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ascending Node of Mercury in November, and the descending in May; the former of which is in the 16th degree of Taurus, and the latter in the 16th degree of Scorpio.
All the transits of Mercury ever noticed have occurred in one or the other of these months, and for the reason already assigned. The first ever observed took place November 6, 1631; since which time there have been 29 others by the same planet-in all 30— 8 in May, and 22 in November.
352. The last transit of Mercury occurred November 9, 1848; and the next will take place November 11, 1861. Besides this, there will be five more during the present century-two in May, and three in November.
The accompanying cut is a de lineation of all the transits of Mercury from 1802 to the close of the present century. The dark line running east and west across the Sun's center represents the plane of the ecliptic, and the dotted lines the apparent paths of Mercury in the several transits. The planet is shown at its nearest point to the Sun's center. Its path in the last transit and in the next will easily be found.
The last transit of Mercury was observed in this country by Professor Mitchel, at the Cincinnati Observatory, and by many others both in America and in Europe. The editor had made all necessary preparation for observing the phenomenon at his residence, near Oswego, New York; but, unfortunately, his sky was overhung with clouds, which hid the sun from his view, and disappointed all his hopes.
353. By comparing the mean motion of any of the planets with the mean motion of the Earth, we may readily determine the periods in which they 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 find that,
node months of a planet? The node months of Mercury? transit of Mercury occur? When will the next take place? present century? What said of the last transit of Mercury? mine when transits will occur?
352. When did the last What others during the 353. How may we deterWhat ratio is found between the revolutions of Mercury
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, 18, 33, 46, &c. years. Transits of Venus, as well as eclipses of the Sun and Moon, are calculated upon the same principle.
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 century:
354. 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.
SIDEREAL AND SYNODIC REVOLUTIONS.
From this illustration, it will be seen that always require more time than the sidereal.
In the adjoining cut the revolution of the Earth from A, opposite the star B, around to the same point again, would be a sidereal revolution.
Suppose the Earth and Mercury to start together from the points A C (where Mercury would be in inferior conjunction with the Sun), and to proceed in the direction of the arrows. In 88 days Mercury would come around to the same point again; but as the Earth requires more than four times that number of days for a revolution, she will only have reached the point D when Mercury arrives at C again; so that they will not be in conjunction, and a synodic revolution will not be completed by Mercury. He starts on, however, in
s second round, and constantly gaining upon the Earth, till in 27 days from the time he left C the second time, he overtakes the Earth at E and F, and is again in inferior conjunction.
the synodic revolution of a planet must
355. 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.
The sidereal revolution of Mercury is 87d. 23h. 15m. 44s. Its synodical revolution is
and the Earth? 354. What is a sidereal revolution of a planet? A synodical? 855. What is the absolute motion of Mercury in his orbit? What is that of the Earth? The difference, or relative motion of Mercury? What is his sidereal period? His synodic? H is the latter ascertained?
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 14732".555; that of the Earth is 8548 .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', 24", the period of a synodical revolution of Mercury.
356. There are but few persons who have not observed a beautiful star in the west, a little after sunset, call 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.
357. 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 toward 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 splendor of his light.
358. A few days after the phenomena we have now described, 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
356. Describe Venus. What called? Distance from the Sun? What change of position observable? 357. Greatest distance to which she departs from the Sun? What consequence? How and when seen? 358. What next after these phenomena ?
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 appear
ances of Venus.
359. Venus revolves about the Sun from west to east in 224 days, at the distance of about 68,000,000 of miles, moving in her orbit at the rate of 80,000 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 95,000,000 of miles, and that of Venus being 68,000,000, 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 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 true diameter of Venus is 7700 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 164,000,000 of miles. Were the whole of her enlightened hemisphere turned towards us, when she is nearest, she would exhibit a light and brilliancy
359. 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 ours? 360. How must the Sun appear from Venus, and why? What of her light and heat? 361. Where is the orbit of Venus situated? What proof of this? 862. Venus' diameter? 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 Venu approaches nearest to the Earth, her apparent, or observed diameter is 61.2; when most remote, it is only 9".6; now 61".2+9".6=6%, hence when nearest the Earth her apparent diameter is 6% thnes greater than when most distant, and surface of her disc (%) 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.
363. Mercury and Venus are called Interior planets, because their 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.
Let the student imagine himself stationed upon the earth in the cut. Then the sun and three planets above are in conjunction. The inferior and superior are distinguished; while at A, a planet is shown in quadrature, and at the bottom of the cut the planet Mars in opposition with the sun and interior planet.
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 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 the 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? 363. How are Mercury and Venus distinguished, and why? What said of conjunctions? Describe the inferior and superior? How is the period of Venus' synodical revolution found? 364. When is Venus evening star? Morning?