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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 semidiameter 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 phenomena, 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

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render a rational account of the appearances they successively present, that is to say, 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 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 thein, — 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 objectivehaving 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 seen 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 a considerable effort of imagination necessary to pass from the sensible to the real form.

(79.) Still, preparatory to this ultimate step, it is first necessary that the spectator should free or clear the appearances from the disturbing influence of his own change of place. And this he can always do by the following general rule or proposition:

The relative motion of two bodies is the same as if either of them were at rest, and all its motion communicated to the other in an opposite direction. *

Hence, if two bodies move alike, they will, when seen from each other (without reference to other near bodies, but only to the starry sphere), appear at rest. Hence, also, if the absolute motions of two bodies be uniform and rectilinear, their relative motion is so also.

(80.) The stars are so distant, that as we have seen it is absolutely indifferent from what point of the earth's surface we view them. Their configurations inter se are identically the same. It is otherwise with the sun, moon, and planets, which are near enough (especially the moon) to be parallactically displaced by change of station from place to place on one globe. In order that astronomers residing on different points of the earth's surface should be able to compare their observations with effect, it is necessary that they should clearly understand and take account of this effect of the difference of their stations on the appearance of the outward universe as seen from each. As an exterior object seen from one would appear to have shifted its place were the spectator suddenly transported to the other, so two spectators, viewing it from the two stations at the same instant, do not see it in the same direction. Hence arises a necessity for the adoption of a conventional centre of reference, or imaginary station of observation common to all the world, to which each observer, wherever situated, may refer (or, as it is called, reduce) his observations, by calculating and allowing for the effect of his local position with respect to that common centre (supposing him to possess the necessary data). If there were only two observers, in fixed stations, one might agree to refer his observations to the other station; but, as every locality on the globe may be a station of observation, it is far more convenient and natural to fix upon a point equally related to all, as the common point of reference; and this can be no other than the centre of the globe itself. The parallactic change of apparent place which would arise in an object, could any observer suddenly transport himself to the centre of the earth, is evidently the angle CSP, subtended at the object s by that radius CP of the earth which joins its centre and the place P of observation.

* This proposition is equivalent to the following, which precisely meets the case proposed, but requires somewhat more thought for its clear apprehension than can perhaps be expected from a beginner :-

Prop, — If two bodies, A and B, be in motion independently of each other, the motion which В seen from A would appear to have if A were at rest is the same with that which it would appear to have, A being in motion, if, in addition to its own motion, a motion equal to d's and in the same direction were communicated to it.

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