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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 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
*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 orbit 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.
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 Venus, 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 conjunction, 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?
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. [Relative position of the Planet's Orbits, Plate I-Plane of Venus-Inclination 3° 23'.]
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 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 ratio will be
Why does not Venus pass centrally across the Sun's disc at every inferior conjunction? In what circumstances will she make a transit across the sun? How often can this phenomenon happen? Why can it not happen oftener? State the method of predicting the transits of Venus.
1106515. As the two terms of this fraction cannot be reduced by a common 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 291-6X8-243, another period, and so on. Whence we find that,
8 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 po sition 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.
The Earth passes her ascending node in the beginning of December, and her descending node, in the beginning of June. Hence, the transits of Venus, for ages to come, will happen in December and June. 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 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,
*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 upon 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 forever of an opportunity of observing the transit. If its very commencement 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, Horrox twice suspended his observations, and twice repaired to the House of God, the Great Author of the bright worlds he delighted to contemplate. When his duty was thus performed, 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 any thing 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."
After how long an interval may a transit of Venus happen again at the same node? If it do not happen then, how long a period must elapse before it will occur again at the same node? Where does the orbit of Venus cross the ecliptic, and where are her nodes? In what months, for ages to come, will the transits of Venus happen, and why? At which node, and when, did the first transit of Venus ever known to have been observed, take place? When will the next two transits occur?