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÷9.66, hence when nearest the Earth her apparent diameter is 6 times great than vhen most distant, and surface of her disc (C), or nearly 41 times eater. n this work, the apparent size of the heavenly bodies is estimated firm 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 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 he 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 revo lution around him? Why are Mercury and Venus called Inferior planets? Why are the other planets termed Superior planets?

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 ber orhit 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?

It might be expected that her brilliancy would be propor, ionally increased, in the one case, and diminished, in the other; and so it would be, were it not that her enlightened hemisphere is turned more and more from us, as she approaches the Earth, and comes more and more into view as she recedes from it. It is to this cause alone that we must attribute the uniformity of her splendour as it usually appears to the naked eye.

Mercury and Venus present to us, successively, the various shapes and appearances of the Moon; waxing and waning through different phases, from the beautiful crescent to the full rounded orb. This fact shows, that they revolve around the Sun, and between the Sun and the Earth. Let the pupil endeavour to explain these phases on any other supposition, and he will be convinced that the system of Ptolemy is erroneous, while that of Copernicus is confirmed.

It should be remarked, however, that Venus is never seen when she is entire. ly full, except once or twice in a century, when she passes directly over the Sun's disc. At every other conjunction, she is either behind the Sun, or so near him as to be hidden by the splendour of his light. The diagram on the next page will better illustrate the various appearances of Venus, as she moves around the Sun, than any description of them could do.

From her inferior to her superior conjunction, Venus appears on the west side of the Sun, and is then our morning star; from her superior to her inferior conjunction she appears on the east side of the Sun, and is then our evening

star.

* The eminent astronomer, THOMAS DICK, LL. D., well known in this country as the author of the Christian Philosopher, Philosophy of a Future State, &c., in a review of this remark, observes-" This ought not to be laid down as a general truth. About the year 1813, I made a great variety of observations on Venus in the day time, by an equatorial instrument, and found, that she could be seen when only 1° 27′ from the Sun's margin, and consequently may be seen at the moment of her superior conjunction, when her geocentric latitude, at that time, equals or exceeds 1° 43′. I have some faint expectations of being able to see Venus, in the course of two or three days, at her superior conjunction, if the weather be favourable."-March 3, 1834.

Why is not her brilliancy proportionably increased in the former case, and diminished in the latter? What appearances do Mercury and Venus present to us at different times? What supposition is necessary for the explanation of these phases? What system do they tend to refute? What system do they confirm? How often is Venus seen when she is entirely full? Why is she not seen at the full oftener? In what part of her or bit does Venus appear on the west side of the Sun ? In what on the east? In what parts is she, alternately, morning and evening star?

Like Mercury, she sometimes seems to be stationary. Her apparent motion, like his, is sometimes rapid; at one time, direct, and at another, retrograde; vibrating alternately backwards and forwards, from west to east, and from east to west. These vibrations appear to extend from 45° to 47°, on each side of the Sun.

Consequently she never appears in the eastern horizon, more than three hours before sunrise, nor continues longer in the western horizon, after sunAny star or planet, therefore, however brilliant it may appear, which is seen earlier or later than this, cannot be Venus.

set.

In passing from her western to her eastern elongation, her motion is from west to east, in the order of the signs; it is thence called direct motion. In passing from her eastern to her western elongation, her motion with respect to the Earth, is from east to west, contrary to the order of the signs; it is thence denominated retrograde motion. Her motion appears quickest about the time of her conjunctions; and she seems stationary, at her elongations. She is brightest about 36 days before and after her inferior conjunction, when her light is so great as to project a visible shadow in the night, and sometimes she is visible even at noon-day.

In the following figure, the outer circle represents the Earth's orbit, and the inner circle, that of Vehus, while she moves around the Sun, in the order of the letters a, b, c, d, &c. When Venus is at a, she is in her inferior conjunction, between the Earth and Sun; and is in a situation similar to that of the Moon at her change, being then invisible, because her dark hemisphere is towards the Earth. At c, she appears half enlightened to the Earth, like the Moon in her first quarter; at d, she appears almost full, her enlightened side being then almost directly towards the Earth; at e, she is in her superior conjunc tion, and would appear quite full, were she not directly behind the Sun, or so near him as to be hidden by the splendour of his light; at f, she appears to be on the decrease; and at g, only half enlightened, like the Moon in her last quarter: at a, she disappears again between the Earth and the Sun. In moving from g to c, she seems to go backwards in the heavens, because she moves contrary to the order of the signs. In turning the arc of the circle from retrograde to direct motion, or from direct to retrograde, she appears nearly stationary for a few days; because, in the former case, she is going almost directly from the Earth, and in the latter, coming towards it. As she describes a much larger portion of her orbit in going from c to g, than from g to c, she appears much longer direct than retrograde. At a inean rate, her retrogradations are accomplished in 42 days.

Describe her apparent motion. How far on each side of the Sun do the vibrations of Venus extend? What then is the longest time before sunrise that she appears in the eastern horizon? What the longest time after sunset that she appears in the western? What is the direction of her motion while she passes from her western to her eastern elongation? Why is it called direct motion? What is its direction as she passes from her eastern to her western elongation? Why is it called retrograde? When is her apparent motion quickest? When does she appear stationary? When is she brightest How great is her light at this time?

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