* * *

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 [. 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 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 futo 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 or one mile, from the point of contact; 82 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 tha. 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 Ptole maic theory, with the earth flat; but in this work (page 12), where the same theory is presented, 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 heav enly boʻlies, 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 obeets: as when the shore seems to the mariner to recede as he rapidly sails from it, and is trees and other objects seem to gli le by us, when, on riding swiftly past thein, we lose the consciousness of our own motion." This remark would go to show that the revoluion 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 froin the right over to the left. 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 sys tem around the sun, and then departing. This is the Copernican Theory of the Sola 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 est conclusive and satis factory 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 ruceed hereafter to the study of the heavenly bodies.

ت

13. 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 Cor

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 surfaco as far as we please; or, in other words, to be indefinitely extended. When a plane or line is extended in this way, it is sail to be producer.

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 snill 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.

PARALLEL

PLANES

*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 solil, 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? Il lastrate. What is a plane produced?) What are parallel planes Perpen

are

Perpendicular Planes such as stand exactly upright upon each other, or cross each other at right angles.

in the figuro, one plane is placed horizontally, And the other perpendicular to it. They are therefore perpendicular to each other, however they may stand in relation to the observer.

Inclined Planes are such as are inclined toward, and cut each other obliquely.

The Angle of Inclination is the angle contained between the two surfaces of the planes nearest each other.

The spaces A and B in the adjoining cut represent the Angle of Inclination.

The Area of a plane figure is the amount of surface contained therein.

A Convex Surface is one that is swollen out like the outside of a bowl.

A Concave Surface is one that is hollowed out like the inside of a bowl.

A Sphere is a globe or ball, every part of the surface of which is equidistant from a point within, called its

center.

This is the ordinary definition; but in Astronomy, the term is applied to the apparent concave of the heavens, as if it were the actual concave surface of a hollow sphere.

A SPHERE.

dicular? Inclined? What is meant by the angle of inclination? The are of a plane surface? Describe a convec surface-a concave.

15. Describe a sphere-hemisphere-spheroid. (Derivation of spheroid f)

A Hemisphere is the half of a sphere or globe, or of the apparent concave of the heav

ens.

In Geography we often read of the Eastern and Western, and Northern and Southern hemispheres, but in Astronomy the term is only applied to the Northern and Southern portions of the heavens.

A HEMISPHEB

D

A Spheroid is a body resembling a sphere, but yet not perfectly round or spherical.

The term spheroid is from the Greek sphaira, a sphere, and eidos, form, and signi des sphere-like.

Spheroids are of two kinds-Oblate, and Oblong or Prolate.

An Oblate Spheroid is a globe slightly flattened, as if pressed on opposite sides.

This is a difficult figure to represent upon paper. Should the pupil fail to obtain a correct idea, the Teacher will be at no loss for an illustration.

AN OBLATE SPHEROID.

A Prolate or Oblong Spheroid is an elongated sphere.

This figure, like an Oblate Spheroid, admits of various degrees of departure from the spherical form. It may be much or but slightly elongated, and the ends may be alike or otherwise. A common egg is an Oblong Spheroid.

The Equator of a sphere is an imaginary circle upon its surface, midway between its poles, the plane of which cuts the axis perpendicularly, and divides the sphere into two equal parts or hemispheres.

Kinds of spheroids? Describe each. What is the axis of a sphere? What the poles? The equator? By what other name called? What a Less Cirule? MeridiaLe?