CHAPTER X.

THE ROTATION AND FIGURE OF THE EARTH.

Effect of the Motion of the Earth on the apparent Motion of the Heavens. Distinction between the Earth's yearly and diurnal Motion. Axis of Rotation. The Circles of the Equator and Ecliptic. Shape of the Earth's Orbit. Invariability of the Earth's Rotation. Earth's Figure and Dimensions. Its Ellipticity. Pendulum experiments. Measurement of Arcs of a Degree on the Earth's surface.

$199. The reader will remember those groups of islands which stud the Pacific. On the map they are near neighbors, but in fact they are too far apart to be visible to one another, and are separated by thousands of miles of ocean. Thus the inhabitants of each group might easily suppose their own to be the only group of the Pacific. And as the islands of each group are likewise widely separated from one another, it would not be strange if each island should be deemed by its inhabitants a world in itself.

Let us choose from a group containing some hundreds of islands, an island not precisely in the centre of the group. And let us suppose it endowed with a magnetic power like the Black Mountain of fairy tales. We will suppose several boats of different sizes to circulate round it at distances varying from 3 to 190 yards. Let each boat also twirl continually round an imaginary axis, while it proceeds in its course round the island. Place upon this boat a tiny insect, whose life endures only some seventy revolutions round the island, and this insect, supposing it endowed with reason, will have greater facilities for learning the wide Pacific with all its isles than man has for becoming acquainted with the universe. The earth is our boat, which measures from end to end 8,000 miles or upwards of fortytwo millions of feet. The island round which we circle is our sun, and it is so bright, that from the part of the boat toward him we can discern no other body in the universe. But when our side of the boat is turned from him we see other boats, the planets our companions, and we also see

the myriad isles of our cluster, beaming fixed stars in the heavens.

§ 200. Since the difficulties in the way of learning are so great we will begin modestly and study our own planet first. There are three questions which must be settled before we can take the earth as our stand-point, and our measure for other bodies. The first is whether it is at rest or in motion; the second, what is its shape; the third, what is its size?

On looking into the heavens we find nothing apparently at rest. The sun is not in the same place if we look at him after an interval of an hour; the moon, if she is visible in the heavens, changes her place with rapidity. The stars which at twilight we saw in the east are over our head at midnight, and at dawn set in the west. Not only this, but the sun no two consecutive days rises or sets in the same place; and a different set of stars make their appearance in the east each night. Venus appears sometimes as an evening, sometimes as a morning star. The other planets are often absent from our heavens.

$201. The first division we should attempt to make of these motions is by finding which are common to all, and which are peculiar to some. Those which are common to all may arise from either of two causes, and we must choose the more probable of the two. Either all the objects we look at are moving or we may ourselves be in motion. An observer in a vessel on a wide ocean cannot distinguish whether another vessel within sight is sailing and his own at rest, or whether the other vessel is at rest and his own drifted along by some unsuspected current. An observer on one ship cannot judge accurately the rate of progress or the direction of the other. For supposing them both in parallel directions, the swiftest will appear to advance with only the difference of their velocities. Suppose them sailing in opposite directions, the other will recede with the sum of their velocities. If they are sailing in diverging or converging directions from one another, the apparent direction will not for one moment coincide with the true one.

But instead of being on the ocean let the observer be on a lake whose banks are covered with villages and varied by

woods and hills. If he finds that all these objects pass in the same direction and at an equal rate from his sight, and that in a certain time he has seen them on every side of him, will he not more rationally ascribe the motion to his single vessel than to the whole landscape around him. And if he sees on the lake other ships, not joining in this motion of the shores, but outstripping or lagging behind, he will not hesitate to ascribe to these ships proper motions; remembering always that he does not see these motions as they really are, but altered by his own motion.

§ 202. Thus when we are obliged to choose between the simultaneous motions of many bodies, or the motion of one body, we keep on the side of probability when we attribute the motion to the single body.

Applying this principle to our earth, it is much more probable that by turning round she is a part of the twentyfour hours exposed to the sun, and another part in the presence of the stars, than that the sun and all the stars sweep round her in one uniform diurnal motion. It is much more likely that she is so inclined in her orbit that in one season of the year she presents a given part of her surface but a short time, and in another season a longer time to the sun, than that he, varying his motion, describes now lower and shorter, and again higher and longer arcs in the heavens,

We are therefore warranted in considering the earth's real motion as the cause of all the apparent motions which are common to other bodies. And we may ascribe to the same cause that part of each body's apparent motion for which it will account. Thus we find in the heavens three kinds of motion, one purely apparent caused by the earth's real motion, one made up of the body's proper motion combined with the earth's motion, and one among the fixed stars too distant to be affected by the earth's motion, and for all we know a simple proper motion.

§ 203, Let us now consider what motions the earth must have to account for all the appearances we observe. There are two sets of phenomena to be accounted for, the diurnal and the yearly; we must therefore allow her two motions. We find that the sun appears to pass through an

entire circuit of the heavens in the course of the year, moving from west to east. This apparent path of the sun may be caused by a real motion of the earth in the same direction from west to east. For supposing the sun to be motionless and the earth to be moving round him, the inhabitants of the earth would refer the sun to a point in the concave surface of the sphere precisely 180° from the earth's place. If the earth moved 15° eastward, the sun would move 15° eastward; if in a year the earth passed through the whole circle, the sun would appear to pass through the whole circle, always remaining precisely in opposite quarters of the heavens to those in which the earth would be. All these phenomena would be precisely the same and would occur in the same order whether the sun moves round us or we move round the sun.

We have now to account for the daily rising and setting of the sun and stars. To do this we need only suppose in the earth rotation in the same direction with its revolution. As the earth rotating toward the east turns up a portion of her surface toward the sun, the sun appears to that portion to rise in the east. As the place comes under the direct beams of the sun it is noon at the place; as it turns further round, it leaves the sun behind, he becomes invisible, but the stars rise; the earth still turns round, the place is 180° away from the sun, it is midnight; the earth turns another quarter, the place has left the stars behind, they have set; it has come in sight of the sun, the sun has again risen. This motion of rotation is confirmed even by phenomena on the surface of the earth. A stone let fall from the top of a high tower, falls not at the foot of the tower, but a little further east, showing that being further from the earth's centre it had a greater velocity than the earth it fell on.

§ 204. But while the earth has been turning it has passed on in its orbit, it refers the sun to a different part of the concave sphere, the sun rises among stars lying farther east than those among which it rose yesterday. The stars which rose after sunset the night before are now lost in his beams, those which rose later now appear as soon as he is out of sight. Those which were on the meridian at

midnight now pass it before midnight, and new stars come into view before the sunrise.

The daily and yearly changes may be exhibited in miniature by a bright light placed in the centre of a room whose walls are covered with tapers. Let the light represent the sun, the tapers the fixed stars. By walking round this room and rotating once every minute we shall face the lamp and thus make it rise to us once every minute; we shall also have the tapers facing us a half of every minute. If we walk round the lamp so slowly that we can turn round 365 times before we return to our starting point, we shall perform a course similar to that of the earth during a year. For by our revolution round the lamp we shall have brought it in succession between ourselves and every part of the wall, while by our rotation we shall have brought the light facing us, that is we`shall have had 365 noons, and 365 times we shall have had a partially different set of tapers exhibited to us in each rotation.

§ 205. If the earth rotates it must have an axis or line of immovable particles passing through its centre; and the diameter of this axis, and the fact of its variability or invariability we can only ascertain from the heavens. An axis may be variable in its position within the sphere that is as to the place where its poles touch the surface, it may be invariable with regard to the solid sphere, and may vary in direction carrying along the sphere with it, or it may be invariable in both respects. In the latter case it will always point toward one point, and all surrounding objects will appear to be carried in circles round that one point. As we find one point in the northern celestial hemisphere and another in the southern, round which all the stars appear to describe circles, we have no hesitation in saying that the axis of our earth is immovable, and if prolonged would pass through these points. On the earth's surface and in a line with those two immovable points in the heavens are two points which do not rotate, and partake only of the orbitual motion of the earth. These are the north and south poles of the earth.

The equator is an imaginary great circle on the earth's surface 90° from each pole, dividing the earth's surface