Part 4

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.

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.

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.

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.

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.

Day and Night.

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_.

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.

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.

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.

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.

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.

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. 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.

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.

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_.

Fig. 86 shows the tide that would be produced by the moon alone; Fig. 87, the tide produced by the combined action of the sun and moon; and Fig. 88, by the sun and moon acting at right angles to each other.

The tide is affected by the distance of the moon from the earth, being highest near the time when the moon is in perigee, and lowest near the time when she is in apogee. When the moon is in perigee, at or near the time of a new or full moon, unusually high tides occur.