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.

(21.) 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.

(22.) 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.

(23.) A diagram will elucidate this. Suppose the earth to be represented by the sphere LHNQ, 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 M N n, 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 0, MPP,

CHAP. 1. GENERAL FORM OF THE EARTH.

17

MQq, the point of contact N will mark out on the sur

portion of the earth'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, viz. the line MN, increases; and, 3dly, that the angle NMQ becomes *'Ogicw, to terminate.

C

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, MQ¶ 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 x y.

(24.) This explains what is meant by the dip of the horizon. M m, 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 earth, 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 X M Y, the line so drawn will be at right angles to Mm, and therefore parallel to x my, the tangent to the sphere at m. A spectator placed at M will therefore see not only all the vault of the sky above this line, as X Z Y, 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 Y M Q, by which the visible horizon appears de

See this instrument described in Chap. II

CHAP. I. EFFECT OF THE EARTH'S CURVATURE. 19 pressed below the direction of a spirit-level—that is called the dip of the horizon. It is a correction of constant use in nautical astronomy.

(25.) From the foregoing explanations it appears, 1st, That the general figure of the earth (so far as it can be gathered from this kind of observation) is that of a sphere or globe. In this we also include that of the sea, which, wherever it extends, covers and fills in those inequalities and local irregularities which exist on land, but which can of course only be regarded as trifling deviations from the general outline of the whole mass, as we consider an orange not the less round for the roughnesses on its rind. 2dly, That the appearance of a visible horizon, or sea offing, is a consequence of the curvature of the surface, and does not arise from the inability of the eye to follow objects to a greater distance, or from atmospheric indistinctness. It will be worth while to pursue the general notion thus acquired into some of its consequences, by which its consistency with observations of a different kind, and on a larger scale, will be put to the test, and a clear conception be formed of the manner in which the parts of the earth are related to each other, and held together as a whole.

(26.) In the first place, then, every one who has passed a little while at the sea side is aware that objects may be seen perfectly well beyond the offing or visible horizon-but not the whole of them. We only see their upper parts. Their bases where they rest on, or rise out of the water, are hid from view by the spherical surface of the sea, which protrudes between them and ourselves. Suppose a ship, for instance, to sail directly away from our station; - at first, when the distance of the ship is small, a spectator, S, situated at some certain height above the sea, sees the whole of the ship, even to the water line where it rests on the sea, as at A. As it recedes it diminishes, it is true, in apparent size, but still the whole is seen down to the water line, till it reaches the visible horizon at B. But as soon as it has passed this distance, not only does the visible portion

still continue to diminish in apparent size, but the hull begins to disappear bodily, as if sunk below the surface.

T

C

When it has reached a certain distance, as at C, its hull has entirely vanished, but the masts and sails remain, presenting the appearance c. But if, in this state of things, the spectator quickly ascends to a higher station, T, whose visible horizon is at D, the hull comes again in sight; and when he descends again he loses it. The ship still receding, the lower sails seem to sink below the water, as at d, and at length the whole disappears : while yet the distinctness with which the last portion of the sail d is seen is such as to satisfy us that were it not for the interposed segment of the sea, ABCDE, the distance TE is not so great as to have prevented an equally perfect view of the whole.

(27.) In this manner, therefore, if we could measure the heights and exact distance of two stations which could barely be discerned from each other over the edge of the horizon, we could ascertain the actual size of the earth itself; and, in fact, were it not for the effect of refraction, by which we are enabled to see in some small degree round the interposed segment (as will be hereafter explained), this would be a tolerably good method of ascertaining it. Suppose A and B to be two eminences, whose perpendicular heights Aa and Bb (which, for simplicity, we will suppose to be exactly equal) are known, as well as their exact horizontal interval a Db, by measurement; then it is clear that D, the visible horizon of both, will lie just half-way