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.

(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' (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.

(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

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 SA M just grazing the surface at A, while its superior rays SN, SO, traverse the atmosphere above A without striking the earth, leaving it finally at the points PQR, after being more or less bent in passing through it, the lower most, the bigher less, and that which, like SRO, 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

S

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 BR 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, PQ of the lenticular segment, thus illuminated, lies above the horizon, CQ, 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 greatly increased by the irregularity of temperature caused by the same luminary in its different parts, which, during the daytime, throws it into a constant state of undulation, and, by thus bringing together masses of air of very unequal temperatures, produces partial reflections and refractions at their common boundaries, by which much light is turned aside from the direct course, and diverted to the purposes of general illumination.

(46.) From the explanation we have given, in arts. 39. and 40., of the nature of atmospheric refraction, and the mode in which it is produced in the progress of a ray of light through successive strata, or layers, of the atmosphere, it will be evident, that whenever a ray passes obliquely from a higher level to a lower one, or vice versâ, its course is not rectilinear, but concave downwards; and of course any object seen by means of such a ray, must appear deviated from its true place, whether that object be, like the celestial bodies, entirely beyond the atmosphere, or, like the summits of mountains, seen from the plains, or other terrestrial stations, at different levels, seen from each other, immersed in it. Every difference of level, accompanied, as it must be, with a difference of density in the aërial strata, must also have, corresponding to it, a certain amount of refraction; less, indeed, than what would be produced by the whole atmosphere, but still often of very appreciable, and even considerable, amount. This refraction between terrestrial stations is termed terrestrial refraction, to distinguish it from that total effect which is only produced on celestial objects, or

D

such as are beyond the atmosphere, and which is called celestial or astronomical refraction.

(47.) Another effect of refraction is to distort the visible forms and proportions of objects seen near the horizon. The sun, for instance, which, at a consider able altitude, always appears round, assumes, as it approaches the horizon, a flattened or oval outline; its horizontal diameter being visibly greater than that in a vertical direction. When very near the horizon, this flattening is evidently more considerable on the lower side than on the upper; so that the apparent form is neither circular nor elliptic, but a species of oval, which deviates more from a circle below than above. This singular effect, which any one may notice in a fine sunset, arises from the rapid rate at which the refraction increases in approaching the horizon. Were every visible point in the sun's circumference equally raised by refraction, it would still appear circular, though displaced: but the lower portions being more raised than the upper, the vertical diameter is thereby shortened, while the two extremities of its horizontal diameter are equally raised, and in parallel directions, so that its apparent length remains the same. The dilated size (generally) of the sun or moon, when seen near the horizon, beyond what they appear to have when high up in the sky, has nothing to do with refraction. It is an illusion of the judgment, arising from the terrestrial objects interposed, or placed in close comparison with them. In that situation we view and judge of them as we do of terrestrial objects—in detail, and with an acquired habit of attention to parts. Aloft we have no associations to guide us, and their insulation in the expanse of sky leads us rather to undervalue than to over-rate their apparent magnitudes. Actual measurement with a proper instrument corrects our error, without, however, dispelling our illusion. By this we learn, that the sun, when just on the horizon, subtends at our eyes almost exactly the same, and the moon a materially less angle, than when