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 diurnal motion of the stars, as modified by different 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 parallactic motion in general, and on the appearances presented by an assemblage of remote objects, when viewed from different parts of a small and circumscribed station.

(68.) It has been shown (art. 16.) that a spectator in smooth motion, and surrounded by, and forming part of, a great system partaking of the same motion, is unconscious of his own movement, and transfers it in idea to objects external and unconnected, in a contrary direction; those which he leaves behind appearing to recede from, and those which he advances towards to approach, him. Not only, however, do external objects at rest appear in motion generally, with respect to ourselves when we are in motion among them, but they appear to move one among the other they shift their relative apparent places. Let any one travelling rapidly along a high road fix his eye steadily on any object, but at the same time not entirely withdraw his attention from the general landscape, he will see, or think he sees, the whole landscape thrown into rotation, and moving round that object as a centre; all objects between it and himself appearing to move backwards, or the contrary way

to his own motion; and all beyond it, forwards, or in the direction in which he moves: but let him withdraw his eye from that object, and fix it on another, a nearer one, for instance, immediately the appearance of rotation shifts also, and the apparent centre about which this illusive circulation is performed is transferred to the new object, which, for the moment, appears to rest. This apparent change of situation of objects with respect to one another, arising from a motion of the spectator, is called a parallactic motion. To see the reason of it we must consider 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, carry

D

B

A

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ing this imaginary sphere along with us, the visual rays A P, AQ, by which objects are referred to its surface (at C, for instance), shift their positions with respect to the line in whi h we move, A B, which serves as an axis or line of reference, and assume new positions, B Pp, BQq, 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 P p, at the near object P than at the remote one Q.

(69.) A consequence of the familiar appearance we have adduced in illustration of these principles is worth noticing, as we shall have occasion to refer to it hereafter. We observe that every object nearer to us than that on which our eye is fixed appears to recede, and those farther from us to advance in relation to one another. If then we did not know, or could not judge by any other appearances, which of two objects were nearer to us, this apparent advance or recess of

one of them, when the eye is kept steadily fixed on the other, would furnish a criterion. In a dark night, for instance, when all intermediate objects are unseen, the apparent relative movement of two lights which we are assured are themselves fixed, will decide as to their relative proximities. That which seems to advance with us and gain upon the other, or leave it behind it, is the farthest from us.

(70.) The apparent angular motion of an object, arising from a change of our point of view, is called in general parallax, and it is always expressed by the angle A P B subtended at the object P (see fig. of art. 68.) 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 DB P and D A P; now, D B P being the exterior angle of the triangle A B P, is equal to the sum of the interior and opposite, D B P = DAP AP B, whence DBP-DAP AP B.

=

(71.) It follows from what has been said that the amount of parallactic motion arising from any given change of our 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 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.

us.

(72.) 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 interval between any two of them seen over head would be much greater than

E

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 ab, A B, ab, are three different positions of the same stars, as they would, if near the earth, be seen from

a spectator S, under the visual angles a Sb, AS 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.

(73.) 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 than a few yards in diameter, and from different points in its circumference measure with a sextant or other more exact instrument adapted for the purpose, the angles PAQ, PBQ, PCQ, sub

tended at those stations by two well-defined points in his visible horizon, PQ, he will at once be advertised, by the difference of the results, of his change of distance from them arising from his change of place, although that difference may be so small as to produce no change in their general aspect to his unassisted sight. This is one of the innumerable instances where accurate measurement obtained by instrumental means places us in a totally different situation in respect to matters of fact, and conclusions thence deducible, from what we should

B

hold, were we to rely in all cases on the mere judgment of the eye. To so great a nicety have such observations been carried by the aid of an instrument called a theodolite, that a circle of the diameter above mentioned may thus be rendered sensible, may thus be detected to have a size, and an ascertainable place, by reference to objects distant by fully 100,000 times its own dimensions. Observations, differing, it is true, somewhat in method, but identical in principle, and executed with quite as much exactness, have been applied to the stars, and with a result such as has been already stated. Hence it follows, incontrovertibly, that the distance of the stars from the earth cannot be so small as 100,000 of the earth's diameters. It is, indeed, incomparably greater; for we shall hereafter find it fully demonstrated that the distance just named, immense as it may appear, is yet much underrated.

(74.) From such a distance, to a spectator with our faculties, and furnished with our instruments, the earth would