The difference between mean and apparent time, or, in other words, between Equinoctial and Ecliptic time, may be further shown by this figure, which represents the circles of the

sphere Let it be first premised, that equinoctial time is clock time; and that ecliptic time is solar or apparent time. It appears that from Aries to Cancer, the Sun in the ecliptic comes to the meridian before the equinoctial Sun; from Cancer to Libra, after it; from Libra to Capricorn before it; and from Capricorn to Aries after it. If we notice what months the Sun is in these several quarters, we shall find that from the 25th of December to the 16th of April, and from the 16th of June to the 1st of September, the clock is faster than the sun-dial; and that, from

the 16th of April to the 16th of June, and from the 1st of September to the 25th of Dec., the sun-dial is faster than the clock.

398. It is an universal fact, that, while none of the planets are perfect spheres, none of their orbits are perfect circles. The planets all revolve about the Sun, in ellipses of different degrees of eccentricity; having the Sun, not in the center of the ellipse, but in one of its foci.

D

B

The figure A D B E is an ellipse. The line A B is called the transverse axis, and the line drawn through the middle of this line, and perpendicular to it, is the conjugate axis. The point C, the middle of the transverse axis, is the center of the ellipse. The points F and f, equally distant from C, are called the foci. CF, the distance from the center to one of the foci, Ais called the eccentricity. The orbits of the planets being ellipses, having the Sun in one of the foci, if ADBE be the orbit of a planet, with the Sun in the focus F, when the planet is at the point A, it will be in its perihelion, or nearest the Sun; and when at the point B in its aphelion, or at its greatest distance from the Sun. The difference in these distances is evidently equal to F f, that is, equal to twice the eccentricity of its orbit. In every revolution, a planet passes through its perihelion and aphelion. The eccentricity of the Earth's orbit is about one and a half millions of miles; hence she is 3,000,000 of miles nearer the Sun in her perihelion, than in her aphelion.

E

Now as the Sun remains fixed in the lower focus of the Earth's orbit, it is easy to perceive that a line, passing centrally through the Sun at right angles with the longer axis of the orbit, will divide it into two unequal segments. Precisely thus it is divided by the equinoctial.

399. That portion of the Earth's orbit which lies above the

398. What is the true form of the planets' orbits? Why is equinoctial time irregular? 899. How is the Earth's orbit divided by the equinoctial?

Sun, or north of the equinoctial, contains about 184 degrees, while that portion of it which lies below the Sun, or south of the equinoctial, contains only 176 degrees. This fact shows why the Sun continues about eight days longer on the north side of the equator in summer, than it does on the south side in winter. The exact calculation, for the year 1830, is as follows:

The points of the Earth's orbit which correspond to its greatest and least distances from the Sun, are called, the former the Apogee, and the latter the Perigee; two Greek words, the former of which signifies from the Earth, and the latter about the Earth. These points are also designated by the common name of Apsides.

400. The Earth being in its perihelion about the 1st of January, and in its aphelion the 1st of July, we are 3,000,000 of miles nearer the Sun in winter than in midsummer. The reason why we have not, as might be expected, the hottest weather when the Earth is nearest the Sun, is, because the Sun, at that time, having retreated to the southern tropic, shines so obliquely on the northern hemisphere, that its rays have scarcely half the effect of the summer Sun; and continuing but a short time above the horizon, less heat is accumulated by day than is dissipated by night.

401. As the Earth performs its annual revolution around the Sun, the position of its axis remains invariably the same; always pointing to the North Pole of the heavens, and always maintaining the same inclination to its orbit. This seems to be providentially ordered for the benefit of mankind. If the axis of the Earth always pointed to the center of its orbit, all external objects would appear to whirl about our heads in an inexplicable maze. Nothing would appear permanent. The mariner could no longer direct his course by the stars, and every index in nature would mislead us.

What phenomenon does this explain? 400. When is the Earth in its perihelion? Its aphelion? What difference in its distance from the Sun? Why, then, have we not the warmest weather in January? 401. What said of the permanency of the Earth's axis? How would it be if either pole was toward the Sun?

CHAPTER IV.

THE MOON-HER DISTANCE, MOTIONS, PHASES, &o.

402. THERE is no object within the scope of astronomical observation which affords greater variety of interesting investigation than the various phases and motions of the Moon. From them the astronomer ascertains the form of the Earth, the vicissitudes of the tides, the causes of eclipses and occultations, the distance of the Sun, and, consequently, the magnitude of the solar system. These phenomena, which are perfectly obvious to the unassisted eye, served as a standard of measurement to all nations, until the advancement of science taught them the advantages of solar time. It is to these phenomena that the navigator is indebted for that precision of knowledge which guides him with well-grounded confidence through the pathless ocean./

The Hebrews, the Greeks, the Romans, and, in general, all the ancients, used to assemble at the time of new or full Moon, to discharge the duties of piety and gratitude for her unwearied attendance on the Earth, and all her manifold uses.

The philosophy of the changes of the Moon is illustrated by the following cut:

This cut represents the moon revolving eastward around the Earth. In the outside circle, she is represented as she would appear, if viewed from a direction at right angles with the plane of her orbit. The side toward the Sun is enlightened in every case, and she appears like a half moon at every point.

402. What said of the Moon's motions and phases? What learned from them? How used anciently? How at the present time? How did the ancients observe the new and full moons?

The interior suit represents her as she appears when viewed from the earth. At A it is New Moon; and if seen at all so near the Sun, she would appear like a dark globe. At B she would appear like á crescent, concave toward the east. At C, more of her enlightened side is visible; at D still more; and at E the enlightened hemisphere is fully in view. We then call her a Full Moon. From E around to A again, the dark portion becomes more and more visible, as the luminous part goes out of view, till she comes to her change at A. When at D and F the moon is said to be gibbous.

403. When the Moon, after having been in conjunction with the Sun, emerges from his rays, she first appears in the evening, a little after sunset, like a fine luminous crescent, with its convex side towards the Sun. If we observe her the next evening, we find her about 13° farther east of the Sun than on the preceding evening, and her crescent of light sensibly augmented. Repeating these observations, we perceive that she departs farther and farther from the Sun, as her enlightened surface comes more and more into view, until she arrives at her first quarter, and comes to the meridian at sunset. She has then finished half her course from the new to the full, and half her enlightened hemisphere is turned towards the Earth.

404. After her first quarter, she appears more and more gibbous, as she recedes farther and farther from the Sun, until she has completed just half her revolution around the Earth, and is seen rising in the east when the Sun is setting in the west. She then presents her enlightened orb full to our view, and is said to be in opposition; because she is then on the opposite side of the Earth with respect to the Sun.

In the first half of her orbit she appears to pass over our heads through the upper hemisphere; she now descends below the eastern horizon to pass through that part of her orbit which lies in the lower hemisphere.

405. After her full she wanes through the same changes of pearance as before, but in an inverted order; and we see her in the morning like a fine thread of light, a little west of the rising Sun. For the next two or three days she is lost to our view, rising and setting in conjunction with the Sun; after which, she passes over, by reason of her daily motion, to the east side of the Sun, and we behold her again, a new Moon, as before. In changing sides with the Sun, she changes also the direction of her crescent. Before her conjunction it was turned to the east; it is now turned towards the west. These different appearances of the Moon are called her phases. They prove that she shines

403. Explain the cause of the changes of the Moon? 404. How after her first quarter? 405. How after her full? What change in her crescent? What do the Moon's phases prove?

not by any light of her own; if she did, being globular, we should always see her a round full orb like the Sun.

406. The Moon is a satellite to the Earth, about which she revolves in an elliptical orbit, in 29 days, 12 hours, 44 minutes, and 3 seconds; the time which elapses between one new moon and another. This is called her synodic revolution. Her revolution from any fixed star to the same star again, is called her periodic or sidereal revolution. It is accomplished in 27 days, 7 hours, 43 minutes, and 11 seconds; but in this time, the Earth has advanced nearly as many degrees in her orbit; consequently, the Moon, at the end of one complete revolution, must go as many degrees farther, before she will come again into the same position with respect to the Sun and the Earth.

SIDEREAL AND SYNODIO REVOLUTIONS OF THE MOON.

SIDEREAL REVOLUTION 27 DAYS

SYNODIC REVOLUTION 29 DAYS

SUN AND MOON IN CONJUNOTION-NEW MOON:

On the right, the earth is shown in her orbit, revolving around the sun, and the moon in her orbit, revolving around the earth. At A, the sun and moon are in conjunction, or it is New Moon. As the earth passes from D to E, the moon passes around from A to B, or the exact point in her orbit where she was 27 days before. But she is still west of the sun, and must pass on from B to C, or 1 day and 20 hours longer, before she can again come in conjunction with him. This 1 day and 20 hours constitutes the difference between a sidereal and a synodic revolution.

The student will perceive that the difference between a sidereal and synodic revolution of the moon, like that between solar and sidereal time, is due to the same cause, namely, the revolution of the earth around the sun.

407. Lying along the Moon's path, there are nine conspicuous stars that are used by nautical men for determining their longitude at sea, thence called nautical stars. These stars are, Arietes, Aldebaran, Pollux, Regulus, Spica Virginis, Antares, Altaire, Fomalhaut, and Markab.

The true places of these stars, for every day in the year, are given in the Nautical Almanac, a valuable work published annually by the English "Board of Admiralty," to guide mariners in navigating the seas. They are usually published two or three years in advance, for the benefit of long voyages

Let A in the cut represent Greenwich Observatory, near London. B is the Moon, and Cher apparent place among the distant stars, about 40° west of the star D. The ship E, having Greenwich time, as well as her own local time, sails from London westward;

406. Form of the lunar orbit? Time of synodic revolution? Of sidereal revolution? What difference? 407. What are the nautical stars? Can you explain how longitude is ascertained by them?