Proofs of the Globular Form.

775 4, &c., the squares are 1, 4, 9, 16, &c.; and the inches of descent are 8, 32, 72, 128, &c. For greater distances the descent is calculated in the same way, and it is found that at a distance of 10 miles, it is 66 feet; at 14 miles, 150 feet; at 150 miles (the distance at which the Peak of Teneriffe comes into view over the watery horizon), the descent is 15,840 feet, or nearly three miles,—the height of that mountain.

It is to be observed that the rule explained here for heights and distances tells also what breadth of sea is visible from any given elevation above its surface, whether from the mast of a ship or from the land. The diagram exaggerates some of the proportions to render the effect more apparent.

A simple mode of proving the fact of this sinking down of the true level of a canal from the tangent or apparent level, and of ascertaining its amount is, to set up in the middle of a straight canal a row of poles, rising each, say, ten feet above the surface of the water. If the row be quite straight, a person looking along with the naked eye, or with a telescope, from near one end, can see only the nearest pole, for it would hide all the others, because light moves in straight lines. But if on these poles cross-pieces are affixed at equal heights, say of five feet above the water, and if the telescope, set level at that height, is then directed along the level, instead of the nearest cross-piece hiding all the others, as is true of the vertical poles in a straight line, it leaves them all visible in a curve, like pins projecting sidewise from the rim of a wheel, and the cross-piece on the pole standing at the distance of one mile from the station, B, would be found to appear just eight inches below the apparent straight level, as judged of by the telescope levelled at the station, B. The cross-pieces more distant than one mile, would be found to be lower by increasing differences, as seen in the figure at G H I, &c., and in the tabular statement given above.

1013. In whatever part of the earth this experiment is made, the like results are obtained, proving that the degree of convexity is, in round numbers, the same everywhere, and, therefore, that the earth is really a sphere. There is a slight deviation to be afterwards explained, due to the rotation of the earth. Now a simple arithmetical computation tells that a dip of eight inches in the first mile belongs to a globe of very nearly 8000 miles in diameter. The logbooks of the ships that have sailed round it measure the circumference, and confirm the same estimate.

The most accurate mode of learning the earth's size is by mea

776

Size of the Earth.

suring a degree of latitude in any arc of the meridian. This mode was actually adopted two hundred years before Christ by Eratosthenes, in Egypt, and was the first approach to an estimate of the size of the earth. Many careful measurements have been made in modern times, and from them we ascertain that the polar diameter of the earth is 7899'2 miles, and the equatorial diameter 7925'6 miles; the difference being 26°4 miles, and the mean diameter 7912'4 miles.

It is the same kind of experiment modified, and yet more simple, when in winter the poles are set up on the frozen surface of a canal or a lake. It is still the same when, instead of fixed poles in the water, the masts of two similar boats are used, on which telescopes are fixed. Let A and B (fig. 298) be two such boats on a

H

K

E

A B

Fig. 298.

straight canal. Telescopes, O, S, on their masts, set level while near, would point to each other; but as the boats separated, would have their axes or lines of sight pointing gradually higher and higher as the distance increases, according to the law above explained. At the distance, a b, the boats would have become what sailors call hull-down, or with the body of one vessel concealed from the view of persons on the deck of the other, and the telescopes could see, over the convexity of the globe between them, only the parts of the masts above that level.

Fig. 299 represents the same ship, viewed from the same cliff on

Consequences of the Globular Form.

777

the sea-shore, A, at different distances. The dotted line, A B C, is the line of sight touching the surface of the convex sea when the ship is at B, commanding only part of the rigging at D, and seeing nothing of the ship at C.

1014. There is an interesting case, which in many situations on earth offers itself to notice, namely, where a spectator at E (fig. 300), in looking along the apparent level-line at A, just sees the top

of a hill at B, and of a second loftier summit at C, and of a third loftier still at D, apparently all on the same level. The summit, D, might be one of the Andes, 25,000 feet high, and the others lower as less distant, according to the rule above explained; and in any such case the height being known, the distance is known, or the distance being known, the height is known, by computation.

The surface of the convexity or bulge of the sea, existing between a spectator and a distant object, is called the water-line or natural horizon. It is always of course beneath the tangent, or apparent level, passing through the eye of the spectator; and the angle of depression is called the dip of the horizon, which is greater or less, according as the spectator is placed high or low above the level of the sea. For the use of mariners, books on navigation have a table, stating the amount of dip for different heights of the observer's eye.

1015. The following facts illustrate, and are explained by, what has now been said of the form of the earth.

When two persons approach each other from opposite sides of a river to pass over a bridge, of which the general surface is part of a circle rising high in the middle between them,—as was true of many bridges in former times—each sees first only the hat and head of the other, and then gradually the whole person. After passing they disappear from each other in the reverse way, the feet and lower parts of the body first, the upper part the last. So, on a much larger scale, two ships, approaching over the convex sea, exhibit to telescopes first their upper sails and rigging, and after they have

778

Distant Objects sinking out of Sight.

passed each other, lose sight first of the lower parts. As they vanish they are first hull-down, then half-mast-down, and so on.

A ship departing directly out to sea soon appears to persons near the shore, hull-down, and to have got beyond a distant wall of water. A spectator on a height near the shore, as a lofty building, still sees the whole vessel.

Ships at sea, which are hull-down to persons on the deck are fully seen by the lookers out near the mast head; and distant land may be seen from the mast-head over the bulge of the sea, where persons on deck see nothing.

The extensive plains in America called prairies and pampas, which are nearly as level as the surface of the sca, exhibit the same phenomena of hiding by their bulge distant objects from persons travelling over them.

Rivers crossing such level tracts are not, as generally supposed, straight gently-inclined planes, but portions of hoops, of which the parts towards the mouth of the river are a little nearer to the centre of the earth than the parts behind. It seems strange, until explained, that a ship may be seen hull-down though floating on a higher part of a great river.

When the sun appears half set over the sea, as at s in fig. 301, it is the substance of the convex water which hides the half, unseen by people on the low shore, for they have only to mount a little and they will see all again.

1016. A ship near the centre of a scattered flcet may see the distant ships all round, beyond the water horizon, half-concealed,

Fig. 301.

M

as if to that extent submerged, at T. This appearance is more striking where the ships have a background of high mountain, M, beyond them. They then appear as if they were aground between the near water-horizon and the shore beyond

Cause of the Globular Form.

779

The sun sets entirely to people on a low plain, or on the seashore, long before the inhabitants of neighbouring hills have lost any of his beams. And the peaks of very elevated mountains are seen after sunset shining as brightly as the moon, so long as the sun's rays continue to reach them.

Near the border line, between the enlightened and the shaded portions of the moon in her quarters, the telescope sees always a number of irregular luminous spots, as bright as any part of the shining surface. These are the summits of mountains receiving the slanting rays of the sun, while lower parts near are still in the shade.

It has seemed strange that after sunset the song of a lark, invisible from the earth, should still be heard by people below. The explanation is, that the blithe bird on the wing may still have sight of the sun, when from eyes below he has quite vanished.

Aëronauts, who, in descending, reach the earth just after sunset, may see the sun again, and therefore can make an artificial sunrise, by throwing out some ballast and so remounting into the air.

If the inhabited earth had been, as believed of old, a broad plane surface, beyond the edge of which the sun and stars in setting had to descend, sunset and sunrise would have happened to all the world at the same moment. But, in fact, when the sun sets over the sea, to people on one part of a coast, the telegraph from a part farther west can report that to them he is still at a considerable elevation; and in all parts of the earth he sets and rises just as much later as the place is farther west.

"The globular form of the Earth is the result of the mutual attraction or gravitation of its particles."

1017. The attraction of gravitation, considered as a property of all matter, was explained in the introductory chapter, Art. 13. Under any mode of attraction whatsoever, a mass of loose particles will assume the form of a globe or sphere. If water be allowed to escape through a small opening in the bottom of a glass tube, it appears as a mass rounded below, and increasing until its weight is greater than the attraction between it and the tube above. It then falls as a round drop, the mutual attraction of the particles being equal in all directions, producing this form. The successive drops are all of the same magnitude, and their number in a given time measures the quantity of liquid fallen.

Dew accumulating on the leaves an1 stalks of plants, takes a