12h: 44m. 2.9sec.) The mean lengths of daylight and night are therefore respectively equal to nearly 15 of our entire days of 24 hours duration."

332. At the lunar equator the days and nights are of equal length, each being about 354 hours and 22 minutes long, (14d. 18h. 22m. 1.5sec.,) but they vary with the latitude. Thus at the lunar latitude of 45° the extent of the longest day' is 354h. 19m., and that of the shortest 351h. 26m.; while at latitude 88°, the longest day has a duration of 449h. 28m., and the shortest of 259h. 16m.

333. THE APPEARANCE OF THE EARTH AS SEEN FROM THE MOON. To the inhabitants of the moon (if any there are,) our earth is seen as a moon of immense size, its apparent surface being sixteen times greater than that of the sun as he appears to us. For this reason a vast amount of light must be reflected from our globe to the moon, and all the varied lunar phases which we behold would be exhibited by the earth to a lunar spectator with a wonderful radiance and distinetness, but in an inverse order. Thus when it is new moon to us it would be full earth to an observer on the moon, and when full moon here, new earth there.

334. Another remarkable difference also exists. The moon is seen by us occupying various positions in the heavens, as she displays her successive phases; but the earth would appear to an inhabitant of the moon to be fixed in the heavens, during all her periodical fluctuations of light. The cause of this singular phenomenon is easily explained. The moon turns on her axis from west to east just as the earth does, but an inhabitant of the moon would be as unconscious of its rotation, as we are of the rotation of the earth. Accordingly, as with us, the sun and the other fixed heavenly bodies would appear to him to be moving from east to west, at the same rate that his own orb rotates on its axis. Such would be the apparent motion of the earth to a specta

1. The word day is here used in distinction from night.

What the respective lengths of day and night at the lunar equator? What the duration of the longest and shortest days at the lunar latitude of 45°? What at 88° ? How would our earth appear to an inhabitant of the moon? In what order would the phases of the earth be exhibited?

ACCELERATION OF THE MOON'S MOTION, &C. 171

tor upon the moon, if the earth was actually stationary; but this is not the case, for our globe advances from west to east in her orbit, just as rapidly as the rotation of the moon tends to give it an apparent retrograde motion from east to west. The earth, therefore, apparently moving in one direction exactly as fast as it actually moves in the opposite direction, consequently seems to an inhabitant of the moon to stand still in the heavens.

335. These phenomena would only be seen by a spectator on the side of the moon nearest to us, for to those inhabiting the remote hemisphere the earth would never come into view. Their long nights of nearly 15 days duration would therefore be extremely dark, since the brightest heavenly bodies, whose light could dissipate the gloom, are Mars and Jupiter, which would afford no more illumination to the inhabitants of the moon than they do to us.

336. ACCELERATION OF THE MOON'S MOTION IN HER ORBIT. The time occupied by the moon in revolving about the earth is now really less than it was centuries ago. This remarkable fact was discovered by Dr. Halley, in the following manner. Knowing the periodic time of the moon, as computed from the observations of modern astronomers, he compared it with that, deduced from the Chaldean observations of eclipses at Babylon, in the years 719 and 720, before Christ; and also with the periodic time obtained from observations made at Cairo, by Ebn Junis, an Arabian astronomer who flourished in the 10th century.

1. The moon would present the same phenomenon to us if she completed a revolution in her orbit in a sidereal day, for she would then actually move as fast from west to east as she would apparently move from east to west on account of the rotation of the earth. Under these circumstances, she would seem not to move at all.

2. Though the earth would have no progressive motion in the heavens, she would change her place a little on account of her librations, rocking to and fro to a small extent in a direction parallel to her equator (libration in longitude,) and also in a direction perpendicular to it (libration in latitude.)

Would the earth have any apparent motion as seen from the moon? Give the explanation? Could these phenomena be seen from every point of the moon's surface? Why not? What is said respecting the nights that prevail throughout that hemisphere of the moon which is turned from us? What is said in respect to the time now occupied by the moon in revolving about the earth?

337. These comparisons showed, that the motion of the moon had been accelerated from the era of the Chaldean observations to that of Ebn Junis, and also from his time to that of Dr. Halley.

The investigations of the profound mathematician La Place, have proved the existence of this phenomenon beyond a doubt.

The amount of this acceleration of the moon's motion is extremely small being only a little more than ten seconds (10) in every hundred years.

338. This variation in the moon's velocity, was at first accounted for, by supposing that the space through which she moved was filled with a fluid like air, which, by the resistance, it opposed to the mass of the moon, lessened her centrifugal force. The earth would conse quently draw the moon closer to herself, thus diminishing the magnitude of her orbit and decreasing her periodic time.1

339. La Place, however, showed that this view was erroneous, and proved that this increase of motion was caused by a gradual diminution in the eccentricity of the earth's orbit. Moreover, that this diminution will continue for ages, when it will cease, and then the eccentricity will begin in turn to increase; and that these alternate changes will continue while the solar system exists. The acceleration of the moon must therefore follow the same law. For ages the motion will grow swifter and swifter until the eccentricity of the earth's orbit begins to increase; after that era the moon's motion will be gradually slower and slower; until again, at the end of countless ages, the limit will be reached, and her speed once more accelerated.

340. THE MOON'S PATH IN SPACE. Since the moon revolves about the earth, and at the same time about the

1. The periodic time of the moon is the time occupied by this orb, in completing a revolution about the earth.

2. The periodic time being decreased, the motion of the moon must be increased.

Who discovered this fact? In what manner? Whose investigations clearly proved its existence? What is the rate of the acceleration? How was this phenomenon at first accounted for? What did La Place prove?

ECLIPSES OF THE SUN AND MOON.

173

sun,' moving along with the earth in its annual circuit, her path in space necessarily partakes of these two motions. Being now inside of the earth's orbit, and now outside, the course she describes around the sun will be a circular waving line, alternately convex and concave toward this luminary. In fact her path is similar in form to that described by the pole of the equator around the pole of the ecliptic, under the combined influences of precession and nutation; and the waving line in Fig. 35, represents approximately the kind of path marked out by the moon in her circuit around the sun.

341. The moon in her motions is subject to numerous irregularities, the explanation of which has tasked the highest powers of the most gifted astronomers.

CHAPTER III.

ECLIPSES OF THE SUN AND MOON.

342. THE eclipses of the sun and moon are among the most grand and sublime of the phenomena of the heavens. In all ages of the world, they have been viewed by the ignorant with wonder and awe; while to the man of science they have ever been subjects of deep interest and profound study.

LUNAR ECLIPSES.

343. An eclipse of the moon is the partial or total obscuration of her light, when she passes into the shadow of the earth. The sun, earth, and moon, are then in nearly the same straight line with the earth between the other two bodies. If the moon were self-luminous, like the sun, a

1. The moon is not borne along by the earth, around the sun, she would revolve about the latter, if the earth was annihilated.

State what is said respecting the moon's path in space? What in regard to her motions? Of what does Chapter III. treat? What is said respecting the eclipses of the sun and moon? What is an eclipse of the moon? When it occurs, what are the relative positions of the sun, moon, and earth?

lunar eclipse could never occur; but shining as she does by reflection from the sun, the interposition of the solid body of the earth, cuts off the solar light, and the portions of the moon that enter the earth's shadow appear dark to our view. A lunar eclipse can never happen except when the moon is full, for it is only at this time that the earth is between the sun and moon, and its shadow is extended in the direction of the latter.

344. If the plane of the moon's orbit coincided exactly with the plane of the ecliptic, she would pass through the earth's shadow at every revolution, and a lunar eclipse would take place at every full moon. But as the former is inclined to the latter at an angle of about 5° (Art. 312,) the shadow of the earth may at one time pass above the full moon, and at another below it. The full moon must therefore take place within a certain distance of one of her nodes, that is, near the plane of the ecliptic, to make it possible for an eclipse to occur.

1

345. When the moon, at the full, has her centre exactly at her node, it is in the same straight line with the centres of the sun and earth, and she is placed centrally in the shadow of the earth. But it is not necessary that the moon should be precisely in this position in order that an eclipse may happen; for since she possesses an apparent breadth of about 30, and the shadow of the earth extends on each side of the node, her disk may be obscured when she is within a short distance of this point.

The calculations of astronomers accordingly show that an eclipse may happen when the moon at the full, is not more than 12° 24' distant from one of her nodes, and must happen if her distance does not exceed 9°.

1. It will be remembered that the moon's nodes are those points in her orbit where the latter intersects with the plane of the ecliptic. They are consequently at once in the plane of the moon's orbit, and in that of the earth's.

2. Eclipses are so called from the fact here stated; viz., that they occur in or near the plane of the ecliptic.

If the moon was self-luminous would there be any lunar eclipses? In what phase must the moon be when a lunar eclipse happens? If the plane of the ecliptic and that of the moon's orbit coincided, how often would lunar eclipses occur? Why do they not now take place every month? Near what point must the full moon be to make it possible for an eclipse to happen? Explain why it is not necessary for the moon to be exactly at one phenomenon to occur? State the limits within which a lunar Those within which it must happen?

of her nodes for this eclipse may happen?