find that he has both the centres of diurnal motion in his horizon, occupying opposite points, the northern Pole having been depressed, and the southern raised; so that, in this geographical position, the diurnal rotation of the heavens will appear to him to be performed about a horizontal axis, every star describing half its diurnal circle above and half beneath his horizon, remaining alternately visible for twelve hours, and concealed during the same interval. In this situation, no part of the heavens is concealed from his successive view. In a night of twelve hours (supposing such a continuance of darkness possible at the equator) the whole sphere will have passed in review over him the whole hemisphere with which he began his night's observation will have been carried down beneath him, and the entire opposite one brought up from below.

(65.) If he pass the equator, and travel still farther southwards, the southern pole of the heavens will become elevated above his horizon, and the northern will sink below it; and the more, the farther he advances southwards; and when arrived at a station as far to the south of the equator as that from which he started was to the north, he will find the whole phenomena of the heavens reversed. The stars which at his original station described their whole diurnal circles above his horizon, and never set, now describe them entirely below it, and never rise, but remain constantly invisible to him; and, vice versa, those stars which at his former station he never saw, he will now never cease to see.

(66.) Finally, if, instead of advancing southwards from his first station, he travel northwards, he will observe the northern pole of the heavens to become more elevated above his horizon, and the southern more depressed below it. In consequence, his hemisphere will present a less variety of stars, because a greater proportion of the whole surface of the heavens remains constantly visible or constantly invisible: the circle described by each star, too, becomes more nearly parallel to the

CHAP. I.

POLES OF THE EARTH.

47

horizon; and, in short, every appearance leads to suppose that could he travel far enough to the north, he would at length attain a point vertically under the northern pole of the heavens, at which none of the stars would either rise or set, but each would circulate round the horizon in circles parallel to it. Many endeavours have been made to reach this point, which is called the north pole of the earth, but hitherto without success; a barrier of almost insurmountable difficulty being presented by the increasing rigour of the climate: but a very near approach to it has been made; and the phenomena of those regions, though not precisely such as we have described as what must subsist at the pole itself, have proved to be in exact correspondence with its near proximity. A similar remark applies to the south pole of the earth, which, however, is more unapproachable, or, at least, has been less nearly approached, than the north.

(67.) The above is an account of the phenomena of the dïurnal motion of the stars, as modified by dif ferent geographical situations, not grounded on any speculation, but actually observed and recorded by travellers and voyagers. It is, however, in complete accordance with the hypothesis of a rotation of the earth round a fixed axis. In order to show this, however, it will be necessary to premise a few observations on the appearances presented by an assemblage of remote objects, when viewed from different parts of a small and circumscribed station.

(68.) Imagine a landscape, in which a great multitude of objects are placed at every variety of distance from the beholder. If he shift his point of view, though but for a few paces, he will perceive a very great change in the apparent positions of the nearer objects, both with respect to himself and to each other. If he advance northwards, for instance, near objects on his right and left, which were, therefore, to the east and west of his original station, will be left behind him, and appear to have receded southwards; some, which covered

each other at first, will appear to separate, and others to approach, and perhaps conceal each other. Remote objects, on the contrary, will exhibit no such great and remarkable changes of relative position. An object to the east of his original station, at a mile or two distance, will

still be referred by him to the east point of his horizon, with hardly any perceptible deviation. The reason of this is, that the position of every object is referred by us to the surface of an imaginary sphere of an indefinite radius, having our eye for its centre; and, as we advance in any direction, A B, carrying this imaginary sphere along with us, the visual rays A P, A Q, by which objects are referred to its surface (at C, for instance), shift their positions with respect to the line in which we move, A B, which serves as an axis or line of reference, and assume new positions, BP p, BQ q, revolving round their respective objects as centres. Their intersections, therefore, p, q, with our visual sphere, will appear to recede on its surface, but with different degrees of angular velocity in proportion to their proximity; the same distance of advance A B subtending a greater angle, APB = c Pp, at the near object P than at the remote one Q.

(69) This apparent angular motion of an object on our sphere of vision*, arising from a change of our

*The ideal sphere without us, to which we refer the places of objects, and which we carry along with us wherever we go, is no doubt intimately connected by association, if not entirely dependent on that obscure perception of sensation in the retinæ of our eyes, of which, even when closed and unexcited, we cannot entirely divest them. We have a real spherical surface

CHAP. I.

DISTANCE OF THE STARS.

49

point of view, is called parallax, and it is always expressed by the angle B A P subtended at the object P by a line joining the two points of view A B under consideration. For it is evident that the difference of angular position of P, with respect to the invariable direction A B D, when viewed from A and from B, is the difference of the two angles D BP and DA P; now, DB P being the exterior angle of the triangle, A B P is equal to the sum of the interior and opposite, DBP = DAP + APB, whence D B P—DAP=A P B.

(70.) It follows from this, that the amount of parallactic motion arising from any given change of cur point of view is, cæteris paribus, less, as the distance of an object viewed is greater; and when that distance is extremely great in comparison with the change in our point of view, the parallax becomes insensible; or, in other words, objects do not appear to vary in situation at all. It is on this principle, that in alpine regions visited for the first time we are surprised and confounded at the little progress we appear to make by a considerable change of place. An hour's walk, for instance, produces but a small parallactic change in the relative situations of the vast and distant masses which surround us. Whether we walk round a circle of a hundred yards in diameter, or merely turn ourselves round in its centre, the distant panorama presents almost exactly the same aspect, we hardly seem to have changed our point of view.

(71.) Whatever notion, in other respects, we may form of the stars, it is quite clear they must be immensely distant. Were it not so, the apparent angular

within our eyes, the seat of sensation and vision, corresponding, point for point, to the external sphere. On this the stars, &c. are really mapped down, as we have supposed them in the text to be, on the imaginary concave of the heavens. When the whole surface of the retina is excited by light, habit leads us to associate it with the idea of a real surface existing without us. Thus we become impressed with the notion of a sky and a heaven, but the concave surface of the retina itself is the true seat of all visible angular dimension and angular motion. The substitution of the retina for the heavens would be awkward and inconvenient in language, but it may always be mentally made. (See Schiller's pretty enigma on the eye in his Turandot.)

E

interval between any two of them seen over head would be much greater than when seen near the horizon, and the constellations, instead of preserving the same appearances and dimensions during their whole diurnal course, would appear to enlarge as they rise higher in the sky, as we see a small cloud in the horizon swell into a great overshadowing canopy when drifted by the wind across our zenith, or as may be seen in the annexed figure, where a b, A B, ab, are three different positions

H

B

a

of the same stars, as they would, if near the earth, be seen from a spectator S, under the visual angles a S b, A S B. No such change of apparent dimension, however, is observed. The nicest measurements of the apparent angular distance of any two stars inter se, taken in any parts of their diurnal course, (after allowing for the unequal effects of refraction, or when taken at such times that this cause of distortion shall act equally on both,) manifest not the slightest perceptible variation. Not only this, but at whatever point of the earth's surface the measurement is performed, the results are absolutely identical. No instruments ever yet invented by man are delicate enough to indicate, by an increase or diminution of the angle subtended, that one point of the earth is nearer to or further from the stars than another.

(72.) The necessary conclusion from this is, that the dimensions of the earth, large as it is, are comparatively nothing, absolutely imperceptible, when compared with the interval which separates the stars from the earth. If an observer walk round a circle not more