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 A S, but in that of As, a tangent to the curve S D C B A, at A. But because the curve described by the refracted ray is concave downwards, the tangent A s will lie above A S, 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, S A C', 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, A H, of the spectator, becomes visible to him, as if it stood at p, by the refracted ray P q r t 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, H A S, is raised in appearance above its true place, is, unfortunately, a very difficult subject of physical inquiry, 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 effected 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 inquiries, 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 similar cases, with referring the reader to works especially destined to furnish these useful aids * From an Arabic word of this signification. See this term technically defined in Chap. II. to calculation. It is, however, desirable that he should bear in mind the following general notions of its amount, and law of variations. (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, at least if the air be tranquil. 2dly. In descending from the zenith to the horizon, the refraction continually increases. Objects near the horizon appear more elevated by it above their true directions than those at 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' (more 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. 5thly. That when the barometer is higher than its average or mean state, the amount of refraction is greater than its mean amount; when lower, less: and, 6thly. That in one and the same state of the barometer the refraction is greater, the colder the air. The variation, owing to these two causes, from its mean amount (at temp. 55°, pressure 30 inches), are about one 420th part of that amount for each degree of the thermometer of Fahrenheit, and one 300th for each tenth of an inch in the height of the barometer. (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 con tinues 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 the actual material atoms of the air itself. To understand how this takes place, we must recollect, that it is not only by the direct light of a luminous object that we see, but that whatever portion of its light which would not otherwise reach our eyes is intercepted in its course, and thrown back, or laterally, upon us, becomes to us a means of illumination. Such reflective obstacles always exist floating in the air. The whole course of a sunbeam penetrating through the chink of a window-shutter into a dark room is visible as a bright line in the air: and even if it be stifled, or let out through an opposite crevice, the light scattered through the apartment from this source is sufficient to prevent entire darkness in the room. The luminous lines occasionally seen in the air, in a sky full of partially broken clouds, which the vulgar term "the sun drawing water," are similarly caused. They are sunbeams, through apertures in clouds, partially intercepted and reflected on the dust and vapours of the air below. Thus it is with those solar rays which, after the sun is itself concealed by the convexity of the earth, continue to traverse the higher regions of the atmosphere above our heads, and pass through and out of it, without directly striking on the earth at all. Some portion of them is intercepted and reflected by the floating particles above mentioned, and thrown back, or laterally, so as to reach us, and afford us that secondary illumination, which is twilight. The course of such rays will be immediately understood from the annexed figure, in which A B C D is the earth; A a point on its surface, where the sun S is in the act of setting; its last lower ray S A M just grazing the surface at A, while its superior rays S N, S O, traverse the atmosphere above A without striking the earth, leaving it finally at the points P Q R, after being more or less bent in passing through it, the lower most, the higher less, and that which, like S R O, merely grazes the exterior limit of the atmosphere, not at all. Let us consider several points, A, B, C, D, each more remote than the last from A, and each more deeply involved in the earth's shadow, which occupies the whole space from A beneath the line A M. Now, A just receives the sun's last direct ray, and, besides, is illuminated by the whole reflective atmosphere PQRT. It therefore receives twilight from the whole sky. The point B, to which the sun has set, receives no direct solar light, nor any, direct or reflected, from all that part of its visible atmosphere which is below A P M; but from the lenticular portion P R x, which is traversed by the sun's rays, and which lies above the visible horizon B R of B, it receives a twilight, which is strongest at R, the point immediately below which the sun is, and fades away gradually towards P, as the luminous part of the atmosphere thins off. At C, only the last or thinnest portion, P Q z of the lenticular segment thus illuminated, lies above the horizon, C Q, of that place; here, then, the twilight is feeble, and confined to a small space in and near the horizon, which the sun has quitted, while at D the twilight has ceased altogether. (45.) When the sun is above the horizon, it illuminates the atmosphere and clouds, and these again disperse and scatter a portion of its light in all directions, so as to send some of its rays to every exposed point, from every point of the sky. The generally diffused light, therefore, which we enjoy in the daytime, is a phenomenon originating in the very same causes as the twilight. Were it not for the reflective and scattering power of the atmosphere, no objects would be visible to us out of direct sunshine; every shadow of a passing cloud would be pitchy darkness; the stars would be visible all day, and every apartment, into which the sun had not direct admission, would be involved in nocturnal obscurity. This scattering action of the atmosphere on the solar light, it should be observed, is increased by the irregularity of temperature caused by the same luminary in its different parts, which, during the day |