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.

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.

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.

Fig. 86.

Fig. 87.

Fig. 88.

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.

76. Diurnal Inequality of Tides.—The height of the tide at a given place is influenced by the declination of the moon. When the moon has no declination, the highest tides should occur along the equator, and the heights should diminish from thence toward the north and south; but the two daily tides at any place should have the same height. When the moon has north declination, as shown in Fig. 89, the highest tides on the side of the earth next the moon will be at places having a corresponding north latitude, as at B, and on the opposite side at those which have an equal south latitude. Of the two daily tides at any place, that which occurs when the moon is nearest the zenith should be the greatest: hence, when the moon's declination is north, the height of the tide at a place in north latitude should be greater when the moon is above the horizon than when she is below it. At the same time, places south of the equator have the highest tides when the moon is below the horizon, and the least when she is above it. This is called the diurnal inequality, because its cycle is one day; but it varies greatly in amount at different places.

Fig. 89.

77. Height of Tides.—At small islands in mid-ocean the tides never rise to a great height, sometimes even less than one foot; and the average height of the tides for the islands of the Atlantic and Pacific Oceans is only three feet and a half. Upon approaching an extensive coast where the water is shallow, the height of the tide is increased; so that, while in mid-ocean the average height does not exceed three feet and a half, the average in the neighborhood of continents is not less than four or five feet.

The Day and Time.

78. The Day.—By the term day we sometimes denote the period of sunshine as contrasted with that of the absence of sunshine, which we call night, and sometimes the period of the earth's rotation on its axis. It is with the latter signification that the term is used in this section. As the earth rotates on its axis, it carries the meridian of a place with it; so that, during each complete rotation of the earth, the portion of the meridian which passes overhead from pole to pole sweeps past every star in the heavens from west to east. The interval between two successive passages of this portion of the meridian across the same star is the exact period of the complete rotation of the earth. This period is called a sidereal day. The sidereal day may also be defined as the interval between two successive passages of the same star across the meridian; the passage of the meridian across the star, and the passage or transit of the star across the meridian, being the same thing looked at from a different point of view. The interval between two successive passages of the meridian across the sun, or of the sun across the meridian, is called a solar day.

79. Length of the Solar Day.—The solar day is a little longer than the sidereal day. This is owing to the sun's eastward motion among the stars. We have already seen that the sun's apparent position among the stars is continually shifting towards the east at a rate which causes it to make a complete circuit of the heavens in a year, or three hundred and sixty-five days. This is at the rate of about one degree a day: hence, were the sun and a star on the meridian together to-day, when the meridian again came around to the star, the sun would appear about one degree to the eastward: hence the meridian must be carried about one degree farther in order to come up to the sun. The solar day must therefore be about four minutes longer than the sidereal day.

Fig. 90.

Fig. 91.

The fact that the earth must make more than a complete rotation is also evident from Figs. 90 and 91. In Fig. 90, ba represents the plane of the meridian, and the small arrows indicate the direction the earth is rotating on its axis, and revolving in its orbit. When the earth is at 1, the sun is on the meridian at a. When the earth has moved to 2, it has made a complete rotation, as is shown by the fact that the plane of the meridian is parallel with its position at 1; but it is evident that the meridian has not yet come up with the sun. In Fig. 91, OA represents the plane of the meridian, and OS the direction of the sun. The small arrows indicate the direction of the rotation and revolution of the earth. In passing from the first position to the second the earth makes a complete rotation, but the meridian is not brought up to the sun.

80. Inequality in the Length of Solar Days.—The sidereal days are all of the same length; but the solar days differ somewhat in length. This difference is due to the fact that the sun's apparent position moves eastward, or away from the meridian, at a variable rate.

There are three reasons why this rate is variable:—

(1) The sun's eastward motion is due to the revolution of the earth in its orbit. Now, the earth's orbital motion is not uniform, being fastest when the earth is at perihelion, and slowest when the earth is at aphelion: hence, other things being equal, solar days will be longest when the earth is at perihelion, and shortest when the earth is at aphelion.

Fig. 92.

Fig. 93.

(2) The sun's eastward motion is along the ecliptic. Now, from Figs. 92 and 93, it will be seen, that, when the sun is at one of the equinoxes, it will be moving away from the meridian obliquely; and, from Figs. 94 and 95, that, when the sun is at one of the solstices, it will be moving away from the meridian perpendicularly: hence, other things being equal, the sun would move away from the meridian fastest, and the days be longest, when the sun is at the solstices; while it would move away from the meridian slowest, and the days be shortest, when the sun is at the equinoxes. That a body moving along the ecliptic must be moving at a variable angle to the meridian becomes very evident on turning a celestial globe so as to bring each portion of the ecliptic under the meridian in turn.

Fig. 94.

Fig. 95.

(3) The sun, moving along the ecliptic, always moves in a great circle, while the point of the meridian which is to overtake the sun moves in a diurnal circle, which is sometimes a great circle and sometimes a small circle. When the sun is at the equinoxes, the point of the meridian which is to overtake it moves in a great circle. As the sun passes from the equinoxes to the solstices, the point of the meridian which is to overtake it moves on a smaller and smaller circle: hence, as we pass away from the celestial equator, the points of the meridian move slower and slower. Therefore, other things being equal, the meridian will gain upon the sun most rapidly, and the days be shortest, when the sun is at the equinoxes; while it will gain on the sun least rapidly, and the days will be longest, when the sun is at the solstices.

The ordinary or civil day is the mean of all the solar days in a year.

81. Sun Time and Clock Time.—It is noon by the sun when the sun is on the meridian, and by the clock at the middle of the civil day. Now, as the civil days are all of the same length, while solar days are of variable length, it seldom happens that the middles of these two days coincide, or that sun time and clock time agree. The difference between sun time and clock time, or what is often called apparent solar time and mean solar time, is called the equation of time. The sun is said to be slow when it crosses the meridian after noon by the clock, and fast when it crosses the meridian before noon by the clock. Sun time and clock time coincide four times a year; during two intermediate seasons the clock time is ahead, and during two it is behind.

The following are the dates of coincidence and of maximum deviation, which vary but slightly from year to year:—

February 10 True sun fifteen minutes slow.

April 15 True sun correct.

May 14 True sun four minutes fast.

June 14 True sun correct.

July 25 True sun six minutes slow.

August 31 True sun correct.

November 2 True sun sixteen minutes fast.

December 24 True sun correct.

One of the effects of the equation of time which is frequently misunderstood is, that the interval from sunrise until noon, as given in the almanacs, is not the same as that between noon and sunset. The forenoon could not be longer or shorter than the afternoon, if by "noon" we meant the passage of the sun across the meridian; but the noon of our clocks being sometimes fifteen minutes before or after noon by the sun, the former may be half an hour nearer to sunrise than to sunset, or vice versa.

The Year.

82. The Year.—The year is the time it takes the earth to revolve around the sun, or, what amounts to the same thing, the time it takes the sun to pass around the ecliptic.

(1) The time it takes the sun to pass from a star around to the same star again is called a sidereal year. This is, of course, the exact time it takes the earth to make a complete revolution around the sun.

Fig. 96.

(2) The time it takes the sun to pass around from the vernal equinox, or the first point of Aries, to the vernal equinox again, is called the tropical year. This is a little shorter than the sidereal year, owing to the precession of the equinoxes. This will be evident from Fig. 96. The circle represents the ecliptic, S the sun, and E the vernal equinox. The sun moves around the ecliptic eastward, as indicated by the long arrow, while the equinox moves slowly westward, as indicated by the short arrow. The sun will therefore meet the equinox before it has quite completed the circuit of the heavens. The exact lengths of these respective years are:—

Sidereal year 365.25636=365 days 6 hours 9 min 9 sec

Tropical year 365.24220=365 days 5 hours 48 min 46 sec

Since the recurrence of the seasons depends on the tropical year, the latter is the one to be used in forming the calendar and for the purposes of civil life generally. Its true length is eleven minutes and fourteen seconds less than three hundred and sixty-five days and a fourth.

It will be seen that the tropical year is about twenty minutes shorter than the sidereal year.

(3) The time it takes the earth to pass from its perihelion point around to the perihelion point again is called the anomalistic year. This year is about four minutes longer than the sidereal year. This is owing to the fact that the major axis of the earth's orbit is slowly moving around to the east at the rate of about ten seconds a year. This causes the perihelion point P (Fig. 97) to move eastward at that rate, as indicated by the short arrow. The earth E is also moving eastward, as indicated by the long arrow. Hence the earth, on starting at the perihelion, has to make a little more than a complete circuit to reach the perihelion point again.

Fig. 97.

83. The Calendar.—The solar year, or the interval between two successive passages of the same equinox by the sun, is 365 days, 5 hours, 48 minutes, 46 seconds. If, then, we reckon only 365 days to a common or civil year, the sun will come to the equinox 5 hours, 48 minutes, 46 seconds, or nearly a quarter of a day, later each year; so that, if the sun entered Aries on the 20th of March one year, he would enter it on the 21st four years after, on the 22d eight years after, and so on. Thus in a comparatively short time the spring months would come in the winter, and the summer months in the spring.

Among different ancient nations different methods of computing the year were in use. Some reckoned it by the revolution of the moon, some by that of the sun; but none, so far as we know, made proper allowances for deficiencies and excesses. Twelve moons fell short of the true year, thirteen exceeded it; 365 days were not enough, 366 were too many. To prevent the confusion resulting from these errors, Julius Cæsar reformed the calendar by making the year consist of 365 days, 6 hours (which is hence called a Julian year), and made every fourth year consist of 366 days. This method of reckoning is called Old Style.

But as this made the year somewhat too long, and the error in 1582 amounted to ten days, Pope Gregory XIII., in order to bring the vernal equinox back to the 21st of March again, ordered ten days to be struck out of that year, calling the next day after the 4th of October the 15th; and, to prevent similar confusion in the future, he decreed that three leap-years should be omitted in the course of every four hundred years. This way of reckoning time is called New Style. It was immediately adopted by most of the European nations, but was not accepted by the English until the year 1752. The error then amounted to eleven days, which were taken from the month of September by calling the 3d of that month the 14th. The Old Style is still retained by Russia.

According to the Gregorian calendar, every year whose number is divisible by four is a leap-year, except, that, in the case of the years whose numbers are exact hundreds, those only are leap-years which are divisible by four after cutting off the last two figures. Thus the years 1600, 2000, 2400, etc., are leap-years; 1700, 1800, 1900, 2100, 2200, etc., are not. The error will not amount to a day in over three thousand years.

84. The Dominical Letter.—The dominical letter for any year is that which we often see placed against Sunday in the almanacs, and is always one of the first seven in the alphabet. Since a common year consists of 365 days, if this number is divided by seven (the number of days in a week), there will be a remainder of one: hence a year commonly begins one day later in the week than the preceding one did. If a year of 365 days begins on Sunday, the next will begin on Monday; if it begins on Thursday, the next will begin on Friday; and so on. If Sunday falls on the 1st of January, the first letter of the alphabet, or A, is the dominical letter. If Sunday falls on the 7th of January (as it will the next year, unless the first is leap-year), the seventh letter, G, is the dominical letter. If Sunday falls on the 6th of January (as it will the third year, unless the first or second is leap-year), the sixth letter, F, will be the dominical letter. Thus, if there were no leap-years, the dominical letters would regularly follow a retrograde order, G, F, E, D, C, B, A.

But leap-years have 366 days, which, divided by seven, leaves two remainder: hence the years following leap-years will begin two days later in the week than the leap-years did. To prevent the interruption which would hence occur in the order of the dominical letters, leap-years have two dominical letters, one indicating Sunday till the 29th of February, and the other for the rest of the year.

By Table I. below, the dominical letter for any year (New Style) for four thousand years from the beginning of the Christian Era may be found; and it will be readily seen how the Table could be extended indefinitely by continuing the centuries at the top in the same order.

To find the dominical letter by this table, look for the hundreds of years at the top, and for the years below a hundred, at the left hand.

Thus the letter for 1882 will be opposite the number 82, and in the column having 1800 at the top; that is, it will be A. In the same way, the letters for 1884, which is a leap-year, will be found to be FE.

Having the dominical letter of any year, Table II. shows what days of every month of the year will be Sundays.

To find the Sundays of any month in the year by this table, look in the column, under the dominical letter, opposite the name of the month given at the left.

From the Sundays the date of any other day of the week can be readily found.

Thus, if we wish to know on what day of the week Christmas falls in 1889, we look opposite December, under the letter F (which we have found to be the dominical letter for the year), and find that the 22d of the month is a Sunday; the 25th, or Christmas, will then be Wednesday.

In the same way we may find the day of the week corresponding to any date (New Style) in history. For instance, the 17th of June, 1775, the day of the fight at Bunker Hill, is found to have been a Saturday.

These two tables then serve as a perpetual almanac.

Table I.

100200300400
500600700800
900100011001200
1300140015001600
1700180019002000
2100220023002400
—-—-—-——
CEGBA
1295785BDFG
2305886ACEF
3315987GBDE
4326088FEAGCBDC
5336189DFAB
6346290CEGA
7356391BDFG
8366492AGCBEDFE
9376593FACD
10386694EGBC
11396795DFAB
12406896CBEDGFAG
13416997ACEF
14427098GBDE
15437199FACD
164472..EDGFBACB
174573..CEGA
184674..BDFG
194775..ACEF
204876..GFBADCED
214977..EGBC
225078..DFAB
235179..CEGA
245280..BADCFEGF
255381..GBDE
265482..FACD
275583..EGBC
285684..DCFEAGBA

Table II.

ABCDEFG
1234567
Jan. 31.891011121314
15161718192021
Oct. 31.22232425262728
293031........
Feb. 28-29.......1234
567891011
March 31.12131415161718
19202122232425
Nov. 30.262728293031..
............1
April 30.2345678
9101112131415
July 3116171819202122
23242526272829
3031..........
....12345
6789101112
Aug. 31.13141516171819
20212223242526
2728293031....
..........12
Sept. 30.3456789
10111213141516
17181920212223
Dec. 31.24252627282930
31............
..123456
78910111213
May. 31.14151617181920
21222324252627
28293031......
........123
45678910
June 30.11121314151617
18192021222324
252627282930..

Weight of the Earth and Precession.

85. The Weight of the Earth.—There are several methods of ascertaining the weight and mass of the earth. The simplest, and perhaps the most trustworthy method is to compare the pull of the earth upon a ball of lead with that of a known mass of lead upon it. The pull of a known mass of lead upon the ball may be measured by means of a torsion balance. One form of the balance employed for this purpose is shown in Figs. 98 and 99. Two small balls of lead, b and b, are fastened to the ends of a light rod e, which is suspended from the point F by means of the thread FE. Two large balls of lead, W and W, are placed on a turn-table, so that one of them shall be just in front of one of the small balls, and the other just behind the other small ball. The pull of the large balls turns the rod around a little so as to bring the small balls nearer the large ones. The small balls move towards the large ones till they are stopped by the torsion of the thread, which is then equal to the pull of the large balls. The deflection of the rod is carefully measured. The table is then turned into the position indicated by the dotted lines in Fig. 99, so as to reverse the position of the large balls with reference to the small ones. The rod is now deflected in the opposite direction, and the amount of deflection is again carefully measured. The second measurement is made as a check upon the accuracy of the first. The force required to twist the thread as much as it was twisted by the deflection of the rod is ascertained by measurement. This gives the pull of the two large balls upon the two small ones. We next calculate what this pull would be were the balls as far apart as the small balls are from the centre of the earth. We can then form the following proportion: the pull of the large balls upon the small ones is to the pull of the earth upon the small ones as the mass of the large balls is to the mass of the earth, or as the weight of the large balls is to the weight of the earth. Of course, the pull of the earth upon the small balls is the weight of the small balls. In this way it has been ascertained that the mass of the earth is about 5.6 times that of a globe of water of the same size. In other words, the mean density of the earth is about 5.6.

Fig. 99.

Fig. 99.

The weight of the earth in pounds may be found by multiplying the number of cubic feet in it by 62-1/2 (the weight, in pounds, of one cubic foot of water), and this product by 5.6.

Fig. 100.

86. Cause of Precession.—We have seen that the earth is flattened at the poles: in other words, the earth has the form of a sphere, with a protuberant ring around its equator. This equatorial ring is inclined to the plane of the ecliptic at an angle of about 23-1/2°. In Fig. 100 this ring is represented as detached from the enclosed sphere. S represents the sun, and Sc the ecliptic. As the point A of the ring is nearer the sun than the point B is, the sun's pull upon A is greater than upon B: hence the sun tends to pull the ring over into the plane of the ecliptic; but the rotation of the earth tends to keep the ring in the same plane. The struggle between these two tendencies causes the earth, to which the ring is attached, to wabble like a spinning-top, whose rotation tends to keep it erect, while gravity tends to pull it over. The handle of the top has a gyratory motion, which causes it to describe a curve. The axis of the heavens corresponds to the handle of the top.

II. THE MOON.

Distance, Size, and Motions.

87. The Distance of the Moon.—The moon is the nearest of the heavenly bodies. Its distance from the centre of the earth is only about sixty times the radius of the earth, or, in round numbers, two hundred and forty thousand miles.

The ordinary method of finding the distance of one of the nearer heavenly bodies is first to ascertain its horizontal parallax. This enables us to form a right-angled triangle, the lengths of whose sides are easily computed, and the length of whose hypothenuse is the distance of the body from the centre of the earth.

Fig. 101.

Horizontal parallax has already been defined (32) as the displacement of a heavenly body when on the horizon, caused by its being seen from the surface, instead of the centre, of the earth. This displacement is due to the fact that the body is seen in a different direction from the surface of the earth from that in which it would be seen from the centre. Horizontal parallax might be defined as the difference in the directions in which a body on the horizon would be seen from the surface and from the centre of the earth. Thus, in Fig. 101, C is the centre of the earth, A a point on the surface, and B a body on the horizon of A. AB is the direction in which the body would be seen from A, and CB the direction in which it would be seen from C. The difference of these directions, or the angle ABC, is the parallax of the body.

The triangle BAC is right-angled at A; the side AC is the radius of the earth, and the hypothenuse is the distance of the body from the centre of the earth. When the parallax ABC is known, the length of CB can easily by found by trigonometrical computation.

We have seen (32) that the parallax of a heavenly body grows less and less as the body passes from the horizon towards the zenith. The parallax of a body and its altitude are, however, so related, that, when we know the parallax at any altitude, we can readily compute the horizontal parallax.

The usual method of finding the parallax of one of the nearer heavenly bodies is first to find its parallax when on the meridian, as seen from two places on the earth which differ considerably in latitude: then to calculate what would be the parallax of the body as seen from one of these places and the centre of the earth: and then finally to calculate what would be the parallax were the body on the horizon.

Fig. 102.

Thus, we should ascertain the parallax of the body B (Fig. 102) as seen from A and D, or the angle ABD. We should then calculate its parallax as seen from A and C, or the angle ABC. Finally we should calculate what its parallax would be were the body on the horizon, or the angle AB'C.

The simplest method of finding the parallax of a body B (Fig. 102) as seen from the two points A and D is to compare its direction at each point with that of the same fixed star near the body. The star is so distant, that it will be seen in the same direction from both points: hence, if the direction of the body differs from that of the star 2° as seen from one point, and 2° 6' as seen from the other point, the two lines AB and DB must differ in direction by 6'; in other words, the angle ABD would be 6'.

The method just described is the usual method of finding the parallax of the moon.

88. The Apparent Size of the Moon.—The apparent size of a body is the visual angle subtended by it; that is, the angle formed by two lines drawn from the eye to two opposite points on the outline of the body. The apparent size of a body depends upon both its magnitude and its distance.

The apparent size, or angular diameter, of the moon is about thirty-one minutes. This is ascertained by means of the wire micrometer already described (19). The instrument is adjusted so that its longitudinal wire shall pass through the centre of the moon, and its transverse wires shall be tangent to the limbs of the moon on each side, at the point where they are cut by the longitudinal wire. The micrometer screw is then turned till the wires are brought together. The number of turns of the screw needed to accomplish this will indicate the arc between the wires, or the angular diameter of the moon.

Fig. 103.

In order to be certain that the longitudinal wire shall pass through the centre of the moon, it is best to take the moon when its disc is in the form of a crescent, and to place the longitudinal wire against the points, or cusps, of the crescent, as shown in Fig. 103.

Fig. 104.

89. The Real Size of the Moon.—The real diameter of the moon is a little over one-fourth of that of the earth, or a little more than two thousand miles. The comparative sizes of the earth and moon are shown in Fig. 104.

Fig. 105.

The distance and apparent size of the moon being known, her real diameter is found by means of a triangle formed as shown in Fig. 105. C represents the centre of the moon, CB the distance of the moon from the earth, and CA the radius of the moon. BAC is a triangle, right-angled at A. The angle ABC is half the apparent diameter of the moon. With the angles A and B, and the side CB known, it is easy to find the length of AC by trigonometrical computation. Twice AC will be the diameter of the moon.

The volume of the moon is about one-fiftieth of that of the earth.

90. Apparent Size of the Moon on the Horizon and in the Zenith..—The moon is nearly four thousand miles farther from the observer when she is on the horizon than when she is in the zenith. This is evident from Fig. 106. C is the centre of the earth, M the moon on the horizon, M' the moon in the zenith, and O the point of observation. OM is the distance of the moon when she is on the horizon, and OM' the distance of the moon from the observer when she is in the zenith. CM is equal to CM', and OM is about the length of CM; but OM' is about four thousand miles shorter than CM': hence OM' is about four thousand miles shorter than OM.

Fig. 106.

Notwithstanding the moon is much nearer when at the zenith than at the horizon, it seems to us much larger at the horizon.

This is a pure illusion, as we become convinced when we measure the disc with accurate instruments, so as to make the result independent of our ordinary way of judging. When the moon is near the horizon, it seems placed beyond all the objects on the surface of the earth in that direction, and therefore farther off than at the zenith, where no intervening objects enable us to judge of its distance. In any case, an object which keeps the same apparent magnitude seems to us, through the instinctive habits of the eye, the larger in proportion as we judge it to be more distant.

91. The Apparent Size of the Moon increased by Irradiation.—In the case of the moon, the word apparent means much more than it does in the case of other celestial bodies. Indeed, its brightness causes our eyes to play us false. As is well known, the crescent of the new moon seems part of a much larger sphere than that which it has been said, time out of mind, to "hold in its arms." The bright portion of the moon as seen with our measuring instruments, as well as when seen with the naked eye, covers a larger space in the field of the telescope than it would if it were not so bright. This effect of irradiation, as it is called, must be allowed for in exact measurements of the diameter of the moon.

Fig. 107.

92. Apparent Size of the Moon in Different Parts of her Orbit.—Owing to the eccentricity of the moon's orbit, her distance from the earth varies somewhat from time to time. This variation causes a corresponding variation in her apparent size, which is illustrated in Fig. 107.

93. The Mass of the Moon.—The moon is considerably less dense than the earth, its mass being only about one-eightieth of that of the earth; that is, while it would take only about fifty moons to make the bulk of the earth, it would take about eighty to make the mass of the earth.

One method of finding the mass of the moon is to compare her effect in producing the tides with that of the sun. We first calculate what would be the moon's effect in producing the tides, were she as far off as the sun. We then form the following proportion: as the sun's effect in producing the tides is to the moon's effect at the same distance, so is the mass of the sun to the mass of the moon.

The method of finding the mass of the sun will be given farther on.

94. The Orbital Motion of the Moon.—If we watch the moon from night to night, we see that she moves eastward quite rapidly among the stars. When the new moon is first visible, it appears near the horizon in the west, just after sunset. A week later the moon will be on the meridian at the same hour, and about a week later still on the eastern horizon. The moon completes the circuit of the heavens in a period of about thirty days, moving eastward at the rate of about twelve degrees a day. This eastward motion of the moon is due to the fact that she is revolving around the earth from west to east.

Fig. 108.

95. The Aspects of the Moon.—As the moon revolves around the earth, she comes into different positions with reference to the earth and sun. These different positions of the moon are called the aspects of the moon. The four chief aspects of the moon are shown in Fig. 108. When the moon is at M, she appears in the opposite part of the heavens to the sun, and is said to be in opposition; when at M' and at M''', she appears ninety degrees away from the sun, and is said to be in quadrature; when at M'', she appears in the same part of the heavens as the sun, and is said to be in conjunction.

96. The Sidereal and Synodical Periods of the Moon.—The sidereal period of the moon is the time it takes her to pass around from a star to that star again, or the time it takes her to make a complete revolution around the earth. This is a period of about twenty-seven days and a third. It is sometimes called the sidereal month.

The synodical period of the moon is the time that it takes the moon to pass from one aspect around to the same aspect again. This is a period of about twenty-nine days and a half, and it is sometimes called the synodical month.

Fig. 109.

The reason why the synodical period is longer than the sidereal period will appear from Fig. 109. S represents the position of the sun, E that of the earth, and the small circle the orbit of the moon around the earth. The arrow in the small circle represents the direction the moon is revolving around the earth, and the arrow in the arc between E and E' indicates the direction of the earth's motion in its orbit. When the moon is at M1, she is in conjunction. As the moon revolves around the earth, the earth moves forward in its orbit. When the moon has come round to m1, so that m3m1 is parallel with M3M1, she will have made a complete or sidereal revolution around the earth; but she will not be in conjunction again till she has come round to M, so as again to be between the earth and sun. That is to say, the moon must make more than a complete revolution in a synodical period.

Fig. 110.

The greater length of the synodical period is also evident from Fig. 110. T represents the earth, and L the moon. The arrows indicate the direction in which each is moving. When the earth is at T, and the moon at L, the latter is in conjunction. When the earth has reached T', and the moon L', the latter has made a sidereal revolution; but she will not be in conjunction again till the earth has reached T'', and the moon L''.

97. The Phases of the Moon.—When the new moon appears in the west, it has the form of a crescent, with its convex side towards the sun, and its horns towards the east. As the moon advances towards quadrature, the crescent grows thicker and thicker, till it becomes a half-circle at first quarter. When it passes quadrature, it begins to become convex also on the side away from the sun, or gibbous in form. As it approaches opposition, it becomes more and more nearly circular, until at opposition it is a full circle. From full moon to last quarter it is again gibbous, and at last quarter a half-circle. From last quarter to new moon it is again crescent; but the horns of the crescent are now turned towards the west. The successive phases of the moon are shown in Fig. 111.

Fig. 111.

98. Cause of the Phases of the Moon.—Take a globe, half of which is colored white and the other half black in such a way that the line which separates the white and black portions shall be a great circle which passes through the poles of the globe, and rotate the globe slowly, so as to bring the white half gradually into view. When the white part first comes into view, the line of separation between it and the black part, which we may call the terminator, appears concave, and its projection on a plane perpendicular to the line of vision is a concave line. As more and more of the white portion comes into view, the projection of the terminator becomes less and less concave. When half of the white portion comes into view, the terminator is projected as a straight line. When more than half of the white portion comes into view, the terminator begins to appear as a convex line, and this line becomes more and more convex till the whole of the white half comes into view, when the terminator becomes circular.

Fig. 112.

The moon is of itself a dark, opaque globe; but the half that is towards the sun is always bright, as shown in Fig. 112. This bright half of the moon corresponds to the white half of the globe in the preceding illustration. As the moon revolves around the earth, different portions of this illumined half are turned towards the earth. At new moon, when the moon is in conjunction, the bright half is turned entirely away from the earth, and the disc of the moon is black and invisible. Between new moon and first quarter, less than half of the illumined side is turned towards the earth, and we see this illumined portion projected as a crescent. At first quarter, just half of the illumined side is turned towards the earth, and we see this half projected as a half-circle. Between first quarter and full, more than half of the illumined side is turned towards the earth, and we see it as gibbous. At full, the whole of the illumined side is turned towards us, and we see it as a full circle. From full to new moon again, the phases occur in the reverse order.

99. The Form of the Moon's Orbit.—The orbit of the moon around the earth is an ellipse of slight eccentricity. The form of this ellipse is shown in Fig. 113. C is the centre of the ellipse, and E the position of the earth at one of its foci. The eccentricity of the ellipse is only about one-eighteenth. It is impossible for the eye to distinguish such an ellipse from a circle.

Fig. 113.

100. The Inclination of the Moon's Orbit.—The plane of the moon's orbit is inclined to the ecliptic by an angle of about five degrees. The two points where the moon's orbit cuts the ecliptic are called her nodes. The moon's nodes have a westward motion corresponding to that of the equinoxes, but much more rapid. They complete the circuit of the ecliptic in about nineteen years.

The moon's latitude ranges from 5° north to 5° south; and since, owing to the motion of her nodes, the moon is, during a period of nineteen years, 5° north and 5° south of every part of the ecliptic, her declination will range from 23-1/2° + 5° = 28-1/2° north to 23-1/2° + 5° = 28-1/2° south.

101. The Meridian Altitude of the Moon.—The meridian altitude of any body is its altitude when on the meridian. In our latitude, the meridian altitude of any point on the equinoctial is forty-nine degrees. The meridian altitude of the summer solstice is 49° + 23-1/2° = 72-1/2°, and that of the winter solstice is 49° - 23-1/2° = 25-1/2°. The greatest meridian altitude of the moon is 72-1/2° + 5° = 77-1/2°, and its least meridian altitude, 25-1/2° - 5° = 20-1/2°.

When the moon's meridian altitude is greater than the elevation of the equinoctial, it is said to run high, and when less, to run low. The full moon runs high when the sun is south of the equinoctial, and low when the sun is north of the equinoctial. This is because the full moon is always in the opposite part of the heavens to the sun.

102. Wet and Dry Moon.—At the time of new moon, the cusps of the crescent sometimes lie in a line which is nearly perpendicular with the horizon, and sometimes in a line which is nearly parallel with the horizon. In the former case the moon is popularly described as a wet moon, and in the latter case as a dry moon.

Fig. 114.

The great circle which passes through the centre of the sun and moon will pass through the centre of the crescent, and be perpendicular to the line joining the cusps. Now the ecliptic makes the least angle with the horizon when the vernal equinox is on the eastern horizon and the autumnal equinox is on the western. In our latitude, as we have seen, this angle is 25-1/2°: hence in our latitude, if the moon were at new on the ecliptic when the sun is at the autumnal equinox, as shown at M3 (Fig. 114), the great circle passing through the centre of the sun and moon would be the ecliptic, and at New York would be inclined to the horizon at an angle of 25-1/2°. If the moon happened to be 5° south of the ecliptic at this time, as at M4, the great circle passing through the centre of the sun and moon would make an angle of only 20-1/2° with the horizon. In either of these cases the line joining the cusps would be nearly perpendicular to the horizon.

Fig. 115.

If the moon were at new on the ecliptic when the sun is near the vernal equinox, as shown at M1 (Fig. 115), the great circle passing through the centres of the sun and moon would make an angle of 72-1/2° with the horizon at New York; and were the moon 5° north of the ecliptic at that time, as shown at M2, this great circle would make an angle of 77-1/2° with the horizon. In either of these cases, the line joining the cusps would be nearly parallel with the horizon.

At different times, the line joining the cusps may have every possible inclination to the horizon between the extreme cases shown in Figs. 114 and 115.

103. Daily Retardation of the Moon's Rising.—The moon rises, on the average, about fifty minutes later each day. This is owing to her eastward motion. As the moon makes a complete revolution around the earth in about twenty-seven days, she moves eastward at the rate of about thirteen degrees a day, or about twelve degrees a day faster than the sun. Were the moon, therefore, on the horizon at any hour to-day, she would be some twelve degrees below the horizon at the same hour to-morrow. Now, as the horizon moves at the rate of one degree in four minutes, it would take it some fifty minutes to come up to the moon so as to bring her upon the horizon. Hence the daily retardation of the moon's rising is about fifty minutes; but it varies considerably in different parts of her orbit.

There are two reasons for this variation in the daily retardation:—

(1) The moon moves at a varying rate in her orbit; her speed being greatest at perigee, and least at apogee: hence, other things being equal, the retardation is greatest when the moon is at perigee, and least when she is at apogee.

Fig. 116.

Fig. 117.

(2) The moon moves at a varying angle to the horizon. The moon moves nearly in the plane of the ecliptic, and of course she passes both equinoxes every lunation. When she is near the autumnal equinox, her path makes the greatest angle with the eastern horizon, and when she is near the vernal equinox, the least angle: hence the moon moves away from the horizon fastest when she is near the autumnal equinox, and slowest when she is near the vernal equinox. This will be evident from Figs. 116 and 117. In each figure, SN represents a portion of the eastern horizon, and Ec, E'c', a portion of the ecliptic. AE, in Fig. 116, represents the autumnal equinox, and AEM the daily motion of the moon. VE, in Fig. 117, represents the vernal equinox, and VEM' the motion of the moon for one day. In the first case this motion would carry the moon away from the horizon the distance AM, and in the second case the distance A'M'. Now, it is evident that AM is greater than A'M': hence, other things being equal, the greatest retardation of the moon's rising will be when the moon is near the autumnal equinox, and the least retardation when the moon is near the vernal equinox.

The least retardation at New York is twenty-three minutes, and the greatest an hour and seventeen minutes. The greatest and least retardations vary somewhat from month to month; since they depend not only upon the position of the moon in her orbit with reference to the equinoxes, but also upon the latitude of the moon, and upon her nearness to the earth.

Fig. 118.

The direction of the moon's motion with reference to the ecliptic is shown in Fig. 118, which shows the moon's motion for one day in July, 1876.

104. The Harvest Moon—The long and short retardations in the rising of the moon, though they occur every month, are not likely to attract attention unless they occur at the time of full moon. The long retardations for full moon occur when the moon is near the autumnal equinox at full. As the full moon is always opposite to the sun, the sun must in this case be near the vernal equinox: hence the long retardations for full moon occur in the spring, the greatest retardation being in March.

The least retardations for full moon occur when the moon is near the vernal equinox at full: the sun must then be near the autumnal equinox. Hence the least retardations for full moon occur in the months of August, September, and October. The retardation is, of course, least for September; and the full moon of this month rises night after night less than half an hour later than the previous night. The full moon of September is called the "Harvest Moon," and that of October the "Hunter's Moon."

105. The Rotation of the Moon.—A careful examination of the spots on the disc of the moon reveals the fact that she always presents the same side to the earth. In order to do this, she must rotate on her axis while making a revolution around the earth, or in about twenty-seven days.

106. Librations of the Moon.—The moon appears to rock slowly to and fro, so as to allow us to see alternately a little farther around to the right and the left, or above and below, than we otherwise could. This apparent rocking of the moon is called libration. The moon has three librations:—

(1) Libration in Latitude.—This libration enables us to see alternately a little way around on the northern and southern limbs of the moon.

This libration is due to the fact that the axis of the moon is not quite perpendicular to the plane of her orbit. The deviation from the perpendicular is six degrees and a half. As the axis of the moon, like that of the earth, maintains the same direction, the poles of the moon will be turned alternately six degrees and a half toward and from the earth.

(2) Libration in Longitude.—This libration enables us to see alternately a little farther around on the eastern and western limbs of the moon.

Fig. 119.

It is due to the fact that the moon's axial motion is uniform, while her orbital motion is not. At perigee her orbital motion will be in advance of her axial motion, while at apogee the axial motion will be in advance of the orbital. In Fig. 119, E represents the earth, M the moon, the large arrow the direction of the moon's motion in her orbit, and the small arrow the direction of her motion of rotation. When the moon is at M, the line AB, drawn perpendicular to EM, represents the circle which divides the visible from the invisible portion of the moon. While the moon is passing from M to M', the moon performs less than a quarter of a rotation, so that AB is no longer perpendicular to EM'. An observer on the earth can now see somewhat beyond A on the western limb of the moon, and not quite up to B on the eastern limb. While the moon is passing from M' to M'', her axial motion again overtakes her orbital motion, so that the line AB again becomes perpendicular to the line joining the centre of the moon to the centre of the earth. Exactly the same side is now turned towards the earth as when the moon was at M. While the moon passes from M'' to M''', her axial motion gets in advance of her orbital motion, so that AB is again inclined to the line joining the centres of the earth and moon. A portion of the eastern limb of the moon beyond B is now brought into view to the earth, and a portion of the western limb at A is carried out of view. While the moon is passing from M''' to M, the orbital motion again overtakes the axial motion, and AB is again perpendicular to ME.

(3) Parallactic Libration.—While an observer at the centre of the earth would get the same view of the moon, whether she were on the eastern horizon, in the zenith, or on the western horizon, an observer on the surface of the earth does not get exactly the same view in these three cases. When the moon is on the eastern horizon, an observer on the surface of the earth would see a little farther around on the western limb of the moon than when she is in the zenith, and not quite so far around on the eastern limb. On the contrary, when the moon is on the western horizon, an observer on the surface of the earth sees a little farther around on the eastern limb of the moon than when she is in the zenith, and not quite so far around on her western limb.

Fig. 120.

This will be evident from Fig. 120. E is the centre of the earth, and O a point on its surface. AB is a line drawn through the centre of the moon, perpendicular to a line joining the centres of the moon and the earth. This line marks off the part of the moon turned towards the centre of the earth, and remains essentially the same during the day. CD is a line drawn through the centre of the moon perpendicular to a line joining the centre of the moon and the point of observation. This line marks off the part of the moon turned towards O. When the moon is in the zenith, CD coincides with AB; but, when the moon is on the horizon, CD is inclined to AB. When the moon is on the eastern horizon, an observer at O sees a little beyond B, and not quite to A; and, when she is on the western horizon, he sees a little beyond A, and not quite to B. B is on the western limb of the moon, and A on her eastern limb.

Since this libration is due to the point from which the moon is viewed, it is called parallactic libration; and, since it occurs daily, it is called diurnal libration.

Fig. 121.

107. Portion of the Lunar Surface brought into View by Libration.—The area brought into view by the first two librations is between one-twelfth and one-thirteenth of the whole lunar surface, or nearly one-sixth of the hemisphere of the moon which is turned away from the earth when the moon is at her state of mean libration. Of course a precisely equal portion of the hemisphere turned towards us during mean libration is carried out of view by the lunar librations.

If we add to each of these areas a fringe about one degree wide, due to the diurnal libration, and which we may call the parallactic fringe, we shall find that the total area brought into view is almost exactly one-eleventh part of the whole surface of the moon. A similar area is carried out of view; so that the whole region thus swayed out of and into view amounts to two-elevenths of the moon's surface. This area is shown in Fig. 121, which is a side view of the moon.

Fig. 122.

108. The Moon's Path through Space.—Were the earth stationary, the moon would describe an ellipse around it similar to that of Fig. 113; but, as the earth moves forward in her orbit at the same time that the moon revolves around it, the moon is made to describe a sinuous path, as shown by the continuous line in Fig. 122. This feature of the moon's path is greatly exaggerated in the upper portion of the diagram. The form of her path is given with a greater degree of accuracy in the lower part of the figure (the broken line represents the path of the earth); but even here there is considerable exaggeration. The complete serpentine path of the moon around the sun is shown, greatly exaggerated, in Fig. 123, the broken line being the path of the earth.

Fig. 123.

The path described by the moon through space is much the same as that described by a point on the circumference of a wheel which is rolled over another wheel. If we place a circular disk against the wall, and carefully roll along its edge another circular disk (to which a piece of lead pencil has been fastened so as to mark upon the wall), the curve described will somewhat resemble that described by the moon. This curve is called an epicycloid, and it will be seen that at every point it is concave towards the centre of the larger disk. In the same way the moon's orbit is at every point concave towards the sun.

Fig. 124.

The exaggeration of the sinuosity in Fig. 123 will be more evident when it is stated, that, on the scale of Fig. 124, the whole of the serpentine curve would lie within the breadth of the fine circular line MM'.

109. The Lunar Day.—The lunar day is twenty-nine times and a half as long as the terrestrial day. Near the moon's equator the sun shines without intermission nearly fifteen of our days, and is absent for the same length of time. Consequently, the vicissitudes of temperature to which the surface is exposed must be very great. During the long lunar night the temperature of a body on the moon's surface would probably fall lower than is ever known on the earth, while during the day it must rise higher than anywhere on our planet.

Fig. 125.

It might seem, that, since the moon rotates on her axis in about twenty-seven days, the lunar day ought to be twenty-seven days long, instead of twenty-nine. There is, however, a solar, as well as a sidereal, day at the moon, as on the earth; and the solar day at the moon is longer than the sidereal day, for the same reason as on the earth. During the solar day the moon must make both a synodical rotation and a synodical revolution. This will be evident from Fig. 125, in which is shown the path of the moon during one complete lunation. E, E', E'', etc., are the successive positions of the earth; and 1, 2, 3, 4, 5, the successive positions of the moon. The small arrows indicate the direction of the moon's rotation. The moon is full at 1 and 5. At 1, A, at the centre of the moon's disk, will have the sun, which lies in the direction AS, upon the meridian. Before A will again have the sun on the meridian, the moon must have made a synodical revolution; and, as will be seen by the dotted lines, she must have made more than a complete rotation. The rotation which brings the point A into the same relation to the earth and sun is called a synodical rotation.

It will also be evident from this diagram that the moon must make a synodical rotation during a synodical revolution, in order always to present the same side to the earth.

110. The Earth as seen from the Moon.—To an observer on the moon, the earth would be an immense moon, going through the same phases that the moon does to us; but, instead of rising and setting, it would only oscillate to and fro through a few degrees. On the other side of the moon it would never be seen at all. The peculiarities of the moon's motions which cause the librations, and make a spot on the moon's disk seem to an observer on the earth to oscillate to and fro, would cause the earth as a whole to appear to a lunar observer to oscillate to and fro in the heavens in a similar manner.

It is a well-known fact, that, at the time of new moon, the dark part of the moon's surface is partially illumined, so that it becomes visible to the naked eye. This must be due to the light reflected to the moon from the earth. Since at new moon the moon is between the earth and sun, it follows, that, when it is new moon at the earth, it must be full earth at the moon: hence, while the bright crescent is enjoying full sunlight, the dark part of its surface is enjoying the light of the full earth. Fig. 126 represents the full earth as seen from the moon.

Fig. 126.

The Atmosphere of the Moon.

111. The Moon has no Appreciable Atmosphere.—There are several reasons for believing that the moon has little or no atmosphere.

(1) Had the moon an atmosphere, it would be indicated at the time of a solar eclipse, when the moon passes over the disk of the sun. If the atmosphere were of any considerable density, it would absorb a part of the sun's rays, so as to produce a dusky border in front of the moon's disk, as shown in Fig. 127. In reality no such dusky border is ever seen; but the limb of the moon appears sharp, and clearly defined, as in Fig. 128.

Fig. 127.

Fig. 128.

If the atmosphere were not dense enough to produce this dusky border, its refraction would be sufficient to distort the delicate cusps of the sun's crescent in the manner shown at the top of Fig. 125; but no such distortion is ever observed. The cusps always appear clear and sharp, as shown at the bottom of the figure: hence it would seem that there can be no atmosphere of appreciable density at the moon.

(2) The absence of an atmosphere from the moon is also shown by the absence of twilight and of diffused daylight.

Upon the earth, twilight continues until the sun is eighteen degrees below the horizon; that is, day and night are separated by a belt twelve hundred miles in breadth, in which the transition from light to darkness is gradual. We have seen (66) that this twilight results from the refraction and reflection of light by our atmosphere; and, if the moon had an atmosphere, we should notice a similar gradual transition from the bright to the dark portions of her surface. Such, however, is not the case. The boundary between the light and darkness, though irregular, is sharply defined. Close to this boundary the unillumined portion of the moon appears just as dark as at any distance from it.

The shadows on the moon are also pitchy black, without a trace of diffused daylight.

Fig. 129.

(3) The absence of an atmosphere is also proved by the absence of refraction when the moon passes between us and the stars. Let AB (Fig. 129) represent the disk of the moon, and CD an atmosphere supposed to surround it. Let SAE represent a straight line from the earth, touching the moon at A, and let S be a star situated in the direction of this line. If the moon had no atmosphere, this star would appear to touch the edge of the moon at A; but, if the moon had an atmosphere, a star behind the edge of the moon, at S', would be visible at the earth; for the ray S'A would be bent by the atmosphere into the direction AE'. So, also, on the opposite side of the moon, a star might be seen at the earth, although really behind the edge of the moon: hence, if the moon had an atmosphere, the time during which a star would be concealed by the moon would be less than if it had no atmosphere, and the amount of this effect must be proportional to the density of the atmosphere.

The moon, in her orbital course across the heavens, is continually passing before, or occulting, some of the stars that so thickly stud her apparent path; and when we see a star thus pass behind the lunar disk on one side, and come out again on the other side, we are virtually observing the setting and rising of that star upon the moon. The moon's apparent diameter has been measured over and over again, and is known with great accuracy; the rate of her motion across the sky is also known with perfect accuracy: hence it is easy to calculate how long the moon will take to travel across a part of the sky exactly equal in length to her own diameter. Supposing, then, that we observe a star pass behind the moon, and out again, it is clear, that, if there is no atmosphere, the interval of time during which it remains occulted ought to be exactly equal to the computed time which the moon would take to pass over the star. If, however, from the existence of a lunar atmosphere, the star disappears too late, and re-appears too soon, as we have seen it would, these two intervals will not agree; the computed time will be greater than the observed time, and the difference will represent the amount of refraction the star's light has sustained or suffered, and hence the extent of atmosphere it has had to pass through.

Comparisons of these two intervals of time have been repeatedly made, the most extensive being executed under the direction of the Astronomer Royal of England, several years ago, and based upon no less than two hundred and ninety-six occultation observations. In this determination the measured or telescopic diameter of the moon was compared with the diameter deduced from the occultations; and it was found that the telescopic diameter was greater than the occultation diameter by two seconds of angular measurement, or by about a thousandth part of the whole diameter of the moon. This discrepancy is probably due, in part at least, to irradiation (91), which augments the apparent size of the moon, as seen in the telescope as well as with the naked eye; but, if the whole two seconds were caused by atmospheric refraction, this would imply a horizontal refraction of one second, which is only one two-thousandth of the earth's horizontal refraction. It is possible that an atmosphere competent to produce this refraction would not make itself visible in any other way.

But an atmosphere two thousand times rarer than our air can scarcely be regarded as an atmosphere at all. The contents of an air-pump receiver can seldom be rarefied to a greater extent than to about a thousandth of the density of air at the earth's surface; and the lunar atmosphere, if it exists at all, is thus proved to be twice as attenuated as what we commonly call a vacuum.

The Surface of the Moon.

Fig. 130.

112. Dusky Patches on the Disk of the Moon.—With the naked eye, large dusky patches are seen on the moon, in which popular fancy has detected a resemblance to a human face. With a telescope of low power, these dark patches appear as smooth as water, and they were once supposed to be seas. This theory was the origin of the name mare (Latin for sea), which is still applied to the larger of these plains; but, if there were water on the surface of the moon, it could not fail to manifest its presence by its vapor, which would form an appreciable atmosphere. Moreover, with a high telescopic power, these plains present a more or less uneven surface; and, as the elevations and depressions are found to be permanent, they cannot, of course, belong to the surface of water.

The chief of these plains are shown in Fig. 130. They are Mare Crisium, Mare Foecunditatis, Mare Nectaris, Mare Tranquillitatis, Mare Serenitatis, Mare Imbrium, Mare Frigoris, and Oceanus Procellarum. All these plains can easily be recognized on the surface of the full moon with the unaided eye.

113. The Terminator of the Moon.—The terminator of the moon is the line which separates the bright and dark portions of its disk. When viewed with a telescope of even moderate power, the terminator is seen to be very irregular and uneven. Many bright points are seen just outside of the terminator in the dark portion of the disk, while all along in the neighborhood of the terminator are bright patches and dense shadows. These appearances are shown in Figs. 131 and 132, which represent the moon near the first and last quarters. They indicate that the surface of the moon is very rough and uneven.

Fig. 131.

Fig. 132.

As it is always either sunrise or sunset along the terminator, the bright spots outside of it are clearly the tops of mountains, which catch the rays of the sun while their bases are in the shade. The bright patches in the neighborhood of the terminator are the sides of hills and mountains which are receiving the full light of the sun, while the dense shadows near by are cast by these elevations.

114. Height of the Lunar Mountains.—There are two methods of finding the height of lunar mountains:—

(1) We may measure the length of the shadows, and then calculate the height of the mountains that would cast such shadows with the sun at the required height above the horizon.

The length of a shadow may be obtained by the following method: the longitudinal wire of the micrometer (19) is adjusted so as to pass through the shadow whose length is to be measured, and the transverse wires are placed one at each end of the shadow, as shown in Fig. 133. The micrometer screw is then turned till the wires are brought together, so as to ascertain the length of the arc between them. We may then form the proportion: the number of seconds in the semi-diameter of the moon is to the number of seconds in the length of the shadow, as the length of the moon's radius in miles to the length of the shadow in miles.

Fig. 133.

The height of the sun above the horizon is ascertained by measuring the angular distance of the mountain from the terminator.

(2) We may measure the distance of a bright point from the terminator, and then construct a right-angled triangle, as shown in Fig. 134. A solution of this triangle will enable us to ascertain the height of the mountain whose top is just catching the level rays of the sun.

Fig. 134.

B is the centre of the moon, M the top of the mountain, and SAM a ray of sunlight which just grazes the terminator at A, and then strikes the top of the mountain at M. The triangle BAM is right-angled at A. BA is the radius of the moon, and AM is known by measurement; BM, the hypothenuse, may then be found by computation. BM is evidently equal to the radius of the moon plus the height of the mountain.

By one or the other of these methods, the heights of the lunar mountains have been found with a great degree of accuracy. It is claimed that the heights of the lunar mountains are more accurately known than those of the mountains on the earth. Compared with the size of the moon, lunar mountains attain a greater height than those on the earth.

115. General Aspect of the Lunar Surface.—A cursory examination of the moon with a low power is sufficient to show the prevalence of crater-like inequalities and the general tendency to circular shape which is apparent in nearly all the surface markings; for even the large "seas" and the smaller patches of the same character repeat in their outlines the round form of the craters. It is along the terminator that we see these crater-like spots to the best advantage; as it is there that the rising or setting sun casts long shadows over the lunar landscape, and brings elevations into bold relief. They vary greatly in size; some being so large as to bear a sensible proportion to the moon's diameter, while the smallest are so minute as to need the most powerful telescopes and the finest conditions of atmosphere to perceive them.

Fig. 135.

The prevalence of ring-shaped mountains and plains will be evident from Fig. 135, which is from a photograph of a model of the moon constructed by Nasmyth.

This same feature is nearly as marked in Figs. 131 and 132, which are copies of Rutherfurd's photographs of the moon.

116. Lunar Craters.—The smaller saucer-shaped formations on the surface of the moon are called craters. They are of all sizes, from a mile to a hundred and fifty miles in diameter; and they are supposed to be of volcanic origin. A high telescopic power shows that these craters vary remarkably, not only in size, but also in structure and arrangement. Some are considerably elevated above the surrounding surface, others are basins hollowed out of that surface, and with low surrounding ramparts; some are like walled plains, while the majority have their lowest depression considerably below the surrounding surface; some are isolated upon the plains, others are thickly crowded together, overlapping and intruding upon each other; some have elevated peaks or cones in their centres, and some are without these central cones, while others, again, contain several minute craters instead; some have their ramparts whole and perfect, others have them broken or deformed, and many have them divided into terraces, especially on their inner sides.

A typical lunar crater is shown in Fig. 136.

Fig. 136.

It is not generally believed that any active volcanoes exist on the moon at the present time, though some observers have thought they discerned indications of such volcanoes.

Fig. 137.

117. Copernicus.—This is one of the grandest of lunar craters (Fig. 137). Although its diameter (forty-six miles) is exceeded by others, yet, taken as a whole, it forms one of the most impressive and interesting objects of its class. Its situation, near the centre of the lunar disk, renders all its wonderful details conspicuous, as well as those of objects immediately surrounding it. Its vast rampart rises to upwards of twelve thousand feet above the level of the plateau, nearly in the centre of which stands a magnificent group of cones, three of which attain a height of more than twenty-four hundred feet.

Many ridges, or spurs, may be observed leading away from the outer banks of the great rampart. Around the crater, extending to a distance of more than a hundred miles on every side, there is a complex network of bright streaks, which diverge in all directions. These streaks do not appear in the figure, nor are they seen upon the moon, except at and near the full phase. They show conspicuously, however, by their united lustre on the full moon.

This crater is seen just to the south-west of the large dusky plain in the upper part of Fig. 132. This plain is Mare Imbrium, and the mountain-chain seen a little to the right of Copernicus is named the Apennines. Copernicus is also seen in Fig. 135, a little to the left of the same range.

Under circumstances specially favorable, myriads of comparatively minute but perfectly formed craters may be observed for more than seventy miles on all sides around Copernicus. The district on the south-east side is specially rich in these thickly scattered craters, which we have reason to suppose stand over or upon the bright streaks.

118. Dark Chasms.—Dark cracks, or chasms, have been observed on various parts of the moon's surface. They sometimes occur singly, and sometimes in groups. They are often seen to radiate from some central cone, and they appear to be of volcanic origin. They have been called canals and rills.

Fig. 138.

One of the most remarkable groups of these chasms is that to the west of the crater named Triesneker. The crater and the chasms are shown in Fig. 138. Several of these great cracks obviously diverge from a small crater near the west bank of the great one, and they subdivide as they extend from the apparent point of divergence, while they are crossed by others. These cracks, or chasms, are nearly a mile broad at the widest part, and, after extending full a hundred miles, taper away till they become invisible.

Fig. 139.

119. Mountain-Ranges.—There are comparatively few mountain-ranges on the moon. The three most conspicuous are those which partially enclose Mare Imbrium; namely, the Apennines on the south, and the Caucasus and the Alps on the east and north-east. The Apennines are the most extended of these, having a length of about four hundred and fifty miles. They rise gradually, from a comparatively level surface towards the south-west, in the form of innumerable small elevations, which increase in number and height towards the north-east, where they culminate in a range of peaks whose altitude and rugged aspect must form one of the most terribly grand and romantic scenes which imagination can conceive. The north-east face of the range terminates abruptly in an almost vertical precipice; while over the plain beneath, intensely black spire-like shadows are cast, some of which at sunrise extend full ninety miles, till they lose themselves in the general shading due to the curvature of the lunar surface. Many of the peaks rise to heights of from eighteen thousand to twenty thousand feet above the plain at their north-east base (Fig. 139).

Fig. 140.

Fig. 140 represents an ideal lunar landscape near the base of such a lunar range. Owing to the absence of an atmosphere, the stars will be visible in full daylight.

Fig. 141.

120. The Valley of the Alps.—The range of the Alps is shown in Fig. 141. The great crater at the north end of this range is named Plato. It is seventy miles in diameter.

The most remarkable feature of the Alps is the valley near the centre of the range. It is more than seventy-five miles long, and about six miles wide at the broadest part. When examined under favorable circumstances, with a high magnifying power, it is seen to be a vast flat-bottomed valley, bordered by gigantic mountains, some of which attain heights of ten thousand feet or more.

Fig. 142.

121. Isolated Peaks.—There are comparatively few isolated peaks to be found on the surface of the moon. One of the most remarkable of these is that known as Pico, and shown in Fig. 142. Its height exceeds eight thousand feet, and it is about three times as long at the base as it is broad. The summit is cleft into three peaks, as is shown by the three-peaked shadow it casts on the plain.

122. Bright Rays.—About the time of full moon, with a telescope of moderate power, a number of bright lines may be seen radiating from several of the lunar craters, extending often to the distance of hundreds of miles. These streaks do not arise from any perceptible difference of level of the surface, they have no very definite outline, and they do not present any sloping sides to catch more sunlight, and thus shine brighter, than the general surface. Indeed, one great peculiarity of them is, that they come out most forcibly when the sun is shining perpendicularly upon them: hence they are best seen when the moon is at full, and they are not visible at all at those regions upon which the sun is rising or setting. They are not diverted by elevations in their path, but traverse in their course craters, mountains, and plains alike, giving a slight additional brightness to all objects over which they pass, but producing no other effect upon them. "They look as if, after the whole surface of the moon had assumed its final configuration, a vast brush charged with a whitish pigment had been drawn over the globe in straight lines, radiating from a central point, leaving its trail upon every thing it touched, but obscuring nothing."

Fig. 143.

The three most conspicuous craters from which these lines radiate are Tycho, Copernicus, and Kepler. Tycho is seen at the bottom of Figs. 143 and 130. Kepler is a little to the left of Copernicus in the same figures.

It has been thought that these bright streaks are chasms which have been filled with molten lava, which, on cooling, would afford a smooth reflecting surface on the top.

123. Tycho.—This crater is fifty-four miles in diameter, and about sixteen thousand feet deep, from the highest ridge of the rampart to the surface of the plateau, whence rises a central cone five thousand feet high. It is one of the most conspicuous of all the lunar craters; not so much on account of its dimensions as from its being the centre from whence diverge those remarkable bright streaks, many of which may be traced over a thousand miles of the moon's surface (Fig. 143). Tycho appears to be an instance of a vast disruptive action which rent the solid crust of the moon into radiating fissures, which were subsequently filled with molten matter, whose superior luminosity marks the course of the cracks in all directions from the crater as their common centre. So numerous are these bright streaks when examined by the aid of the telescope, and they give to this region of the moon's surface such increased luminosity, that, when viewed as a whole, the locality can be distinctly seen at full moon by the unassisted eye, as a bright patch of light on the southern portion of the disk.