marked on this diagram, and he will be enabled to understand more easily what is meant by the inclination of the planets' orbits.

It will be perceived on the diagram, that the inclination of Mercury's orbit to the plane of the ecliptic is 7° 9''.

These points of intersection are called the Nodes of the orbit. Mercury's ascending node is in the 16th degree of Taurus; its descending node in the 16th degree of Scorpio. As the Earth passes these nodes in November and May, the transits of Mercury must happen, for many ages to come, in one of these months.

The following is a list of all the Transits of Mercury from the time the first was observed by Gassendi, November 6, 1631, to the end of the present cen

By comparing the mean motion of any of the planets with the mean motion of the Earth, we may, in like manner, determine the periods in which these bodies will return to the same points of their orbit, and the same positions with respect to the Sun. The knowledge of these periods will enable us to determine the hour when the planets rise, set, and pass the meridian, and in general, all the phenomena dependent upon the relative position of the Earth, the planet, and the Sun; for at the end of one of these periods they commence again, and all recur in the same order. We have only to find a number of sidereal years, in which the planet completes exactly, or very nearly, a certain number of revolutions; that is, to find such a number of planetary revolutions, as, when taken together, shall be exactly equal to one, or any number of revolutions of the Earth. In the case of Mercury, this ratio will be, as 87.969 is to 365.256. Whence we find, that,

7 periodical revolutions of the Earth, are equal to 29 of Mercury: 13 periodical revolutions of the Earth, are equal to 54 of Mercury: 33 periodical revolutions of the Earth, are equal to 137 of Mercury: 46 periodical revolutions of the Earth, are equal to 191 of Mercury. Therefore, transits of Mercury, at the same node, may happen at intervals of 7, 13, 33, 46, &c. years. Transits of Venus, as well as eclipses of the Sun and Moon, are calculated upon the same principle.

The sidereal revolution of a planet respects its absolute motion; and is measured by the time the planet takes to revolve from any fixed star to the same star again.

The synodical revolution of a planet respects its relative motion; and is measured by the time that a planet occupies in coming back to the same position with respect to the Earth and the Sun.

The sidereal revolution of Mercury, is 87d. 23h. 15m. 44s. Its synodical revolution is found by dividing the whole circumference of 360° by its relative motion in respect to the Earth. Thus, the mean daily motion of Mercury is

What are the points where the orbits of the planets intersect the orbit of the Earth called? Where is Mercury's ascending node? Where is its descending node? In what months must the transit of Mercury occur for many ages to come? Why must they occur in these months? How can we determine the periods in which the planets will return to the same points of their orbits, and the same positions in respect to the Sun? Why is it useful to know these periods? State the method of making the computation. What will the ratio be in the case of Mercury? State the ratio between the periodi cal revolutions of the Earth and Mercury. At what intervals then may transits of Mercury at the same node happen? Upon what principle are transits of Venus, and eclipses of the Sun and Moon, calculated? What is the sidereal revolution of a planet? What is the synodical revolution? What is the time of the sidereal revo lution of Mercury? State the method of computing the time of the synodical revo lution. Compute the synodical revolution of Mercury.

14732" .555; that of the Earth is 3548.318; and their difference is 11184" .237, being Mercury's relative motion, or what it gains on the Earth every day. Now by simple proportion, 11184.237 is to 1 day, as 360° is to 115d. 21h. 3', 25′′, the period of a synodical revolution of Mercury.

The absolute motion of Mercury in its orbit, is 109,757 miles an hour; that of the Earth, is 68,288 miles: the difference, 41,469 miles, is the mean relative motion of Mercury, with respect to the Earth.

VENUS.

THERE are but few persons who have not observed a beautiful star in the west, a little after sunset, called the evening star. This star is Venus. It is the second planet from the Sun. It is the brightest star in the firmament, and on this account easily distinguished from the other planets.

If we observe this planet for several days, we shall find that it does not remain constantly at the same distance from the Sun, but that it appears to approach, or recede from him, at the rate of about three fifths of a degree every day; and that it is sometimes on the east side of him, and sometimes on the west, thus continually oscillating backwards and forwards between certain limits.

As Venus never departs quite 48° from the Sun, it is never seen at midnight, nor in opposition to that luminary; being visible only about three hours after sunset, and as long before sunrise, according as its right ascension is greater or less than that of the Sun. At first, we behold it only a few minutes after sunset; the next evening we hardly discover any sensible change in its position; but after a few days, we perceive that it has fallen considerably behind the Sun, and that it continues to depart farther and farther from him, setting later and later every evening, until the distance between it and the Sun, is equal to a little more than half the space from the horizon to the zenith, or about 46°.

It now begins to return towards the Sun, making the same daily progress that it did in separating from him, and to set earlier and earlier every succeeding evening, until it finally sets with the Sun, and is lost in the splendour of his light.

A few days after the phenomena we have now described,

What is the rate per hour of the absolute motion of Mercury in its orbit? Of the Earth? What is the mean relative motion of Mercury with respect to the Earth? What beautiful star sometimes appears in the west a little after sunset? What is the comparative distance of Venus from the Sun? What is its comparative brightness? In what direction is its apparent motion? Why is it never seen at midnight, nor in opposition to the Sun? At what times is it visible? How long after sunset is it when we first behold it in the west Describe its changes of position.

we perceive, in the morning, near the eastern horizon, a bright star which was not visible before. This also is Venus, which is now called the morning star. It departs farther and farther from the Sun, rising a little earlier every day, until it is seen about 46°. west of him, where it appears stationary for a few days; then it resumes its course towards the Sun, appearing later and later every morning, until it rises with the Sun, and we cease to behold it. In a few days, the evening star again appears in the west, very near the setting-sun, and the same phenomena are again exhibited. Such are the visible appearances of Venus.

Venus revolves about the Sun from west to east in 224 days, at the distance of abont 68 millions of miles, moving in her orbit at the rate of 80 thousand miles an hour. She turns around on her axis once in 23 hours, 21 minutes, and 7 seconds. Thus her day is about 25 minutes shorter than ours, while her year is equal to 7 of our months, or 32 weeks.

The mean distance of the Earth from the Sun is estimated at 95 millions of miles, and that of Venus being 68 millions, the diameter of the Sun, as seen from Venus, will be to his diameter as seen from the Earth, as 95 to 68, and the surface of his disc as the square of 95 to the square of 68, that is, as 9025 to 4626, or as 2 to 1 nearly. The intensity of light and heat being inversely as the squares of their distances from the Sun, Venus receives twice as much light and heat as the Earth.

Her orbit is within the orbit of the Earth; for if it were not, she would be seen as often in opposition to the Sun, as in conjunction with him; but she was never seen rising in the east while the Sun was setting in the west. Nor was she ever seen in quadrature, or on the meridian, when the Sun was either rising or setting. Mercury being about 23° from the Sun, and Venus 46°, the orbit of Venus must be outside of the orbit of Mercury.

The true diameter of Venus is 7621 miles; but her apparent diameter and brightness are constantly varying, according to her distance from the Earth. When Venus and the Earth are on the same side of the Sun, her distance

In what direction, and in what time, does Venus revolve about the Sun? What is her distance from the Sun? What is the rate per hour of her motion in her orbit? In what time does she revolve on her axis? How are the lengths of her day and year, compared with those of the Earth? How much larger does the Sun appear at Venus than he does at the Earth? How much more light and heat does she receive from him, than the Earth? How much farther is Venus from the Sun than Mercary? On which side of the orbit of Mercury must her orbit be? What is her true diameter? In what proportion do her ap parent diameter and brightness constantly vary? What is her distance from the Earth when they are both on the same side of the Sun

from the Earth is only 26 millions of miles; when they are on opposite sides of the Sun, her distance is 164 millions of miles. Were the whole of her enlightened hemisphere turned towards us, when she is nearest, she would exhibit a light and brilliancy twenty-five times greater than she generally does, and appear like a small brilliant moon; but, at that time, her dark hemisphere is turned towards the Earth.

When Venus approaches nearest to the Earth, her apparent, or observed diameter, is 61.2; when most remote, it is only 9".6 now 612÷9′′.6 =6}, hence when nearest the Earth her apparent diameter is 63 times greater than when most distant, and surface of her disc (C), or nearly 41 times greater. In this work, the apparent size of the heavenly bodies is estimated from the apparent surface of their discs, which is always proportional to the squares of their apparent diameters.

When Venus' right ascension is less than that of the Sun, she rises before him; when greater, she appears after his setting. She continues alternately morning and evening star, for a period of 292 days, each time.

To those who are but little acquainted with astronomy, it will seem strange, at first, that Venus should apparently I continue longer on the east or west side of the Sun, than the whole time of her periodical revolution around him. But it will be easily understood, when it is considered, that while Venus moves around the Sun, at the rate of about 1° 36' of angular motion per day, the Earth follows at the rate of 59'; so that Venus actually gains on the Earth, only 37′ in a day. Now it is evident that both planets will appear to keep on the same side of the Sun, until Venus has gained half her orbit, or 180° in advance of the Earth; and this, at a mean rate, will require 292 days, since 292X37-10804', or 180° nearly.

Mercury and Venus are called Inferior* planets, because their orbits are within the Earth's orbit, or between it and the Sun. The other planets are denominated Superior, because their orbits are without or beyond the orbit of the

*In almost all works on Astronomy, Mercury and Venus are denominated inferior planets, and the others, superior. But as these terms are employed, not to express the relative size of the planets, but to indicate their situation with respect to the Earth, it would be better to adopt the terms interior and exterior.

What is it when they are on opposite sides of the Sun? Which hemisphere is turned towards the Earth when she is nearest to us? Were her enlightened hemisphere turned towards us at that time, how would her light and brilliancy be compared with that which she generally exhibits, and what would be her appearance? What is the length of her apparent diameter when she is nearest to the Earth? What is it when she is most remote? How is the apparent size of a heavenly body estimated in this work? In what circumstances does Venus rise before, and in what set after, the Sun? How long does she continue, each time, alternately morning and evening star? Why does she ap pear longer on the east or west side of the Sun than the whole time of her periodical revolution around him? Why are Mercury and Venus called Inferior planets? Why are the other planets termed Superior planets?

In unison to beat with mine. I want that noble heart of thine

Earth. [Plate I.] As the orbits of Mercury and Venus lie within the Earth's orbit, it is plain, that once in every synodical revolution, each of these planets will be in conjunction on the same side of the Sun. In the former case, the planet is said to be in its inferior conjunction, and in the latter case, in its superior conjunction; as in the following figure.

The period of Venus' synodical revolution is found in the same manner as that of Mercury; namely, by dividing the whole circumference of her orbit by her mean relative motion in a day. Thus, Venus' absolute mean daily motion is 1° 36′ 7.8, the Earth's is 59' 8'.3, and their difference 36′59′′.5. Divide 360° by 36' 59''.5, and it gives 583.920, or nearly 584 days, for Venus' synodical revolution, or the period in which she is twice in conjunction with the Earth.

Venus passes from her inferior to her superior conjunction in about 292 days. At her inferior conjunction, she is 26 millions of miles from the Earth; at her superior conjunction, 164 millions of miles.

How often, in every synodical revolution, will each of these planets be in conjunction on the same side of the Sun that the Earth is? How often on the opposite side? Explain this. What names distinguish these two species of conjunction? How is the sy nodical revolution of Venus found? Make the calculation. How long is she in passing from her inferior to her superior conjunction? How far is she from the Earth at her inferior conjunction? How far at her superior