free air; and smoke ascends in the same manner as it would do in an apartment on shore. If, indeed, we come on deck, the case is, in some respects, different; the air, not being carried along with us, drifts away smoke and other light bodies such as feathers abandoned to it-apparently, in the opposite direction to that of the ship's progress; but, in reality, they remain at rest, and we leave them behind in the air. Still, the illusion, so far as massive objects and our own movements are concerned, remains complete; and when we look at the shore, we then perceive the effect of our own motion transferred, in a contrary direction, to external objects -external, that is, to the system of which we form a part.

"Provehimur portu, terræque urbesque recedunt."

(17.) In order, however, to conceive the earth as in motion, we must form to ourselves a conception of its shape and size. Now, an object cannot have shape and size unless it is limited on all sides by some definite outline, so as to admit of our imagining it, at least, disconnected from other bodies, and existing insulated in space. The first rude notion we form of the earth is that of a flat surface, of indefinite extent in all directions from the spot where we stand, above which are the air and sky; below, to an indefinite profundity, solid matter. This is a prejudice to be got rid of, like that of the earth's immobility;- but it is one much easier to rid ourselves of, inasmuch as it originates only in our own mental inactivity, in not questioning ourselves where we will place a limit to a thing we have been accustomed from infancy to regard as immensely large; and does not, like that, originate in the testimony of our senses unduly interpreted. On the contrary, the direct testimony of our senses lies the other way. When we see the sun set in the evening in the west, and rise again in the east, as we cannot doubt that it is the same sun we see after a temporary absence, we must do violence to all our notions of solid matter, to suppose it to have made its way through the substance of the earth. It must, therefore, have gone under it, and that not by a mere subterraneous channel; for if we notice the points where it

sets and rises for many successive days, or for a whole year, we shall find them constantly shifting, round a very large extent of the horizon; and, besides, the moon and stars also set and rise again in all points of the visible horizon. The conclusion is plain: the earth cannot extend indefinitely in depth downwards, nor indefinitely in surface laterally; it must have not only bounds in a horizontal direction, but also an under side round which the sun, moon, and stars can pass; and that side must, at least, be so far like what we see, that it must have a sky and sunshine, and a day when it is night to us, and vice versâ; where, in short,

"

redit a nobis Aurora, diemque reducit. Nosque ubi primus equis oriens afflavit anhelis, Illic sera rubens accendit lumina Vesper."

Georg.

(18.) As soon as we have familiarized ourselves with the conception of an earth without foundations or fixed supports — existing insulated in space from contact of every thing external, it becomes easy to imagine it in motion-or, rather, difficult to imagine it otherwise; for, since there is nothing to retain it in one place, should any causes of motion exist, or any forces act upon it, it must obey their impulse. Let us next see what obvious circumstances there are to help us to a knowledge of the shape of the earth.

(19.) Let us first examine what we can actually see of its shape. Now, it is not on land (unless, indeed, on uncommonly level and extensive plains), that we can see any thing of the general figure of the earth;-the hills, trees, and other objects which roughen its surface, and break and elevate the line of the horizon, though obviously bearing a most minute proportion to the whole earth, are yet too considerable with respect to ourselves and to that small portion of it which we can see at a single view, to allow of our forming any judgment of the form of the whole, from that of a part so disfigured. But with the surface of the sea or any vastly extended level plain, the case is otherwise. If we sail out of sight of land, whether we stand on the deck of the ship or climb the mast, we see the surface of the sea-not losing

itself in distance and mist, but terminated by a sharp, clear, well-defined line or offing as it is called, which runs all round us in a circle, having our station for its centre. That this line is really a circle, we conclude, first, from the perfect apparent similarity of all its parts; and, secondly, from the fact of all its parts appearing at the same distance from us, and that, evidently, a moderate one; and thirdly, from this, that its apparent diameter, measured with an instrument called the dip sector, is the same (except under some singular atmospheric circumstances, which produce a temporary distortion of the outline), in whatever direction the measure is taken,-properties which belong only to the circle among geometrical figures. If we ascend a high eminence on a plain (for instance, one of the Egyptian pyramids), the same holds good.

(20.) Masts of ships, however, and the edifices erected by man, are trifling eminences compared to what nature itself affords; Ætna, Teneriffe, Mowna Roa, are eminences from which no contemptible aliquot part of the whole earth's surface can be seen; but from these again-in those few and rare occasions when the transparency of the air will permit the real boundary of the horizon, the true sea-line, to be seen the very same appearances are witnessed, but with this remarkable addition, viz. that the angular diameter of the visible area, as measured by the dip sector, is materially less than at a lower level; or, in other words, that the apparent size of the earth has sensibly diminished as we have receded from its surface, while yet the absolute quantity of it seen at once has been increased.

(21.) The same appearances are observed universally, in every part of the earth's surface visited by man. Now, the figure of a body which, however seen, appears always circular, can be no other than a sphere or globe.

(22.) A diagram will elucidate this. Suppose the earth to be represented by the sphere LHN Q, whose centre is C, and let A, G, M be stations at different elevations above various points of its surface, represented by a, g, m respectively. From each of them (as from M) let a line be drawn, as MN n,

C

a tangent to the surface at N, then will this line represent the visual ray along which the spectator at M will see the visible horizon; and as this tangent sweeps round M, and comes successively into the positions MO o, MPP, MQq, the point of contact N will mark out on the surface the circle NOPQ. The area of the spherical surface compre

hended within this circle is the portion of the carth's surface visible to a spectator at M, and the angle N M Q included between the two extreme visual rays is the measure of its apparent angular diameter. Leaving, at present, out of consideration the effect of refraction in the air below M, of which more hereafter, and which always tends, in some degree, to increase that angle, or render it more obtuse, this is the angle measured by the dip sector. Now, it is evident, 1st, that as the point M is more elevated above m, the point immediately below it on the sphere, the visible area, i. e. the spherical segment or slice NOPQ, increases; 2dly, that the distance. of the visible horizon or boundary of our view from the eye,

Opigw, to terminate.

viz. the line MN, increases; and, 3dly, that the angle NMQ becomes less obtuse, or, in other words, the apparent angular diameter of the earth diminishes, being nowhere so great as 180°, or two right angles, but falling short of it by some sensible quantity, and that more and more the higher we ascend. The figure exhibits three states or stages of elevation, with the horizon, &c. corresponding to each, a glance at which will explain our meaning; or, limiting ourselves to the larger and more distinct, MNOPQ, let the reader imagine n N M, MQ7 to be the two legs of a ruler jointed at M, and kept extended by the globe N m Q between them. It is clear, that as the joint M is urged home towards the surface, the legs will open, and the ruler will become more nearly straight, but will not attain perfect straightness till M is brought fairly up to contact with the surface at m, in which case its whole length will become a tangent to the sphere at m, as is the line ry.

*

(23.) This explains what is meant by the dip of the horizon. Mm, which is perpendicular to the general surface of the sphere at m, is also the direction in which a plumb-line* would hang; for it is an observed fact, that in all situations, in every part of the carth, the direction of a plumb-line is exactly perpendicular to the surface of still water; and, moreover, that it is also exactly perpendicular to a line or surface truly adjusted by a spirit-level. Suppose, then, that at our station M we were to adjust a line (a wooden ruler for instance) by a spirit-level, with perfect exactness; then, if we suppose the direction of this line indefinitely prolonged both ways, as XMY, the line so drawn will be at right angles to Mm, and therefore parallel to a my, the tangent to the sphere at A spectator placed at M will therefore see not only all the vault of the sky above this line, as XZY, but also that portion or zone of it which lies between X N and Y Q; in other words, his sky will be more than a hemisphere by the zone YQXN. It is the angular breadth of this redundant zone-the angle YMQ, by which the visible horizon appears depressed below the direction of a spirit-level- that is called See these instruments described in Chap. III.

m.