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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 292 x 37'-10804', or 180° nearly.
365. Venus passes from her inferior to her superior conjunction in about 292 days. At her inferior conjunction, she is 26,000,000 of miles from the Earth; at her superior conjunction, 164,000,000 of miles. It might be expected that her brilliancy 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.
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. At 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 her periodic revolution is performed in about 225 days? 365. What is the time from one conjunction of Venus to another? Is her brilliancy in proportion to her nearness? Why not? 366. What phases do Mercury and Venus exhibit, and what do they prove? Are they ever seen entirely full? 367. When is Venus morning star? When evening?
star; from her superior to her inferior conjunction she appears on the east side of the Sun, and is then our evening star. phenomena are illustrated by the following diagram.
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 before 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? 869. When is her motion direct? When retrogrude? 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 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 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 sometimes she may be seen with the naked eye even at noon-day.
DIRECT AND RETROGRADE MOTIONS.
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 at B, she would appear to be at C, among the stars. 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 G; 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 near 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 equally well to those of Venus; that is, we must find such sets of numbers (representing brightest? State the cause of the apparent retrograde motion? 870. Why have we not a transit at every revolution of Venus? How frequent, therefore? How predicted? When do her nodes cut the ecliptic?
complete revolutions of the Earth and Venus) as shall be to each other in the ratio of their periodical times, or as 365.256 is to 224.7. Thus: the motion of Venus, in the Julian years, is 2106591".52; that of the Earth for the same period being 129627".45, the ratic will be 2_10_6591.5 As the two terms of this fraction cannot be reduced by a com129627 45 mon divisor, we must multiply them by such numbers as will make one a multiple of the other; accordingly, 13 times the denominator will be nearly equal to 8 times the numerator; and 475 times the denominator will equal 291 times the numerator.
By combining these two periods and their multiples by addition and subtraction, we shall obtain the period of all the transits that have ever happened. Thus : 291-8x7=235, another period; and 291-6 x 8=243, another period, and so on. Whence we find that
S periodical revolutions of the Earth are equal to 13 of Venus: 235 periodical revolutions of the Earth are equal to 382 of Venus: 243 periodical revolutions of the Earth are equal to 395 of Venus: 251 periodical revolutions of the Earth are equal to 408 of Venus: 291 periodical revolutions of the Earth are equal to 475 of Venus. Hence a transit of Venus may happen at the same node, after an interval of 8 years; but if it do not happen then, it cannot take place again at the same node, in less than 235 years. The orbit of Venus crosses the ecliptic near the middle of Gemini and Sagittarius; and these points mark the position of her nodes. At present, her ascending node is in the 14th degree of Gemini, and her descending node in the same degree of Sagittarius.
371. The node months of Venus are December and June. The line of her nodes lies in Gemini (II) and Sagittarius (4); and as the Earth always passes those points in the months named, it follows that all transits of Venus must occur in those months for ages to come.
This proposition will be well understood by consulting the cut on page 000; for as the line of Venus' nodes is only one sign ahead of that of Mercury, the Earth will reach that point in the ecliptic in one month after she passes the line of Mercury's nodes; so that if his transits occur in May and November, hers should occur in June and December, as is always the case.
272. The first transit ever known to have been seen by any human being, took place at the ascending node, December 4th, 1639.* If to this date we add 235 years, we shall have the
This phenomenon was first witnessed by Horrox, a young gentleman about 21 years of age, living in an obscure village 15 miles north of Liverpool. The tables of Kepler, constructed upon the observations of Tycho Brahe, indicated a transit of Venus in 1631, but none was observed. Horrox, without much assistance from books and instruments, set himself to inquire into the error of the tables, and found that such a phenomenon might be expected to happen in 1639. He repeated his calculations during this interval, with all the carefulness and enthusiasm of a scholar ambitious of being the first to predict and observe a celestial phenomenon, which, from the creation of the world, had never been witnessed. Confident of the result, he communicated his expected triumph to a confidential friend residing in Manchester, and desired him to watch for the event, and to take observations. So anxious was Horrox not to fail of witnessing it himself, that he commenced his observations the day before it was expected, and resumed them at the rising of the Sun on the morrow. But the very hour when his calculations led him to expect the visible appearance of Venus on the Sun's disc, was also the appointed hour for the public worship of God on the Sabbath. The delay of a few minutes might deprive him for ever of an opportunity of observing the transit. If its very commence. ment were not noticed, clouds might intervene, and conceal it until the Sun should set: and nearly a century and a half would elapse before another opportunity would occur. He had been waiting for the event with the most ardent anticipation for eight years, and the result promised much benefit to the science. Notwithstanding all this, Horror twice suspended his observations and twice repaired to the House of God, the Great Author of the bright works he delighted to contemplate. When his duty was thus per
871. Which are her node months? interesting anecdote?
372. When was the first transit observed? What
time of the next transit at the same node, which will accordingly happen in 1874. There will be another at the same node in 1882, eight years afterwards. It is not more certain that this phenomenon will recur, than that the event itself will engross the attention of all the astronomers then living upon the Earth. It will be anticipated, and provided for, and observed, in every inhabited quarter of the globe, with an intensity of solicitude which no natural phenomenon, since the creation, has ever excited.
373. The reason why a transit of Venus should excite so great an interest is, because it may be expected to solve an important problem in astronomy, which has never yet been satisfactorily done a problem whose solution will make known to us the magnitudes and masses of all the planets, the true dimensions of their orbits, their rates of motion around the Suu, and their respective distances from the Sun, and from each other. It may be expected, in short, to furnish an universal standard of astronomical measure. Another consideration will render the observation of this transit peculiarly favorable; and that is, astronoiners will be supplied with better instruments, and more accurate means of observation, than on any former occasion.
So important, says Sir John Herschel, have these observations appeared to astronomers, that at the last transit of Venus, in 1769, expeditions were fitted out, on the most efficient scale, by the British, French, Russian, and other governments, to the remotest corners of the globe, for the express purpose of making them. The celebrated expedition of Captain Cook to Otaheite, was one of them. The general result of all the observations made on this most memorable occasion, gives 8".5776 for the Sun's horizontal parallax.
374. The phenomena of the seasons of each of the planets, like those of the Earth, depend upon the inclination of the axis of the planet to the plane of its orbit, and its revolution around the Sun. The inclination of the axis of Venus to the plane of her orbit, though not precisely known, is commonly estimated at 75°, as represented to the eye in the following cut:
formed, and he had returned to his chamber the second time, his love of science was gratified with full success; and he saw what no mortal eye had observed before!
If anything can add interest to this incident, it is the modesty with which the young astronomer apologizes to the world, for suspending his observations at all.
"I observed it," says he, "from sunrise till nine o'clock, again a little before ten, and lastly at noon, and from one to two o'clock; the rest of the day being devoted to higher duties, which might not be neglected for these pastimes."
How will it be regarded?
373. Why should such What expedition and
When the next? When another? an event excite general interest? what results? 374. Upon what do the seasons of the planets depend? What is the inclination of Venus' axis to the plane of her orbit? How is her orbit situated with reference to the ecliptic?