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CHAP. I.

DISTANCE OF THE STARS.

51

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 nearly 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 under-rated.

(73.) 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 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, which, like the vanishing point in perspective to which all parallel lines in a picture appear to converge, is, in fact, the vanishing line to which all planes parallel to the horizon offer a similar appearance of ultimate convergence in the great panorama of nature.

(74.) The two planes just described are termed, in astronomy, the sensible and rational horizon of the observer's station; and the great circle in the heavens which marks their vanishing line, is also spoken of as a circle of the sphere, under the name of the celestial horizon, or simply the horizon.

From what has been said (art. 72.) 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 the same manner as that of a corresponding spectator on the surface is by his sensible

CHAP. I.

DIURNAL ROTATION OF THE EARTH.

53

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.

(75.) 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 66 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. Meanwhile, it will be proper to define a variety of terms which will be continually employed hereafter.

(77.) DEFINITION 1. The axis of the earth is that diameter about which it revolves, with a uniform motion, from west to east; performing one revolution in the interval which elapses between any star leaving a certain point in the heavens, and returning to the same point again.

(78.) DEF. 2. The poles of the earth are the points where its axis meets its surface. The North Pole is that nearest to Europe; the South Pole that most remote from it.

(79.) DEF. 3. The sphere of the heavens, or the sphere of the stars, is an imaginary spherical surface, of infinite radius, and having the centre of the earth, or, which comes to the very same thing, the eye of any spectator on its surface, for its centre. Every point in this sphere may be regarded as the vanishing point of a system of lines parallel to that radius of the sphere which passes through it, seen in perspective from the earth; and any great circle on it, as the vanishing line of a system of planes parallel to its own. This mode of conceiving such points and circles has great advantages in a variety of cases.

(80.) DEF. 4. The zenith and nadir * are the two points of the sphere of the heavens, vertically over a spectator's head, and vertically under his feet; they are, therefore, the vanishing points of all lines mathematically parallel to the direction of a plumb-line at his station. The plumb-line itself is, at every point of the earth, perpendicular to its spherical surface: at no two stations, therefore, can the actual directions of

From Arabic words. Nadir corresponds evidently to the German nieder (down).

CHAP. I.

DEFINITIONS.

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two plumb-lines be regarded as mathematically parallel. They converge towards the centre of the earth: but for very small intervals (as in the area of a building — in one and the same town, &c.) the difference from exact parallelism is so small, that it may be practically disregarded. An interval of a mile corresponds to a convergence of plumb-lines amounting to about 1 minute. The zenith and nadir are the poles of the celestial horizon; that is to say, points 90° distant from every point in it. The celestial horizon itself is the vanishing line of a system of planes parallel to the sensible and rational horizon.

(81.) DEF. 5. Vertical circles of the sphere are great circles passing through the zenith and nadir, or great circles perpendicular to the horizon. On these are measured the altitudes of objects above the horizon -the complements to which are their zenith distances.

(82.) DEF. 6. The poles of the heavens are the points of the sphere to which the earth's axis is directed; or the vanishing points of all lines parallel thereto.

(83.) DEF. 7. The earth's equator is a great circle on its surface, equidistant from its poles, dividing it into two hemispheres a northern and a southern; in the midst of which are situated the respective poles of the earth of those names. The plane of the equator is, therefore, a plane perpendicular to the earth's axis, and passing through its centre. The celestial equator is a great circle of the heavens, marked out by the indefinite extension of the plane of the terrestrial, and is the vanishing line of all planes parallel to it. This circle is called by astronomers the equinoctial.

(84.) DEF. 8. The terrestrial meridian of a station on the earth's surface is a great circle passing through both the poles and through the place. When its plane is prolonged to the sphere of the heavens, it marks out the celestial meridian of a spectator stationed at that place. When we speak of the meridian of a

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