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 APB 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 ABD, when viewed from A and from B, is the difference of the two angles DBP and DAP; now, DBP being the exterior angle of the triangle ABP, is equal to the sum of the interior and opposite, DBP - DAP + APB, whence DBP DAP : APB.

=

(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 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 scem to have changed our point of view.

may form of the stars, it Were it not so, the appa

(72.) Whatever notion, in other respects, we is quite clear they must be immensely distant. rent angular 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 ab, AB, 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, ASB. 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 carth, 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, subtended 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 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

Fig. 9.

B

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 be imperceptible; and, reciprocally, an object of the earth's size, placed at the distance of the stars, would be equally undiscernible. If, therefore, at the point on which a spectator stands, we draw a plane touching the globe, and prolong it in imagination till it attain the region of the stars, and through the centre of the earth conceive another plane parallel to the former, and co-extensive with it, to pass; these, although separated throughout their whole extent by the same interval, viz., a semi-diameter of the earth, will yet, on account of the vast distance at which that interval is seen, be confounded together, and undistinguishable from each other in the region of the stars, when viewed by a spectator on the earth. The zone they there include will be of evanescent breadth to his eye, and will only mark out a great circle in the heavens, one and the same for both the stations. This great circle, when spoken of as a circle of the sphere, is called the celestial horizon or simply the horizon, and the two planes just described are also spoken of as the sensible and the rational horizon of the observer's station.

(75.) From what has been said (art. 73) of the distance of the stars, it follows, that if we suppose a spectator at the centre of the earth to have his view bounded by the rational horizon, in exactly the same manner as that of a corresponding spectator on the surface is by his sensible horizon, the two observers will see the same stars in the same relative situations, each beholding that entire hemisphere of the heavens which is above the celestial horizon, corresponding to their common zenith. Now, so far as

appearances go, it is clearly the same thing whether the heavens, that is, all space, with its contents, revolve round a spectator at rest in the earth's centre, or whether that spectator simply turn round in the opposite direction in his place, and view them in succession. The aspect of the heavens, at every instant, as referred to his horizon (which must be supposed to turn with him), will be the same in both suppositions. And since, as has been shown, appearances are also, so far as the stars are concerned, the same to a spectator on the surface as to one at the centre, it follows that, whether we suppose, the heavens to revolve without the earth, or the earth within the heavens, in the opposite direction, the diurnal phenomenon, to all its inhabitants, will be no way different.

(76.) The Copernican astronomy adopts the latter as the true explanation of these phenomena, avoiding thereby the necessity of otherwise resorting to the cumbrous mechanism of a solid but invisible sphere, to which the stars must be supposed attached, in order that they may be carried round the earth without derangement of their relative situations inter se. Such a contrivance would, indeed, suffice to explain the diurnal revolution of the stars, so as to "save appearances;" but the movements of the sun and moon, as well as those of the planets, are incompatible with such a supposition, as will appear when we come to treat of these bodies. On the other hand, that a spherical mass of moderate dimensions (or, rather, when compared with the surrounding and visible universe, of evanescent magnitude), held by no tie, and free to move and to revolve, should do so, in conformity with those general laws which, so far as we know, regulate the motions of all material bodies, is so far from being a postulate difficult to be conceded, that the wonder would rather be should the fact prove otherwise. As a postulate, therefore, we shall henceforth regard it; and as, in the progress of our work, analogies offer themselves in its support from what we observe of other celestial bodies, we shall not fail to point them out to the reader's notice.

(77.) The earth's rotation on its axis so admitted, explaining, as it evidently does, the apparent motion of the stars in a completely satisfactory manner, prepares us for the further admission of its motion, bodily, in space, should such a motion enable us to explain, in a manner equally so, the apparently complex and enigmatical motions of the sun, moon, and planets. The Copernican astronomy adopts this idea in its full extent, ascribing to the earth, in addition to its motion of rotation about an axis, also one of translation or transference through space, in such a course or orbit, and so regulated in direction and celerity, as, taken in conjunction with the motions of the other bodies of the universe, shall render a ration

that is to say,

al account of the appearances they successively present, an account of which the several parts, postulates, propositions, deductions, intelligibly cohere, without contradicting each other or the nature of things as concluded from experience. In this view of the Copernican doctrine it is rather a geometrical conception than a physical theory, inasmuch as it simply assumes the requisite motions, without attempting to explain their mechanical origin, or assign them any dependence on physical causes. The Newtonian theory of gravitation supplies this deficiency, and, by showing that all the motions required by the Copernican conception must, and that no others can, result from a single, intelligible, and very simple dynamical law, has given a degree of certainty to this conception, as a matter of fact, which attaches to no other creation of the human mind.

(78.) To understand this conception in its further developments, the reader must bear steadily in mind the distinction between relative and absolute motion. Nothing is easier to perceive than that, if a spectator at rest view a certain number of moving objects, they will group and arrange themselves to his eye, at each successive moment, in a very different way from what they would do were he in active motion among them,- if he formed one of them, for instance, and joined in their dance. This is evident from what has been said before of parallactic motion; but it will be asked, How is such a spectator to disentangle from each other the two parts of the apparent motions of these external objects, that which arises from the effect of his own change of place, and which is therefore only apparent (or, as a German metaphysician would say, subjective- having reference only to him as perceiving it), and that which is real (or objective-having a positive existence, whether perceived by him or not)? By what rule is he to ascertain, from the appearances presented to him while himself in motion, what would be the appearances were he at rest? It by no means follows, indeed, that he would even then at once obtain a clear conception of all the motions of all the objects. The appearances so presented to him would have still something subjective about them. They would be still appearances, not geometrical realities. They would still have a reference to the point of view, which might be very unfavourably situated (as, indeed, is the case in our system) for affording a clear notion of the real movement of each object. No geometrical figure, or curve, is scen by the eye as it is conceived by the mind to exist in reality. The laws of perspective interfere and alter the apparent directions and foreshorten the dimensions of its several parts. If the spectator be unfavourably situated, as, for instance, nearly in the plane of the figure (which is the case we have to deal with), they may do so to such an extent, as to make