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all points of the earth's surface; that is to say, on the great scale, and leaving out of consideration temporary and local causes of derangement, such as winds, and great fluctuations, of the nature of waves, which prevail in it to an immense extent: in other words, that the law of diminution of the air's density as we recede upwards from the level of the sea is the same in every column into which we may conceive it divided, or from whatever point of the surface we may set out. It may therefore be considered as consisting of successively superposed strata or layers, each of the form of a spherical shell, concentric with the general surface of the sea and land, and each of which is rarer, or specifically lighter, than that immediately beneath it; and denser, or specifically heavier, than that immediately above it. This kind of distribution of its ponderable mass is necessitated by the laws of the equilibrium of fluids, whose results barometric observations demonstrate to be in perfect accordance with experience.

It must be observed, however, that with this distribution of its strata the inequalities of mountains and valleys have no concern : these exercise no more influence in modifying their general spherical figure than the inequalities at the bottom of the sea interfere with the general sphericity of its surface.

(38.) It is the power which air possesses, in common with all transparent media, of refracting the rays of light, or bending them out of their straight course, which renders a knowledge of the constitution of the atmosphere important to the astronomer. Owing to this property, objects seen obliquely through it appear otherwise situ. ated than they would to the same spectator, had the atmosphere no existence: it thus produces a false impression respecting their places, which must be rectified by ascertaining the amount and direction of the displacement so apparently produced on each, before we can come at a knowledge of the true directions in which they are situated from us at any assigned moment.

(39.) Suppose a spectator placed at A, any point

of the earth's surface KAk; and let Ll, Mm, Nn, represent the successive strata or layers, of decreasing density, into which we may conceive the atmosphere to be divided, and which are spherical surfaces concentric with Kk, the earth's surface. Let S represent a star, or other heavenly body, beyond the utmost limit of the atmosphere; then, if the air were away, the spectator would see it in the direction of the straight line AS. But, in reality, when the ray of light SA reaches the atmosphere, suppose at d, it will, by the laws of optics, begin to bend downwards, and take a more inclined direction, as dc. This bending will at first be imperceptible, owing to the

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extreme tenuity of the uppermost strata ; but as it advances downwards, the strata continually increasing in density, it will continually undergo greater and greater refraction in the same direction; and thus, instead of pursuing the straight line S dA, it will describe a curve sdcba, continually more and more concave down. wards, and will reach the earth, not at A, but at a certain point a, nearer to S. This ray, consequently, will not reach the spectator's eye. The ray by which he will see the star is, therefore, not SdA, but another ray which, had there been no atmosphere would have struck the earth at K, a point behind the spectator; but which, being bent by the air into the curve SDCBA, actually strikes on A. Now, it is a law of optics, that an object is seen in the direction which the visual ray has at the instant of arriving at the eye, without regard to what may have been otherwise its course between the object and the eye. Hence the star S will be seen, not in the direction AS, but in that of As, a tangent to the curve SDCBA, at A. But because the curve described by the refracted ray is concave downwards, the tangent As will lie above AS, the unrefracted ray: consequently the object S will appear more elevated above the horizon A H,when seen through the refracting atmosphere, than it would appear were there no such atmosphere. Since, however, the disposition of the strata is the same in all directions around A, the visual ray will not be made to deviate laterally, but will remain constantly in the same vertical plane, SAC', passing through the eye, the object, and the earth's centre.

(40.) The effect of the air's refraction, then, is to raise all the heavenly bodies higher above the horizon in appearance than they are in reality. Any such body, situated actually in the true horizon, will appear above it, or will have some certain apparent altitude (as it is called). Nay, even some of those actually below the horizon, and which would therefore be invisible but for the effect of refraction, are, by that effect, raised above it and brought into sight. Thus, the sun, when situated at P below the true horizon, AH, of the spectator, becomes visible to him, as if it stood at p, by the refracted ray Port A, to which A p is a tangent.

(41.) The exact estimation of the amount of atmospheric refraction, or the strict determination of the angle S As, by which a celestial object at any assigned altitude, HAS, is raised in appearance above its true place, is, unfortunately, a very difficult subject of physical enquiry, and one on which geometers (from whom alone we can look for any information on the subject) are not yet entirely agreed. The difficulty arises from this, that the density of any stratum of air (on which its refracting power depends) is affected not merely by the superincumbent pressure, but also by its temperature or degree of heat. Now, although we know that as we recede from the earth's surface the temperature of the air is constantly diminishing, yet the law, or amount of this diminution at different heights, is not yet fully ascertained. Moreover, the refracting power of air is perceptibly affected by its moisture; and this, too, is not the same in every part of an aërial column; neither are we acquainted with the laws of its distribution. The consequence of our ignorance on these points is to introduce a corresponding degree of uncertainty into the determination of the amount of refraction, which affects, to a certain appreciable extent, our knowledge of several of the most important data of astronomy. The uncertainty thus induced is, however, confined within such very narrow limits as to be no cause of embarrassment, except in the most delicate enquiries, and to call for no further allusion in a treatise like the present.

(42.) A “ Table of Refractions," as it is called, or a statement of the amount of apparent displacement arising from this cause, at all altitudes, or in every situation of a heavenly body, from the horizon to the zenith*, or point of the sky vertically above the spectator, and, under all the circumstances in which astronomical observations are usually performed which may influence the result, is one of the most important and indispensable of all astronomical tables, since it is only by the use of such a table we are enabled to get rid of an illusion which must otherwise pervert all our notions respecting the celestial motions. Such have been, accordingly, constructed with great care, and are to be found in every collection of astronomical tables. Our design, in the present treatise, will not admit of the introduction of tables; and we must, therefore, content ourselves here, and in si. milar cases, with referring the reader to works especially destined to furnish these useful aids to calculation. It is, however, desirable that he should bear in mind the following general notions of its amount, and law of variation.

* From an Arabic word of this signification.

+ Vide “ Requisite Tables to be used with the Nautical Almanac." See also Nautical Almanac for 1833, Dr. Pearson's Astronomical Tables, and Mr. Baily's Astronomical Tables and Formulæ,

(43.) 1st. In the zenith there is no refraction ; a celestial object, situated vertically over head, is seen in its true direction, as if there were no atmosphere.

2dly. In descending from the zenith to the horizon, the refraction continually increases ; objects near the horizon appearing more elevated by it above their true directions than those at a high altitude.

3dly. The rate of its increase is nearly in proportion to the tangent of the apparent angular distance of the object from the zenith. But this rule, which is not far from the truth, at moderate zenith distances, ceases to give correct results in the vicinity of the horizon, where the law becomes much more complicated in its expression.

4thly. The average amount of refraction, for an object half-way between the zenith and horizon, or at an apparent altitude of 45°, is about 1' (inore exactly 57"), a quantity hardly sensible to the naked eye; but at the visible horizon it amounts to no less a quantity than 33', which is rather more than the greatest apparent diameter of either the sun or the moon. Hence it follows, that when we see the lower edge of the sun or moon just apparently resting on the horizon, its whole disk is in reality below it, and would be entirely out of sight and concealed by the convexity of the earth but for the bending round it, which the rays of light have undergone in their passage through the air, as alluded to in art. 40.

(44.) It follows from this, that one obvious effect of refraction must be to shorten the duration of night and darkness, by actually prolonging the stay of the sun and moon above the horizon. But even after they are set, the influence of the atmosphere still continues to send us a portion of their light; not, indeed, by direct transmission, but by reflection upon the vapours, and minute solid particles, which float in it, and, perhaps, also on

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