780

Gravitation the Cause of the round Form.

similar globular form. Small quantities of quicksilver scattered or a level table exhibit it also very remarkably by their reflecting light strongly, and if several of these are gently pushed together they at once coalesce and form a larger globule flattened a little on the under side, which rests on the table. Still more complete instances of this kind are the little perfect spheres of the lead-shot used by sportsmen. These begin as melted lead showered down from a height, and the drops are solidified by cooling during their descent. In small masses of liquid, the attraction of particles is, from their proximity, very strong, and is called cohesive attraction. (See page 10.)

1018. But the general attraction, named by its discoverer, Newton, gravitation, acts at all distances. Thus, a plummet, or ball of lead, hanging by a thread, when it is over an extended plain has the thread pointing directly downwards, or at right angles to the surface of still water; but if the experiment be made near a steep mountain, the ball and string lean, or are attracted towards it, and by delicate tests are found to be less attracted towards the mountain than towards the earth below it, owing to what is called its weight-only because the mountain is so much smaller than the earth, notwithstanding that its influence is increased by its centre being nearer. A strictly corresponding result is obtained by the experiment of balancing two little balls of metal, A and B (fig. 302), at the end of a horizontal rod of wood, hanging from a lofty support, C, by a single wire, C D. If, when the loaded wood is perfectly at rest, a heavy mass of any kind is brought near to the side of one of the balls, it attracts the ball, twisting the suspending wire in a degree which indicates the force operating. This arrangement constitutes a torsion balance.

D

Fig. 302.

B

It is gravitation that makes the whole earth take the form of a globe. Although now firm and rigid, at least in the surface crust for many miles down, the mass of the earth was formerly liquid or soft, and in that state there was nothing to hinder the free movement of the particles under their mutual gravitation. As all liquids are seen to find their level, this means that all portions of the surface tend to become equally distant from the centre. If any portion were elevated above the rest—that is, were farther removed from the centre-it would flow down, or

Nearest to the Earth is the Moon.

781

centreward, until an equal distance was attained. This is the true meaning of being "level" on the surface of a globe.

That the earth's surface is not perfectly level, but is made up of heights and valleys, sometimes very steep or abrupt, is owing to internal forces which have upheaved parts of the superficial crust after it had become hardened or coherent. This coherence resists the force of gravity, which operates only on the particles loosened by the action of air and water.

Although the globular form of the earth is compatible with mountains of a considerable elevation, as the Himalayas, whose highest summits exceed five miles above the sea level, these heights are insignificant compared with the entire diameter, being only about one sixteen hundredth part of the whole. In a globe of four feet diameter, the tops of the highest Himalayas would have to be represented as projections about the one hundred and sixtieth of an inch.

The globular form is the reason of the inequality of the sun's heat on different parts of the earth, as explained in the section on HEAT.

"At a distance from the Earth, nearly thirty times the

Earth's diameter, is the body nearest to it, the Moon."

1019. That the moon is nearer to us than any of the other celestial bodies is proved by the fact that when she comes over the place where the sun, a planet, or a star is at the time, she hides them from our view. When this happens with the sun it makes a solar eclipse; when with a star, or a planet, it is called an occulting, or occultation.

The means of ascertaining the distances of the heavenly bodies from the earth may be understood by the following considerations:

In the section on LIGHT it was explained that in regard to objects comparatively near, persons judge of the distance by several means, but especially by the degree of convergence, or angular approach, of the axes of the two eyes, which have to meet at the object in order to see it distinctly. This is recalled in the adjoining diagram (fig. 303), where the small circles mark the eyeballs, from which lines going to A B C D show different inclinations or converg. ence of the axes. The angle or corner formed at the meeting of the axes at A is evidently greater than that at B, and still greater than that at C, &c. The person is conscious of the difference

782

Measurement of the Celestial Distances.

of effort required, at the different distances, to cause the axes to converge sufficiently, and that consciousness serves as a measure. 1020. Now to judge accurately by that angle of convergence, in regard to objects very distant, like the moon, sun, or a planet, we

employ, instead of the two eyes, two telescopes, placed at distant stations, or one telescope used successively in two stations, and then measure accurately the angles of direction of the telescopes, whose axes meet at the object.

The fixed relation of such angles and distances may be rendered intelligible by a simple illustration. Let the lines, A G and BI (fig.

304), represent parts of the parallel sides of a long straight street, with a row of lamp-posts in it, A DEFG, about the width of the street apart. Let a pocket-watch then, with large dial face, be placed on a table at B, directly opposite to the lamp-post, A, where the crossing line, A B, forms a square corner or right angle with the line, A G, lying along the street. Let the minute-hand of the watch point to twelve

Illustration of the Process.

783 o'clock, and at the same time to an attendant standing at the lamppost, A. If the attendant then move to the post, D, and the minutehand be turned to follow him, the eye of an observer through a small telescope, placed in the direction of the hand of the watch, will see the attendant in the direction, B D, which may be represented by a thread stretched from B to D. That thread will cross or cut the divided circumference, a b, of the watch, then serving as an angle-measure instead of a time-measure, at a certain angle (he.e of 45°). The attendant, continuing to advance, would reach the posts, E F G, &c., in succession, and would be seen along the lines, B E, BF, B G, &c., cutting the curve, a b, at different points nearer and nearer to b, and forming angles of less and less magnitude, with the line, B I. This process might be continued until the eye could no longer distinguish the more distant lamp-posts, nor estimate aright the lessening portions cut off on the divided curve, a b. But so long as these could be distinguished, every distance among the posts would form its own distinct angle, and he who could read the angle would always know the corresponding distance of the lamps on the prolonged line, A G. By such an experimental process, and still more accurately by computation, a table of tangents is constructed, showing the distances and angles that mutually correspond.

A common watch is here referred to as an angle-measure, because it is so familiar, and because the hand, in moving forward, so evide:.tly divides the space around the axle into all pɔssible angles. The instruments actually used for measuring angles have always a metallic circle, or portion of a circle, accurately divided into equal degrees, or parts of a degree, over which an index travels. So perfect now is the manufacture of such instruments that they enable the eye, when aided by a microscope, to distinguish less than the hundred-thousandth part of the circumference of a circle.

1021. It is a very important fact that, under certain circumstances, by measuring the angle formed where two straight lines meet, the length of one of them pointing to a distant visible object can be accurately known. This depends on the remarkable properties of the triangle. It is roughly exhibited when a string, A B C (fig. 305), is employed to support a picture-frame, D, on a wall, the string passing through two rings, B and C, on the frame, and resting on a nail at A on the wall; or, when a piece of thread of any length, having its ends joined to form a loop, is laid on a flat table and is opened out into the form of a triangle by outward pressure made at any three points.

784 Application of the Properties of the Triangle.

The properties referred to are, first, that whatever the shapes of triangles be, as here, of A, E, F, G, H, the sum of the three angles of any one is always exactly equal to two square corners, or right angles, so that when any two of the angles are known, the third

E

AL-1

D

Fig. 305.

A

also is known; and second, that, of the six particulars named of sides and angles, if any three, one of these being a side, are known, all the six are knowable, either by simple computation or by drawing the figure of a convenient size on some flat surface.

The simple arrangement here sketched further illustrates this subject. A B (fig. 306) is a flat ruler or rod, in wood or metal, about a yard long. A C and B D are similar rods of any length, hinged movably to the ends, A and B. The rod, A B, called the base of the figure, has, affixed at H and K, two arcs, or portions of circles, H I and K I, divided into degrees, by which the angles formed at A and B by the movable arms and the base can be measured. Laying this on a table, and causing the movable arms to point to any object, the