whole earth was once in a fluid state-one vast drop-the substances now constituting the oceans and continents being indiscriminately mingled together. "And the earth was without form and void [i. e., chaotic, confused, unorganized], and darkness dwelt upon the face of the deep; and the spirit of God moved upon the face of the waters. * * * And God said, Let the waters under the heavens be gathered together unto one place, and let the dry land appear: and it was so. And God called the dry land earth, and the gathering together of the waters called he seas."-Genesis i. 2, 9. 10. Up to this time there was no "earth," either as continents or islands, neither were there any "seas," but all the elements were mingled together; and a mass of fluid thus dropped into space, from the hand of the Creator, would be as certain to assume the form of a globe, as the melted lead from the shot-tower, or the water from the passing cloud. 3. The apparent elevation and depression of the North Star, as we approach toward or recede from it, shows that the surface of the earth is convex, or that the earth is a globe. 4. The fact that the tops of mountains are last seen as we recede from, or first as we approach, the sea-shore, proves that the surface of the water upon which we sail is convex; so when a ship is approaching the shore, the topmasts are always seen first, and the hull or body last. And when seamen wish to survey the horizon at sea to a great distance, in search of whale or other shipping, they "go to the mast-head," as they call it, from which point they can often discover objects that are entirely invisible from the deck of the ships. 5. If an aqueduct is to be constructed a mile long, so as to be filled with water to the brim at every point, it must be about eight inches higher in the middle than at the ends, so as to allow the surface of the water to conform to the convex figure of the globe. We say higher, not that it needs to be higher as determined by a water level, for a water level is convex, but higher as determined by a straight line drawn from one end of the aqueduct to the other. This definite knowledge of the curvature of water, even for small distances, shows that the earth's surface is convex-or, in other words, that the earth is spherical. (The curvature from a tangent line is 8 inches for one mile, from the point of contact; 32 inches for two miles; 72 inches for three miles, &c.) 6. When the moon falls into the shadow of the earth and is eclipsed, or, in other words, the earth gets into her sunlight, and throws its shadow upon her, the shadow is seen to be convex. We must either conclude, therefore, that the earth, which casts the shadow, is in the form of a dinner-plate, and is always kept side wise, and the same side toward the sun (which we know is not the case); or that it is a globe, and casts a conical shadow, whatever its position. 7. The earth is known to be a globe, from the fact that ships are constantly sailing around it. 8. It is not certain whether Ptolemy admitted the earth to be a sphere or not. Some writers maintain that he rejected this doctrine, and others that he admitted it. In the "PRIMARY ASTRONOMY." page 8, the author has inserted a cut representing the Ptolemaic theory, with the earth flat; but in this work (page 12), where the same theory is represented, the earth is shown as a globe. In all other respects, the theory represented is the same in both works; and this is only a minor point in the system. 12. A second leading feature of the Copernican theory is, that the apparent revolution of the sun, moon, and stars westward every day, is caused by the revolution of the earth around its own axis, from west to east, every twenty-four hours. 66 That the heavenly bodies appear to revolve westward, is no proof that they are actually in motion. We often transfer our own motion, in imagination, to bodies that are at rest; especially when carried swiftly forward without any apparent cause, as when one travels in a steamboat or railway car, and when for a time he forgets his own motion. Copernicus tells us that he was first led to think that the apparent motions of the heavenly bodies, in their diurnal revolution, were owing to the real motion of the earth in the opposite direction, from observing instances of the same kind among terrestrial ob'ects; as when the shore seems to the mariner to recede as he rapidly sails from it, and as trees and other objects seem to glide by us, when, on riding swiftly past them, we lose the consciousness of our own motion." This remark would go to show that the revolution of the earth on its own axis was an original discovery with Copernicus. 12. State the second leading feature of the Copernican system. (Do not our own senses furnish proof that the heavenly bodies revolve westward daily? Why not? What remark from Copernicus? What does it seem to imply?) Jupiter, and Saturn in the next three, and the fixed stars in the eighth. The ancients had no knowledge of Uranus or Neptune. This ponderous machinery was supposed to revolve from east to west around the earth, carrying with it the sun, moon, and stars, every twenty-four hours; and the spheres being crystal, the distant stars were visible through them. 2. If the sun was designed to enlighten and warm the different sides of our globe, the Ptolemaic method of effecting this object is most unreasonable. To carry the sun around the earth, to warm and enlighten its different sides, instead of having the earth turn first one side and then the other to the sun, by a revolution on its axis, would be like carrying a fire around a person who was cold, and wished to be warmed, instead of his turning himself to the fire as he pleased. 3. The Ptolemaic theory would require a motion inconceivably rapid in all the heavenly bodies. As the sun is ninety-five millions of miles from the earth, the entire diameter of his sphere would be one hundred and ninety millions of miles, and its circumference about six hundred millions. Divide this distance by twenty-four-the number of hours in a day-and it gives twenty-five million miles an hour, or sixty-nine thousand four hundred and forty-four miles per second, as the velocity of the sun! This theory would require a still more rapid motion in the fixed stars. It would require the nearest of these to move at the rate of nearly fourteen thousand millions of miles per second, or seventy thousand times as swift as light, in order to accomplish their daily course. But with all these difficulties in its way, the Ptolemaic theory was generally believed till about the middle of the sixteenth century, or three hundred years ago. THE COPERNICAN SYSTEM. 10. About the year 1510, the ancient theory of Pythagoras was revived and improved by Copernicus, a Prussian astronomer, and has since been called, after him, the Copernican System. 1. The investigations of Copernicus were conducted between the years 1507 and 1530. In the latter year he finished his tables of the planets, and his great work, The Revolution of the Celestial Orbs; but he did not venture to publish his views till thirteen years after, or 1543, when he received a copy of it only a few hours before his death, and consequently never read it in print. It contains the old philosophy, interspersed with his own original and acute conceptions, and was received under very considerable opposition.-Smyth, vol. 1, p. 38. 2. Copernicus is generally regarded as the discoverer of the system which bears his name, but this is a popular error. There is abundant proof, notwithstanding the loss of his writings, that Pythagoras understood the leading features of what is now called the Copernican Theory. 11. The first prominent feature of the Copernican system is, that the earth is a sphere or globe, inhabited on all sides. The evidence that the earth is a sphere or globe may be arranged and stated as follows: 1. Admitting that the sun, moon, and stars are worlds, the fact that they are round, as we see them to be, affords ground for the presumption, at least, that the earth also is round. 2. Water falling from the clouds is gathered into little globes or drops; and melted lead poured from the summit of a high tower assumes the form of globes, which, when cooled, are called shot. And the same law would cause a larger mass of fluid matter, if left undisturbed in space, to assume the same shape. But the Bible teaches that the light and heat? What in respect to the motions of the heavenly bodies? Was such a theory ever generally believed? Till how recently?) 10. Who was Copernicus? For what distinguished? About what time? (What of his investigations? His work? Its publication? Character? What popular error noticed?) 11. State the first leading feature of the Copernican theory. (What proofs of its correctness? The first? Second? Third? Fourth? Fifth ? Sixth? Seventh ?) whole earth was once in a fluid state-one vast drop-the substances now constituting the oceans and continents being indiscriminately mingled together. "And the earth was without form and void [i. e., chaotic, confused, unorganized], and darkness dwelt upon the face of the deep; and the spirit of God moved upon the face of the waters. And God said, Let the waters under the heavens be gathered together unto one place, and let the dry land appear: and it was so. And God called the dry land earth, and the gathering together of the waters called he seas."-Genesis i. 2, 9, 10. Up to this time there was no "earth," either as continents or islands, neither were there any "seas," but all the elements were mingled together; and a mass of fluid thus dropped into space, from the hand of the Creator, would be as certain to assume the form of a globe, as the melted lead from the shot-tower, or the water from the passing cloud. 3. The apparent elevation and depression of the North Star, as we approach toward or recede from it, shows that the surface of the earth is convex, or that the earth is a globe. 4. The fact that the tops of mountains are last seen as we recede from, or first as we approach, the sea-shore, proves that the surface of the water upon which we sail is convex; so when a ship is approaching the shore, the topmasts are always seen first, and the hull or body last. And when seamen wish to survey the horizon at sea to a great distance, in search of whale or other shipping, they "go to the mast-head," as they call it, from which point they can often discover objects that are entirely invisible from the deck of the ships. 5. If an aqueduct is to be constructed a mile long, so as to be filled with water to the brim at every point, it must be about eight inches higher in the middle than at the ends, so as to allow the surface of the water to conform to the convex figure of the globe. We say higher, not that it needs to be higher as determined by a water level, for a water level is convex, but higher as determined by a straight line drawn from one end of the aqueduct to the other. This definite knowledge of the curvature of water, even for small distances, shows that the earth's surface is convex-or, in other words, that the earth is spherical. (The curvature from a tangent line is 8 inches for one mile, from the point of contact; 32 inches for two miles; 72 inches for three miles, &c.) 6. When the moon falls into the shadow of the earth and is eclipsed, or, in other words, the earth gets into her sunlight, and throws its shadow upon her, the shadow is seen to be convex. We must either conclude, therefore, that the earth, which casts the shadow, is in the form of a dinner-plate, and is always kept side wise, and the same side toward the sun (which we know is not the case); or that it is a globe, and casts a conical shadow, whatever its position. 7. The earth is known to be a globe, from the fact that ships are constantly sailing around it. 8. It is not certain whether Ptolemy admitted the earth to be a sphere or not. Some writers maintain that he rejected this doctrine, and others that he admitted it. In the "PRIMARY ASTRONOMY," page 8, the author has inserted a cut representing the Ptolemaic theory, with the earth flat; but in this work (page 12), where the same theory is represented, the earth is shown as a globe. In all other respects, the theory represented is the same in both works; and this is only a minor point in the system. 12. A second leading feature of the Copernican theory is, that the apparent revolution of the sun, moon, and stars westward every day, is caused by the revolution of the earth around its own axis, from west to east, every twenty-four hours. That the heavenly bodies appear to revolve westward, is no proof that they are actually in motion. We often transfer our own motion, in imagination, to bodies that are at rest; especially when carried swiftly forward without any apparent cause, as when one travels in a steamboat or railway car, and when for a time he forgets his own motion. "Copernicus tells us that he was first led to think that the apparent motions of the heavenly bodies, in their diurnal revolution, were owing to the real motion of the earth in the opposite direction, from observing instances of the same kind among terrestrial ob'ects; as when the shore seems to the mariner to recede as he rapidly sails from it, and as trees and other objects seem to glide by us, when, on riding swiftly past them, we lose the consciousness of our own motion." This remark would go to show that the revolu tion of the earth on its own axis was an original discovery with Copernicus. 12. State the second leading feature of the Copernican system. (Do not our own senses furnish proof that the heavenly bodies revolve westward daily? Why not? What remark from Copernicus? What does it seem to imply?) 13. A third feature of the Copernican theory is, that the sun is the grand center around which the earth and all the other planets revolve. 1. The above cut is a representation of the Copernican Theory of the Solar System. In the center is seen the sun, in a state of rest. Around him, at unequal distances, are the planets and fixed stars-the former revolving about him from west to east, or in the direction of the arrows. The white circles represent the orbits, or paths, in which the planets move around the sun. On the right is seen a comet plunging down into the system around the sun, and then departing. This is the Copernican Theory of the Solar System. "O how unlike the complex works of man, Heaven's easy, artless, unencumber'd plan!" 2. The truth of the Copernican theory is established by the most conclusive and satisfactory evidence. Eclipses of the sun and moon are calculated upon this theory, and astronomers are able to predict thereby their commencement, duration, &c., to a minute, even hundreds of years before they occur. We shall therefore assume the truth of this system without further proof, as we proceed hereafter to the study of the heavenly bodies. 18. State the third prominent feature of the theory of Copernicus. (Describe the cut. What additional evidence of the truth of this theory, as a whole?) CHAPTER II. DEFINITIONS. * 14. SOLIDS, SURFACES, &c. A Solid, or Body, is a figure having length, breadth, and thickness. A Surface is the outside or exterior of a body, and has length and breadth only. Surfaces are of three kinds-Plane, Concave, and Corr vex. A surface may also be rough or smooth, hard or soft; the above definition having reference only to the general figure of bodies. A Plane Surface is one that is perfectly flat or even, like the floor of a building, or the sides of a room. 1. We may imagine what is called a plane, to extend off beyond the plane surface as far as we please; or, in other words, to be indefinitely extended. When a plane or a line is extended in this way, it is said to be produced. 2. An imaginary plane may exist where there is no body having a plane surface; or between two lines, like the plane of a circle. A sheet of tin, laid across a small wire hoop, would represent the plane of that circle, in whatever position it might be held, whether horizontally, perpendicularly, or otherwise; and the place which the tin would pass through, if extended to the starry heavens, is the plane of that circle. 3. All objects which the tin would touch or cut, if extended outward to the heavens, or to infinity, are in the plane of the sheet, or the circle upon which it is laid. A point is in a plane produced, when the plane continued or extended would pass through that point. Parallel Planes are such as would never meet or cut each other, however far they might be extended. The two sides of a board, or two sheets of tin placed equidistant from each other at every point, represent parallel planes. PLANES PARALLEL *To some who will use this work, many of the following diagrams and definitions will be superfluous, the substance of them being already sufficiently understood. With such students the judicious teacher will pass rapidly over the next ten pages, or omit them altogether. 14. Define a solid, or body-a surface. How many kinds of surfaces? (Any other distinctions?) What is a plane surface? (May a plane extend beyond the plane surface? May a plane exist where there is no body? Illustrate. What is a plane produced?) What are parallel planes? Perpen |