which they are leaving. Now these phenomena are evidently caused by the convexity of the water which is between the eye and the object; for, were the surface of the sea merely an extended plain, the largest objects would be visible the Longest, and the smallest disappear first.

CONVEXITY OF THE EARTH.

Fig. 9.

Agáin: 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 con. tinually 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.

These navigators, by sailing in a westerly direction, alowance being made for promontories, &c. arrived at the country they sailed from. Hence, the Fath 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 contrary to observation. The figure of the Earth is, therefore, spherical.

The convexity of the Earth, north and south, is proved by the altitude of the pole, and of the circumpolar stars,

* 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.

Who first sailed around the Earth? Describe briefly his voyage. Who next circumnavigated the Earth? Describe his voyage. Mention the names of some of those who have since accomplished this enterprise. What may we infer from these facts in regard to the figure of the Earth? How is the convexity of her surface proved?

which is found uniformly to increase as we approach them, while the inclination to the horizon, of the circles described by all the stars, gradually diminishes. While proceeding in a southerly direction, the reverse of this takes place. The altitude of the pole, and of the circumpolar stars, continually decreases; and all the stars describe circles whose inclination to the horizon increases with the distance. Whence we derive this general truth: The altitude of one pole, and the depression of the other, at any place on the Earth's surface, is equal to the latitude of that place.

Another proof of the convexity of the earth's surface is, that the higher the eye is raised, the farther is the view extended. An observer may see the setting sun from the top of a house, or any considerable eminence, after he has ceas ed to be visible to those below.

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 3 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 3 of 100, is 664, 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 its half, is 9, and the square root of 9 is 3; the distance is then 3 miles. Ex. 2.—To what distance can a person see a light-house 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.

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

These measurements have been made by the most eminent mathematicians f different countries, and in various places, from the equator to the arctic

To what is the convexity proportional? State the rule, deduced from this fact, for finding the height of an object, when its distance from us is given. State the rule for finding the distance when the height is given. State the rule for finding the curvature of the Earth when the distance exceeds a mile. Is the figure of the Earth an exact sphere? Were the Earth a perfect sphere, how would the length of the degrees of latitude be, compared with each other? How are they, in fact?

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 confined, that the body of the Earth was more rounded and convex between the tropics, but considerably flattened towards the poles.

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 Academy have determined that the mean diameter of the Earth, from the 45th degree of north latitude, to the opposite degree of south latitude, is accurately 7912 miles.

If the Earth were an exact sphere, its diameter might be determined by its curvature, from a single measurement. Thus, in the adjoining figure, we have A B equal to 1 mile, and B D equal to 8 inches, to find A E, or B E, which does not sensibly differ from A E, since BD is only 8 inches. Now it is a proposition of Euclid, (B. 3, prop. 36,) that, when from a point without a circle, two lines be drawn, one cutting and the other touching it, the touching line (B A) is a mean proportional between the cutting line (B E) and that part of it (B D) without the circle.

BD: BA:: BA: BE or A E very nearly. That is, 1 mile being equal to 63360 inches,

Fig. 10.

A B

8: 63360 :: 63360 : 50181120 inches, or 7920 miles. This is very nearly what the most elaborate calculations make the Earth's equatorial diaineter.

The Earth, considered as a planet, occupies a favoured rank in the Solar System. It pleased the All-wise Creator to assign its position among the healy bodies, where nearly all the sister planets are visible the naked eye. It is situated next to Venus, and is the third planet from the Sun.

To the scholar who for the first time takes up a book on astronomy, it will no doubt seem strange to find the Earth classed with the heavenly bodies.

What is the length of a degree at the Arctic circle, compared with a degree at the equator, a found by the measurements of different mathematicians? What have they found to be the ratio of increase for the intermediate degrees? What theory do these facts confirm? What is the length of the Earth's equatorial diameter, as found by these measurements? What, her polar diameter? What is the difference between the two? What is her mean diameter? What have the French academy determined to be the exact mean diameter from the 45th degree of north latitude to the opposite degree of south latitude? Illustrate the method of finding the diameter of the Earth from her curvature, on the supposition that her figure is an exact sphere. What is the length of her diameter as thus found? How is this, compared with the equatorial diameter, as found by the most elaborate calculations? What is the position of the Earth in the Solar System?

For what can appear more unlike, than the Earth, with her vast and seemingly Immeasurable extent, and the stars, which appear but as points? The Earth is dark and opaque, the celestial bodies are brilliant. We perceive in it ne motion; while in them we observe a continual change of place, as we view them at different hours of the day or night, or at different seasons of the year

It moves round the Sun, from west to east, in 365 days 5 hours, 48 minutes, and 48 seconds; and turns, the same way, on its axis, in 23 hours, 56 minutes, and 4 seconds The former is called its annual motion, and causes the vicissitudes of the seasons. The latter is called its diurnal motion, and produces the succession of day and night.

The Earth's mean distance from the Sun is about 95 millions of miles. It consequently moves in its orbit at the mean rate of 68 thousand miles an hour. Its equatorial diameter being 7924 miles, it turns on its axis at the rate of 1040 miles an hour.

Thus, the earth on which we stand, and which has served for ages as the unshaken foundation of the firmest structures, is every moment turning swiftly on its centre, and, at the same time, moving onwards with great rapidity through the empty space.

This compound motion is to be understood of the whole earth, with all that it holds within its substance, or sustains upon its surface-of the solid mass beneath, of the ocean which flows around it, of the air that rests upon it, and of the clouds which float above it in the air.

That the Earth, in common with all the planets, revolves around the Sun as a centre, is a fact which rests upon the clearest demonstrations of philosophy. That it revolves, like them, upon its own axis, is a truth which every rising and setting sun illustrates, and which very many phenomena concur to establish.

There

Either the Earth moves around its axis every day, or the whole universe meyes around it in the same time. is no third opinion, that can be formed on this point. Either the Earth me evolve on its axis every 24 hours, to produce the alternate succession of day and night, or the Sun, Moon, planets, comets, fixed stars, and the whole frame of the universe itself, must move around the Earth, in the same time. To suppose the latter case to be the fact, would be to cast a reflection on the wisdom of the Supreme Architect, whose laws are universal harmony. As well might the beetle, that in a moment turns on its ball, imagine the heav

What revolutions does it perform, and in what direction? What is the time occupied in each of these revolutions? By what terms are these revolutions distinguished, and what important effects do they produce? What is the Earth's mean distance from the Sun? What is the mean rate of its motion in its orbit per hour? What is the rate of its revolu tion on its axis per hour? What are the proofs, that it performs these two revolutions?

ens and the Earth had made a revolution in the same instant. It is evident, that in proportion to the distance of the celestial bodies from the Earth, must, on this supposition, be the rapidity of their movements. The Sun, then, would move at the rate of more than four hundred thousand miles in a minute; the nearest stars, at the inconceivable velocity of 1400 millions of miles in a second; and the most distant luminaries, with a degree of swiftness which no numbers could express, and all this, to save the little globe we tread upon, from turning safely on its axis once in 24 hours.

The idea of the heavens revolving about the Earth, is encumbered with innumerable other difficulties. We will mention only one more. It is estimated on good authority, that there are visible, by means of glasses, no less than one hundred millions of stars, scattered at all possible distances in the heavens above, beneath, and around us. Now. is it in the least degree probable, that the velocities of all these bodies should be so regulated, that, though describing circles so very different in dimensions, they should complete their revolutions in exactly the same time.

In short, there is no more reason to suppose that the heavens revolve around the Earth, than there is to suppose that they revolve around each of the other planets, separately, and at the same time; since the same apparent revolution is common to them all, for they all appear to revolve upon their axis, in different periods.

The rotation of the Earth determines the length of the day, and may be regarded as one of the most important elements in astronomical science. It serves as a universal measure of time, and forms the standard of comparison for the revolutions of the celestial bodies, for all ages, past and to come. Theory and observation concur in proving, that among the innumerable vicissitudes that prevail throughout creation, the period of the Earth's diurnal rotation is immu table.

The Earth performs one complete revolution on its axis in 23 hours, 56 minutes, and 4.09 seconds, of solar time This is called a sidereal day, because, in that time, the stars appear to complete one revolution around the Earth.

But, as the Earth advances almost a degree eastward in its orbit, in the time that it turns eastward around its axis, it is plain that just one rotation never brings the same meridian around from the Sun to the Sun again; so that the Earth requires as much more than one complete revolution

What important purposes does the period of the Earth's rotation serve? What is a sidereal day? What is a solar day ?