place on the surface will be in the sunshine and out of it just half of the time.
61. Day and Night when the Sun is at the Summer Solstice.—When the sun is at the summer solstice, it will be 23-1/2° north of the celestial equator. The diurnal circle described by the sun will then be 23-1/2° north of the celestial equator; and more than half of this diurnal circle will be above the horizon at all places north of the equator, and less than half of it at places south of the equator: hence the days will be longer than the nights at places north of the equator, and shorter than the nights at places south of the equator. At places within 23-1/2° of the north pole, the entire diurnal circle described by the sun will be above the horizon, so that the sun will not set. At places within 23-1/2° of the south pole of the earth, the entire diurnal circle will be below the horizon, so that the sun will not rise.
Fig. 72.
Fig. 73.
The illumination of the earth at this time is shown in Figs. 72 and 73. In Fig. 72 the sun is represented as on the western horizon along the middle line of the figure, and in Fig. 73 as on the meridian. It is seen at once that the illumination extends 23-1/2° beyond the north pole, and falls 23-1/2° short of the south pole. As the earth rotates on its axis, places near the north pole will be in the sunshine all the time, while places near the south pole will be out of the sunshine all the time. All places north of the equator will be in the sunshine longer than they are out of it, while all places south of the equator will be out of the sunshine longer than they are in it.
62. Day and Night when the Sun is at the Winter Solstice.—When the sun is at the winter solstice, it is 23-1/2° south of the celestial equator. The diurnal circle described by the sun is then 23-1/2° south of the celestial equator. More than half of this diurnal circle will therefore be above the horizon at all places south of the equator, and less than half of it at all places north of the equator: hence the days will be longer than the nights south of the equator, and shorter than the nights at places north of the equator. At places within 23-1/2° of the south pole, the diurnal circle described by the sun will be entirely above the horizon, and the sun will therefore not set. At places within 23-1/2° of the north pole, the diurnal circle described by the sun will be wholly below the horizon, and therefore the sun will not rise.
The illumination of the earth at this time is shown in Figs. 74 and 75, and is seen to be the reverse of that shown in Figs. 72 and 73.
Fig. 74.
Fig. 75.
63. Variation in the Length of Day and Night.—As long as the sun is north of the equinoctial, the nights will be longer than the days south of the equator, and shorter than the days north of the equator. It is just the reverse when the sun is south of the equator.
The farther the sun is from the equator, the greater is the inequality of the days and nights.
The farther the place is from the equator, the greater the inequality of its days and nights.
When the distance of a place from the north pole is less than the distance of the sun north of the equinoctial, it will have continuous day without night, since the whole of the sun's diurnal circle will be above the horizon. A place within the same distance of the south pole will have continuous night.
When the distance of a place from the north pole is less than the distance of the sun south of the equinoctial, it will have continuous night, since the whole of the sun's diurnal circle will then be below the horizon. A place within the same distance of the south pole will then have continuous day.
At the equator the days and nights are always equal; since, no matter where the sun is in the heavens, half of all the diurnal circles described by it will be above the horizon, and half of them below it.
64. The Zones.—It will be seen, from what has been stated above, that the sun will at some time during the year be directly overhead at every place within 23-1/2° of the equator on either side. This belt of the earth is called the torrid zone. The torrid zone is bounded by circles called the tropics; that of Cancer on the north, and that of Capricorn on the south.
It will also be seen, that, at every place within 23-1/2° of either pole, there will be, some time during the year, a day during which the sun will not rise, or on which it will not set. These two belts of the earth's surface are called the frigid zones. These zones are bounded by the arctic circles. The nearer a place is to the poles, the greater the number of days on which the sun does not rise or set.
Between the frigid zones and the torrid zones, there are two belts on the earth which are called the temperate zones. The sun is never overhead at any place in these two zones, but it rises and sets every day at every place within their limits.
65. The Width of the Zones.—The distance the frigid zones extend from the poles, and the torrid zones from the equator, is exactly equal to the obliquity of the ecliptic, or the deviation of the axis of the earth from the perpendicular to the plane of its orbit. Were this deviation forty-five degrees, the obliquity of the ecliptic would be forty-five degrees, the torrid zone would extend forty-five degrees from the equator, and the frigid zones forty-five degrees from the poles. In this case there would be no temperate zones. Were this deviation fifty degrees, the torrid and frigid zones would overlap ten degrees, and there would be two belts of ten degrees on the earth, which would experience alternately during the year a torrid and a frigid climate.
Were the axis of the earth perpendicular to the plane of the earth's orbit, there would be no zones on the earth, and no variation in the length of day and night.
66. Twilight.—Were it not for the atmosphere, the darkness of midnight would begin the moment the sun sank below the horizon, and would continue till he rose again above the horizon in the east, when the darkness of the night would be suddenly succeeded by the full light of day. The gradual transition from the light of day to the darkness of the night, and from the darkness of the night to the light of day, is called twilight, and is due to the diffusion of light from the upper layers of the atmosphere after the sun has ceased to shine on the lower layers at night, or before it has begun to shine on them in the morning.
Fig. 76.
Let ABCD (Fig. 76) represent a portion of the earth, A a point on its surface where the sun S is setting; and let SAH be a ray of light just grazing the earth at A, and leaving the atmosphere at the point H. The point A is illuminated by the whole reflective atmosphere HGFE. The point B, to which the sun has set, receives no direct solar light, nor any reflected from that part of the atmosphere which is below ALH; but it receives a twilight from the portion HLF, which lies above the visible horizon BF. The point C receives a twilight only from the small portion of the atmosphere; while at D the twilight has ceased altogether.
67. Duration of Twilight.—The astronomical limit of twilight is generally understood to be the instant when stars of the sixth magnitude begin to be visible in the zenith at evening, or disappear in the morning.
Twilight is usually reckoned to last until the sun's depression below the horizon amounts to eighteen degrees: this, however, varies; in the tropics a depression of sixteen or seventeen degrees being sufficient to put an end to the phenomenon, while in England a depression of seventeen to twenty-one degrees is required. The duration of twilight differs in different latitudes; it varies also in the same latitude at different seasons of the year, and depends, in some measure, on the meteorological condition of the atmosphere. When the sky is of a pale color, indicating the presence of an unusual amount of condensed vapor, twilight is of longer duration. This happens habitually in the polar regions. On the contrary, within the tropics, where the air is pure and dry, twilight sometimes lasts only fifteen minutes. Strictly speaking, in the latitude of Greenwich there is no true night from May 22 to July 21, but constant twilight from sunset to sunrise. Twilight reaches its minimum three weeks before the vernal equinox, and three weeks after the autumnal equinox, when its duration is an hour and fifty minutes. At midwinter it is longer by about seventeen minutes; but the augmentation is frequently not perceptible, owing to the greater prevalence of clouds and haze at that season of the year, which intercept the light, and hinder it from reaching the earth. The duration is least at the equator (an hour and twelve minutes), and increases as we approach the poles; for at the former there are two twilights every twenty-four hours, but at the latter only two in a year, each lasting about fifty days. At the north pole the sun is below the horizon for six months, but from Jan. 29 to the vernal equinox, and from the autumnal equinox to Nov. 12, the sun is less than eighteen degrees below the horizon; so that there is twilight during the whole of these intervals, and thus the length of the actual night is reduced to two months and a half. The length of the day in these regions is about six months, during the whole of which time the sun is constantly above the horizon. The general rule is, that to the inhabitants of an oblique sphere the twilight is longer in proportion as the place is nearer the elevated pole, and the sun is farther from the equator on the side of the elevated pole.
The Seasons.
68. The Seasons.—While the sun is north of the celestial equator, places north of the equator are receiving heat from the sun by day longer than they are losing it by radiation at night, while places south of the equator are losing heat by radiation at night longer than they are receiving it from the sun by day. When, therefore, the sun passes north of the equator, the temperature begins to rise at places north of the equator, and to fall at places south of it. The rise of temperature is most rapid north of the equator when the sun is at the summer solstice; but, for some time after this, the earth continues to receive more heat by day than it loses by night, and therefore the temperature continues to rise. For this reason, the heat is more excessive after the sun passes the summer solstice than before it reaches it.
69. The Duration of the Seasons.—Summer is counted as beginning in June, when the sun is at the summer solstice, and as continuing until the sun reaches the autumnal equinox, in September. Autumn then begins, and continues until the sun is at the winter solstice, in December. Winter follows, continuing until the sun comes to the vernal equinox, in March, when spring begins, and continues to the summer solstice. In popular reckoning the seasons begin with the first day of June, September, December, and March.
The reason why winter is counted as occurring after the winter solstice is similar to the reason why the summer is placed after the summer solstice. The earth north of the equator is losing heat most rapidly at the time of the winter solstice; but for some time after this it loses more heat by night than it receives by day: hence for some time the temperature continues to fall, and the cold is more intense after the winter solstice than before it.
Fig. 77.
Of course, when it is summer in the northern hemisphere, it is winter in the southern hemisphere, and the reverse. Fig. 77 shows the portion of the earth's orbit included in each season. It will be seen that the earth is at perihelion in the winter season for places north of the equator, and at aphelion in the summer season. This tends to mitigate somewhat the extreme temperatures of our winters and summers.
Fig. 78.
70. The Illumination of the Earth at the different Seasons.—Fig. 78 shows the earth as it would appear to an observer at the sun during each of the four seasons; that is to say, the portion of the earth that is receiving the sun's rays. Figs. 79, 80, 81, and 82 are enlarged views of the earth, as seen from the sun at the time of the summer solstice, of the autumnal equinox, of the winter solstice, and of the vernal equinox.
Fig. 79.
Fig. 80.
Fig. 81.
Fig. 82.
Fig. 83.
Fig. 83 is, so to speak, a side view of the earth, showing the limit of sunshine on the earth when the sun is at the summer solstice; and Fig. 84, showing the limit of sunshine when the sun is at the autumnal equinox.
Fig. 84.
71. Cause of the Change of Seasons.—Variety in the length of day and night, and diversity in the seasons, depend upon the obliquity of the ecliptic. Were there no obliquity of the ecliptic, there would be no inequality in the length of day and night, and but slight diversity of seasons. The greater the obliquity of the ecliptic, the greater would be the variation in the length of the days and nights, and the more extreme the changes of the seasons.
Tides.
72. Tides.—The alternate rise and fall of the surface of the sea twice in the course of a lunar day, or of twenty-four hours and fifty-one minutes, is known as the tides. When the water is rising, it is said to be flood tide; and when it is falling, ebb tide. When the water is at its greatest height, it is said to be high water; and when at its least height, low water.
73. Cause of the Tides.—It has been known to seafaring nations from a remote antiquity that there is a singular connection between the ebb and flow of the tides and the diurnal motion of the moon.
Fig. 85.
This tidal movement in seeming obedience to the moon was a mystery until the study of the law of gravitation showed it to be due to the attraction of the moon on the waters of the ocean. The reason why there are two tides a day will appear from Fig. 85. Let M be the moon, E the earth, and EM the line joining their centres. Now, strictly speaking, the moon does not revolve around the earth any more than the earth around the moon; but the centre of each body moves around the common centre of gravity of the two bodies. The earth being eighty times as heavy as the moon, this centre is situated within the former, about three-quarters of the way from its centre to its surface, at the point G. The body of the earth itself being solid, every part of it, in consequence of the moon's attraction, may be considered as describing a circle once in a month, with a radius equal to EG. The centrifugal force caused by this rotation is just balanced by the mean attraction of the moon upon the earth. If this attraction were the same on every part of the earth, there would be everywhere an exact balance between it and the centrifugal force. But as we pass from E to D the attraction of the moon diminishes, owing to the increased distance: hence at D the centrifugal force predominates, and the water therefore tends to move away from the centre E. As we pass from E towards C, the attraction of the moon increases, and therefore exceeds the centrifugal force: consequently at C there is a tendency to draw the water towards the moon, but still away from the centre E. At A and B the attraction of the moon increases the gravity of the water, owing to the convergence of the lines BM and AM, along which it acts: hence the action of the moon tends to make the waters rise at D and C, and to fall at A and B, causing two tides to each apparent diurnal revolution of the moon.
74. The Lagging of the Tides.—If the waters everywhere yielded immediately to the attractive force of the moon, it would always be high water when the moon was on the meridian, low water when she was rising or setting, and high water again when she was on the meridian below the horizon. But, owing to the inertia of the water, some time is necessary for so slight a force to set it in motion; and, once in motion, it continues so after the force has ceased, and until it has acted some time in the opposite direction. Therefore, if the motion of the water were unimpeded, it would not be high water until some hours after the moon had passed the meridian. The free motion of the water is also impeded by the islands and continents. These deflect the tidal wave from its course in such a way that it may, in some cases, be many hours, or even a whole day, behind its time. Sometimes two waves meet each other, and raise a very high tide. In some places the tides run up a long bay, where the motion of a large mass of water will cause an enormous tide to be raised. In the Bay of Fundy both of these causes are combined. A tidal wave coming up the Atlantic coast meets the ocean wave from the east, and, entering the bay with their combined force, they raise the water at the head of it to the height of sixty or seventy feet.
75. Spring-Tides and Neap-Tides.—The sun produces a tide as well as the moon; but the tide-producing force of the sun is only about four-tenths of that of the moon. At new and full moon the two bodies unite their forces, the ebb and flow become greater than the average, and we have the spring-tides. When the moon is in her first or third quarter, the two forces act against each other; the tide-producing force is the difference of the two; the ebb and flow are less than the average; and we have the neap-tides.