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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 saine phenomena are again exhibited. Such are the visible appcarances of Venus.

359. Venus revolves about the Sun from west to east in 2213 Jays, at the distance of about 66,000,000 of miles, moving in her orbit at the rate of 77,000 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.

360. The mean distance of the Earth from the Sun is estimated at 91,500,000 miles, and that of Venus being 66,000,000, the diameter of the Sun, as seen from Venus, will be to his diameter as seen from the Earth, as 91 to 66, and the surface of his disc as the square of 91 to the square of 66, that is, as 8372 to 4356, or as 2 to 1, nearly. The intensity of light and heat being inversely as the square of their distances from the Sun (No. 342), Venus receives twice as much light and heat as the Earth.

361. The orbit of Venus 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's greatest elongation being about 23° from the Sun, and that of Venus about 46°, the orbit of Venus must be outside of the orbit of Mercury.

362. The diameter of Venus is about 7.500 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 from the Earth is only 26,000,000 of miles; when they are on opposite sides of the Sun, her distance is 158,000,000 of miles. Were the whole of her enlightened hemisphere turned towards us when she is nearest, she would exhibit a light and brilliancy

659. What is Venus' sidereal period? Distance from the Sun? Rate of motion Time of rotation upon her axis? How, then, do her day and year compare with curs! 860. How must the Sun appear from Venus, and why? What of her light and hesti 861. Where s the orbit of Venus situated? What proof of this? 362. Venus' diame ter f Her apparent diameter? State her least and greatest distances from the Earth

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 81.2; when inost remote, it is only 9".6; now 61".2+9".6=6%, hence when nearest the Earth her apparent diameter is 6% times greater than when most distant, and surface of her disc (%) or nearly 41 times greater. In this work, the apparent size of the eavenly bodies is estimated from the apparent surface of their discs, which is always #roportional to the squares of their apparent diameters.

363. Mercury and Venus are called Interior planets, because heir orbits are within the Earth's orbit, or between it and the Sun The other planets are denominated Exterior, because their orbits are without or beyond the orbit of the Earth. (Map 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 conjunc tion, and in the latter case, in its superior conjunction; as in the following figure.

MARS IN CONJUNCTION

SUPERIOR

INFERIOR

8

MARS IN OPPOSITION

Let the student imagine himself stationed upon the earth in the cut. Then the sun and three planets above are in conjunc tion. The inferior and superior are distinguished; while at A, a planet is shown in quadra. ture, and at the bottom of the cut the planet Mars in opposi tion with the sun and interior planet.

The period of Venus' synodi cal 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".S, the Earth's is 59' 8.8, and their difference is 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 1.e Earth.

364 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.

How would she appear if we saw her enlightened side when nearest to us? What computation in the fine print? 863. How are Mercury and Venus distinguished, ard why! What said of conjunctions? Describe the inferior and superior? How is the period of Venus synodical revolution found? 864. When is Venus evening star? Morning!

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° 86 of angular motion per day, the Earth follows at the rate of 59'; so that Venus actually gains on the Earth, only 87 in a day.

Now it is evident that both planets will appear to keep on the same side of the Sun, antil Venus has gained half her orbit, or 180° in advance of the Earth; and this, at a ear rate, will require 292 days, since 292 x 37' 10804', or 180° nearly.

365. Venus passes from her inferior to her superior conjunc tion in about 292 days. At her inferior conjunction, she is 26,000,000 of miles from the Earth; at her superior conjunc tion, 158,000,000 of miles. It might be expected that her bril liancy would be proportionally 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 splendor, as it usually appears to the naked eye.

366. Mercury and Venus present to us, successively, the various shapes and appearances of the Moon; waxing and waning through different phases, as shown in the following cut, 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.

PHASES OF VENUS AS SHE REVOLVES AROUND THE SUN.

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It should be remarked, however, that Venus is never seen when she is entirely full Except once or twice in a century, when she passes directly over the Sun's disc. A every other conjunction, she is either behind the Sun, or so near him as to be hidden by the splendor of his light. The preceding diagram better illustrates the various appearances of Venus, as she moves around the Sun, than any description of them could do

367. From her inferior to her superior conjunction, Venus, appears on the west side of the Sun, and is then our morning

How long each? How is it that Venus is east or west of the Sun 292 days, when he (eriodic revolution is performed in about 225 days? 365. What is the time from one onjunction of Venus to another? Is her brilliancy in proportion to her nearness? Why act? 866. What phases do Mercury and Venus exhibit, and what do they prove? Are they ever seen entirely full? $67. When is Venus morning star? When evening?

These

star; from her superior to her inferior conjunction she appeara on the east side of the Sun, and is then our evening star. phenomena are illustrated by the following diagram.

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Let the student hold the book up south of him, and he will at once see why Venus is Alternately morning and evening star. Let the plane A B represent the sensible or visible horizon, C D the apparent daily path of the Sun through the heavens, and E the Earth in her apparent position. The Sun is shown at three different points-namely, rising in the east, on the meridian, and setting in the west; while Venus is seen revolving around him from west to east, or in the direction of the arrows. Now it is obvious that when Venus is at F, or west of the Sun, she sets before him as at G, and rises before him as at H. She must, therefore, be morning star. On the other hand, when she is east of the Sun, as at J, she lingers in the west after the Sun has gone down, as at K, and is consequently evening star.

In this cut, Venus would be at her greatest elongation eastward at J, and westward at F, and in both cases would be "stationary." At L and M she would be in conjunction with the Sun.

Were the earth to suspend her daily rotation, with the Sun on the meridian of the observer, as represented at L, we might readily watch Venus through her whole circuit around the Sun.

368. Like Mercury, Venus 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 befor? sunrise, nor continues longer in the western horizon after sunset Any star or planet therefore, however brilliant it may appear, which is seen earlier or later than this, cannot be Venus.

369. In passing from her western to her eastern elongation,

268. Is she ever stationary? What other irregularities in her apparent motion! 950. When is her motion direct? When retrograde? When most rapid? When

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 het 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 sta tionary at her elongations. She is brightest about thirty-six days before and after her inferior conjunction, when her light is so great as to project a visible shadow in the night, and some times she may be seen with the naked eye even at noon-day.

DIRECT AND RETROGRADE MOTIONS.

G

DIRECT

ETROGRADE

E

The cause of the apparent retrogression of the interior planets is the fact that they revolve much more rapidly than the earth, from which we view them; causing their direct motion to appear to be retrograde.

Suppose the earth to be at A, and Venus t B, she would appear to be at C, among the star3. If the earth remained at A while Venus was passing from B to D, she would seem to retrograde from C to E; but as the earth passes from A to F while Venus goes from B to D, Venus will appear to be at t and the amount of her apparent westward motion will only be from C to G.

370. If the orbit of Venus lay exactly in the plane of the Earth's orbit, she would pass centrally across the Sun's disc, like a dark round spot, at every inferior conjunction; but, as one-half of her orbit lies about 31° above the ecliptic, and the other half as far below it, she will always pass the Sun a very little above or below it, except when her inferior conjunction happens in, or Lear one of her nodes; in which case she will make a transit. (See cuts, pages 179 and 180.)

This phenomenon, therefore, is of very rare occurrence; it can happen only twice in a century; because it is only twice in that time that any number of complete revolutions of Venus are just or nearly equal to a certain number of the Earth's revolutions.

The principle which was illustrated in predicting the transits of Mercury, applies qually well to those of Venus; that is, we inust find such sets of numbers (representing orig test? State the cause of the apparent retrograde motion? 870. Why have we transit at every revolution of Venus?

When do her nodes cut the ecliptic?

How frequent, therefore? How predicted

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