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The orbit of Venus departs from the ecliptic 3°, while her axis is inclined to the plane of her orbit 75°, as shown in the above figure. This distinction should be kept definitely in view by the student.

375. The declination of the Sun on each side of Venus' equator, must be equal to the inclination of her axis; and if this extends to 75°, her tropics are only 15° from her poles, and her polar circles only 15° from her equator. It follows, also, that the Sun must change his declination more in one day at Venus, than in five days on the Earth; and, consequently, that he never shines vertically on the same places for two days in succession. This may, perhaps, be providentially ordered, to prevent the too great effect of the Sun's heat, which, on the supposition that it is in inverse proportion to the square of the distance, is twice as great on this planet as it is on the Earth.

376. At each pole of Venus, the Sun continues half of her year without setting in summer, and as long without rising in winter; consequently, her polar inhabitants, like those of the Earth, have only one day and one night in the year; with this difference, that the polar days and nights of Venus are not quite two-thirds as long as ours.

Between her polar circles, which are but 15° from her equator, there are two winters, two summers, two springs, and two autumns, every year. But because the Sun stays for some time near the tropics, and passes so quickly over the equator, the winters in that zone will be almost twice as long as the summers.

The north pole of Venus' axis inclines towards the 20th degree of Aquarius; the Earth's towards the beginning of Cancer; consequently, the northern parts of Venus have summer in the signs where those of the Earth have winter, and vice versâ.

377. When viewed through a good telescope, Venus exhibits not only all the moon-like phases of Mercury, but also a variety of inequalities on her surface; dark spots, and brilliant shades, hills and valleys, and elevated mountains. But on account of

875. What is the amount of the Sun's declination upon Venus? What results? What supposed design in this arrangement? 876. What said of the polar regions of Venus? What of her seasons? How is her north pole situated with respect to the heavens? What consequence? 877. How does Venus appear through a telescope?

the great density of her atmosphere, these inequalities are perceived with more difficulty than those upon the other planets.


378. The mountains of Venus, like those of Mercury and the Moon, are highest in the southern hemisphere. According to M. Schroeter, a celebrated German astronomer, who spent more than ten years in observations upon this planet, some of her mountains rise to the enormous height of from ten to twentytwo miles. The observations of Dr. Herschel do not indicate so great an altitude; and he thinks, that in general they are considerably overrated. He estimates the diameter of Venus at 8649 miles; making her bulk more than one-sixth larger than that of the Earth. Several eminent astronomers affirm, that they have repeatedly seen Venus attended by a satellite, and they have given circumstantial details of its size and appearance, its periodical revolution and its distance from her. It is said to resemble our Moon in its phases, its distance, and its magnitude. Other astronomers deny the existence of such a body, because it was not seen with Venus on the Sun's disc, at the transits of 1761 and 1769.


379. The Earth is the place from which all our observations of the heavenly bodies must necessarily be made. The apparent motions of these bodies being very considerably affected by her figure, motions, and dimensions, these hold an important place in astronomical science. It will, therefore, be proper to consider, first, some of the methods by which they have been determined.

If, standing on the sea-shore, in a clear day, we view a ship leaving the coast, in any direction, the hull or body of the vessel

Why less distinct than the other planets? 378. Where are her highest mountains situated? Their height? Remark of Dr. Herschel? His estimate of Venus' diameter? What said about a satellite around Venus? 379. Relation of the earth to the other planets in the study of astronomy? What necessary, therefore? What proof of the convexity of her surface?

first disappears; afterwards the rigging, and lastly the top of the mast vanishes from our sight.

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Here the observer upon the shore at A sees only the topmasts of the ship, while the man standing upon the pillar at B sees the masts and sails, and part of the hull. Now, f the water between A and the ship were exactly flat instead of convex, the vision of A would extend along the line C, and he could see the whole ship as well as B. The advantage of B over A, in consequence of his elevation, shows that the surface of the water is convex between A and the ship.


380. Again navigators have sailed quite around the Earth, and thus proved its convexity.

Ferdinand Magellan, a Portuguese, was the first who carried this enterprise into execution. He embarked from Seville, in Spain, and directed his course towards the west. After a long voyage, he descried the continent of America. Not finding an opening to enable him to continue his course in a westerly direction, he sailed along the coast towards the south, till, coming to its southern extremity, he sailed around it, and found himself in the great Southern Ocean. He then resumed his course towards the west. After some time he arrived at the Molucca Islands, in the Eastern Hemisphere; and sailing continually towards the west, he made Europe from the east, arriving at the place from which he set out.*

The next who circumnavigated the Earth was Sir Francis Drake, who sailed from Plymouth, December 13, 1577, with five small vessels, and arrived at the same place, September 26, 1580.


Since that time, the circumnavigation of the Earth has been performed by Cavendish, Cordes, Noort, Sharten, Heremites, Dampier, Woodes, Rogers, Schovten, Roggewin, Lord Anson, Byron, Carteret, Wallis, Bougainville, Cook, King, Clerk, Vancouver, and many others.

381. These navigators, by sailing in a westerly direction, allowance being made for promontories, &c., arrived at the country they sailed from. Hence the Earth must be either cylindrical or globular. It cannot be cylindrical, because, if so, the meridian distances would all be equal to each other, which is

*Magellan sailed from Seville, in Spain, August 10, 1519, in the ship called the Victory, accompanied by four other vessels. In April, 1521, he was killed in a skirmish with the natives, at the island of Sebu, or Zebu, sometimes called Matan, one of the Philippines. One of his vessels, however, arrived at St. Lucar, near Seville, September 7, 1522.

380. What second proof stated? Who first sailed around the world? Who nex? 381. In what direction did they sail? How did these voyages prove the earth to be

contrary to observation. The figure of the Earth is, therefore, spherical.

382. The convexity of the Earth, north and south, is proved by the variation in the altitude of the pole, and of the circumpolar stars; this is found uniformly to increase as we approach them, and to diminish as we recede from them.

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Suppose an observer standing upon the Earth, and viewing the pole star from the 45° of North Iatitude; it would, of course, appear elevated 45° above his visible horizon. But let him recede southward, and as he passed over a degree of latitude, the pole star would settle one degree towards the horizon, or more properly, his northern horizon would be elevated one degree towards the pole star, till at length, as he crossed the equator, the North star would sink below the horizon, and become invisible. Whence we derive the general rule, that the altitude of one pole, or the depression of the other, at any

place on the Earth's surface, is equal to the latitude of that place.

383. The form of the Earth's shadow, as seen upon the Moon in an eclipse, indicates the globular figure of the Earth, and the consequent convexity of its surface.

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382. What further proof have we that the earth is spherical? What rule based upon this phenomenon? 888. What other evidence that the earth is a globe What remarks respecting the curvature of the earth's surface? What rules laid down based upon this curvature?

Were the Earth a cube as shown at A, or in the form of a prism, as represented at B, her shadow would be more or less cubical or prismatic, as seen in the cut; but instead of this, it is convex on all sides, as represented at C, plainly indicating the convexity of the Earth by which it is caused.

The curvature of the Earth for one mile is 8 inches; and this curvature increases with the square of the distance. From this general law it will be easy to calculate the distance at which any object whose height is given, may be seen, or to determine the height of an object when the distance is known.

1st. To find the height of the object when the distance is given.

RULE. Find the square of the distance in miles, and take two-thirds of that number for the height in feet.

Ex. 1.-How high must the eye of an observer be raised, to see the surface of the ocean at the distance of three miles? Ans. The square of 8 ft. is 9 ft., and % of 9 ft. is 6 ft. Ex. 2. Suppose a person can just see the top of a spire over an extended plain of ten miles, how high is the steeple? Ans. The square of 10 is 100, and % of 100 is 66% feet.

2. To find the distance when the height is given.

RULE. Increase the height in feet one-half, and extract the square root, for the distance in miles.

Ex. 1.-How far can a person see the surface of a plain, whose eye is elevated six feet above it? Ans. 6, increased by half, is 9, and the square root of 9 is 3: the distance is then 8 miles. Ex. 2.-To what distance can a person see a lighthouse whose height is 96 feet from the level of the ocean? Ans. 96 increased by its half, is 144, and the square root of 144, is 12; the distance is therefore 12 miles.

3. To find the curvature of the Earth when it exceeds a mile. RULE. Multiply the square of the distance by .000126.

384. Although it appears from the preceding facts, that the Earth is spherical, yet it is not a perfect sphere. If it were, the length of the degrees of latitude, from the equator to the poles, would be uniformly the same; but it has been found, most careful measurement, that as we go from the equator towards the poles, the length increases with the latitude.

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These measurements have been made by the most eminent mathematicians of different countries, and in various places, from the equator to the arctic circle. They have found that a degree of latitude at the arctic circle was nine-sixteenths of a mile longer than a degree at the equator, and that the ratio of increase for the intermediate degrees was nearly as the squares of the sines of the latitude. Thus the theory of Sir Isaac Newton was confirmed, that the body of the Earth was more rounded and convex between the tropics, but considerably flattened towards the poles.

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385. These measurements prove the Earth to be an oblate spheroid, whose longest or equatorial diameter is 7924 miles, and polar diameter, 7898 miles. The mean diameter is, therefore, about 7912, and their difference 26 miles. The French Acade

384. But is the earth a sphere? What proof to the contrary? 885. What, then, is the earth's real figure? What difference in her polar and equatorial diameters? What demonstration that the earth is not an exact sphere?

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