The Angle of Parallax.

785

visual rays, indicated here by dotted lines, will meet at the object, as M, to form an angle which, by the tables spoken of, or by computation, tells the distance of the object. By such a rude instrument, a person without moving from his chair can judge of the distance of any object within view, in a room, a garden, or field.

The angle to be determined in all such cases is called the angle of parallax, the reason of which appellation is thus to be explained. The figure, A B C D (fig. 307), shown here is called a parallelogram, because its opposite sides are parallel to each other;

that is, are at the same distance apart wherever a directly transverse or cross measure is taken, and therefore, however far prolonged in either way, they would never meet. But a line called a diagonal, drawn between opposite corners of the parallelogram, as from B to C, or from A to D, is not parallel to the sides, but has a changed bearing called parallax, and the sharp angle formed at the corners of the parallelogram between the diagonal and the side is the angle of parallax.

If an observer at A look through a telescope with graduated arc towards an object at C, bearing directly east from him (or in any other exactly ascertained direction), and if he then shift his station to a certain known distance, B, at right angles to the line, A C, and he again look towards the object, C, he finds its bearing changed from being directly east to the other line, B C, inclining north of east by the sharp angle, D B C, at the corner, B. This is called the angle of parallax. Whatever part of a whole circle that angle is, just such part of the circumference of a circle which has c for its centre, and the distance, C A, for its radius or semidiameter, is the distance, A B, which has been measured; and from that part being known the whole circumference is known, and, consequently, the semidiameter of the circle, which was the distance sought.

786

The Moon's Distance determined.

In regard to the distance of the moon from the earth, the shape and size of the earth being now well known, the distance of any two remarkable places upon it is also known, and the straight line of distance between any two such places may serve as the base line for measurement. The places that have been chosen for the purpose are the two observatories of Greenwich and the Cape of Good Hope, at which angles can be measured which will declare the angle at the summit of the figure, M (fig. 308), where the moon is supposed to be. A still simpler mode of ascertaining the angle of this parallax is to measure the apparent angular distances, as seen at the same moment from these places, between the moon and a known fixed star. The distance of the moon from this earth is by these means ascertained to be 240,000 miles nearly, or thirty times the diameter of the earth. Knowing the distance in such a case, and the apparent diameter, because the moon, like all the other heavenly bodies, is globular, the size of the moon can be computed. The diameter is thus estimated to be 2160 miles, rather more than a fourth part of the diameter of the earth; the bulk of the moon is consequently nearly a fiftieth part of that of the earth.

Another method of confirming the same result, although in itself not so exact, is the following :—

1022. Let the circle, G (fig. 308), represent the earth; M, the moon

C

M

H

over the head of a person at E; and M H, part of the apparent path of the moon travelling round the earth, always at nearly the same distance from the centre of the earth, G. It is evident that the moon, when at M, is nearer to a spectator on the earth at E by half the diameter of the earth -4000 miles-than when she is setting beyond the horizon at H. According to the law of Optics-that an object appears smaller in proportion as it is farther away, the moon when at H should appear smaller to the spectator at E than when at M. Now, when measured by a fit instrument, it does appear smaller by just one-sixtieth part of its diameter. This proves, therefore, that 4000 miles is the sixtieth part of the moon's distance from the earth; now, sixty times 4000 is 240,000.

Fig. 308.

Rotation of the Earth.

787

This experiment proves another striking fact, namely, that in the six hours between the moon's being over a person's head and its setting, its distance is increased by nearly 4000 miles.

By kindred means to those above described, astronomers have ascertained the distance of the sun. It is four hundred times greater than that of the moon, being ninety-one and a half millions of miles. The distances and magnitudes of the other heavenly bodies are so vast, that the human mind has difficulty to conceive them; and the angle of parallax which measures them becomes so small that instruments of extreme delicacy, and the aid of strong microscopes to read the indications, are required for the purpose.

SECTION II.

"The Earth rotates, or spins; thereby exposing the surface successively to the Sun, and bringing about the changes of day and night."

1023. Judging from first appearances, people necessarily sup posed that the earth stood still, while the stars moved round it. This inference would be confirmed by a natural prejudice founded on the supposition that the motion of the earth would endanger the stability of everything on its surface. A more exact attention to the phenomena of moving bodies dispels this prejudice. Motion, if perfectly equable, disturbs nothing, and is unfelt by the living beings that partake of it. Many illustrations of this fact can be given.

-Aëronauts in the car of their balloon, when moving a hundred miles an hour, have no sensation of being in motion, and if surrounded by a cloud which prevents them from seeing objects around them, they cannot know in what direction they are moving. The same is true of persons on board ships drifting along in sea-currents out of sight of land, as frequent disasters have proved. A person sitting in the cabin of a ship at anchor, if occupied in reading or writing while the ship is swinging round with the turn of tide, has no perception of the change. A man seated in a chair suspended by a rope from a high ceiling, if his eyes are covered, has no sense of any turning motion softly given to his seat. A person in a small floating boat or tub, surrounded by a floating screen which hides from him all beyond it, cannot know, when any gentle motion is produced, whether it is in his boat, or in the screen, or partly in both.

788

Daily Movement of the Celestial Vault

Uniform motion of this globe, then, however rapid, would not be perceived by the inhabitants. The motions of walking, riding, being driven in a carriage over a rough road, being tossed in a boat on a rough sea, and so forth, are contrasting examples. (See Art. 156.) At the time when the stars were regarded as insignificant in size, and not very remote in distance, people might suppose it not unlikely that the entire concave of the heavens should revolve round the earth. But, with our present knowledge of their vast distances and magnitudes, such an enormous sweep as they would have to make every twenty-four hours becomes in the highest degree improbable; while many circumstances suggest that the changes of day and night, and other phenomena, formerly attributed to the motion of the heavens, are due to the motion of the earth itself. We shall first survey the appearances themselves.

1024. Let a person, just after the setting of the sun, of which the intense brilliancy during the day prevents all smaller lights from being seen, ascend to the house-top or other eminence which commands an unobstructed view of the horizon around, and let him there contemplate at leisure the nocturnal sky. He may in the morning have seen the sun appear to rise in the east, and gradually move across the sky to set or disappear in the west. As the setting sun's light fades, he finds himself apparently in the centre of a stupendous vault or concave half-globe, thickly studded with luminous objects, which he has been taught to call stars. Among these he perceives as little order of arrangement as among the first drops of rain falling on a white pavement, but soon, individual stars are distinguished by their greater brilliancy, and others by belonging to certain groups, which bear some resemblance to familiar forms on earth, as of square, cross, triangle, and so forth. He soon perceives that all the stars have a movement towards the west, like that of the sun during the day, and that those near the western horizon are setting or disappearing, to follow the sun, while others are rising into view in the east, and maintaining undiminished, the splendour of the spectacle. In the course of the night, if the observer watch to the end, he will see, not only that starry half-globe or concave which was overhead when the sun disappeared, but also the whole of another half, which, as the night advances, gradually takes the place of the first. With the sun's light returning and producing the dawn of next day, the feebler lights of the stars are first dim, and soon cease to be at all perceived by the naked eye; but a good telescope can see and follow them moving on all through the day, just as the

Illustrated by the Artificial Globe.

789

naked eye did during the night; and those subsequently rising in the east are found to be those which twelve hours before set after the sun in the west. The observer thus finds that he has seen the whole of the surrounding firmament in which the world exists, revolving like the continuous interior of a great wheel. The stars which rise and set nearly with the sun are, for the time, less conspicuous than the others, owing to his overpowering light; but when the sun gradually changes his place among them during his annual circuit, all are, ir like manner, alternately dim and bright.

Now for thousands of years men have been watching the appearances of the stars, and from observing that their relative positions have remained sensibly unchanged, have called them the fixed stars, to distinguish the general mass from a small number, which seem to move about among the others as the sun does, and are called planets (from the Greek word λaváw, to wander).

1025. The spectacle of the nocturnal sky above described is rendered much more interesting by having at hand a globe, formed of wire, like a bird-cage, as here represented, with a spindle, SN, through its centre, C, on which it

turns. One end of the spindle, N, is to be directed to the north pole of the sky, and the other end, S, to the south. At places on or near the equator, as in our colony of Singapore, in the Strait of Malacca, the spindle appears to the inhabitants to be horizontal, as here shown from N to S. A person sitting near the table which supports this globe, so as to be able to look through a small ring at its centre, C, towards every star above the horizon, may attach in some convenient way, on the surface of the globe at the point which is in visual contact with the star, a small glass bead to repre

Fig. 309.

sent it. He may then maintain such bead in contact with the star, by gradually turning the globe round as the star seems to travel westward towards the setting; and in the meantime he may employ himself in affixing other beads to represent the other most conspicuous stars then seen. These representatives of the stars will set with them, by sinking under the level of the spindle, S N, which in