600 LIGHT homogeneity in a refracting medium is capable of producing phe nomena of the most extraordinary character. Mirage. It is difficult to ascertain exactly what is the condition of the atmosphere when multiple images, mirage, &c., are seen ; and it is obvious from the remarks and illustrations already given that many very different arrangements will produce sensibly the same result to a spectator in a given position. Comparison of the appearances seen simultaneously by a great number of scattered observers is the only way in which we can expect to obtain definite information on such a point. But the following investigation suggests the general nature of the explanation. If we suppose the refractive index of the air to depend only upon the vertical height above the earth s surface, rays will all travel in vertical planes, and Hamilton s equation (neglecting the curva ture of the earth s surface) takes the very simple form Scatter ing and absorp tion. x being measured horizontally, and the refractive index being pro portional to V/(y). This equation gives, as before, T - ax + /cW/((/)-<r, and the equation of the path of a ray is =& = x- aj da J Here, on the corpuscular theory, a is the horizontal velocity of the light, and Jf(y) - a? the vertical velocity. If the form of/ and the value of o be such that we can have / (77)- a 2 = 0, it is clear that at y = t) the ray is for a moment horizontal. The form of the equation of the ray shows that it has a vertex at this point, and that it is symmetrical about a vertical axis passing through the vertex. If |, -rj be the coordinates of the vertex for a ray passing through the point 0, b, we have the relation 1 = lis is the equation of the locus of the vertices of all rays which, irting from a given point, return again to the same level. To This starting from" a given point, return again to the same level. To find, then, the various rays by which a distant object near the horizon can be seen, all that we have to do is to draw the curve of vertices which passes through the eye of the spectator, and to find the points in which it is intersected by a vertical line situated mid way between the object and the eye. Each of these points is the vertex of a ray by which the object can be seen. When the curve of vertices leans forward towards the eye at one of these points, two contiguous rays cross one another, and an inverted image is seen ; when it leans from the eye, they do not cross, and the image is erect. Now, when the curve of vertices is traced, from the above for mula, for an arrangement of the air such that the refractive index falls off through a horizontal stratum of air from a greater value below the stratum to a smaller value above it, it is found that the curve of vertices in the- stratum can in general be cut by a vertical line in one point only. But if the refractive index have a nearly stationary value at the upper boundary of the stratum the curve of vertices can be cut twice, or not at all, by a vertical line. When there is no intersection we have only the direct image ; but when there are two intersections a distant ship will be seen as usual through the lower uniform air, while there will be seen above it an inverted image, and then a direct image, both due to the stratum. This is a form of mirage very commonly seen at sea. 1 When there is no stationary value of the index at the upper boundary, the upper erect image is not given by the stratum. This arrangement, however, turned upside down, explains the ordinary mirage of the desert where we see objects directly through the nearly uniform air at some distance above the sand, but also an inverted image (suggesting reflexion from a pool or lake) formed by the refraction in the hot layer of air near the sand. ABSORPTION, FLUORESCENCE. We must now take up the third and fourth of the categories under which light incident on the bounding surface of two media may fall scattering and absorption. We take them together, because in the great majority of bodies, as we have already seen, scattering takes place not merely at the surface but within some distance below the surface, which in general is small, but in some cases considerable. And when the scattering takes place, even in part only, below the surface, the scattered light is usually modified by absorption. J See especially Vince, in the Bakerian Lecture, Phil. Trans., 1799. An excellent instance of this scattering from below the White- surface is afforded by a mass of thin films or small particles ness oi of transparent bodies, such as glass, water, or ice. Thus frotll > 1 T i i 1.1 t tit snow, pounded glass, froth, or loam, snow, clouds, &c., appear c i ol brilliantly white in sunlight, and are, in consequence, &c. opaque when in layers of sufficient thickness. Here the light is obviously scattered by reflexion. What passes through one film, crystal, or particle is, in p irt, reflected from the next, and so on. Even when the froth consists of bubbles of a highly coloured liquid, such as porter for instance, it usually shows but slight traces of colour, for the great majority of the scattered rays have passed through very small thick nesses only of the liquid. In the same way, very finely pounded blue or red glass (unless it be exceedingly deeply coloured when in mass) appears nearly white. But when a mass of water is full of air bubbles, as, for instance, is Colour the case in the neighbourhood of a breaker, the light f the reflected from the surfaces of these bubbles suffers a double sea absorption by the water before it reaches the eye. This is one of the causes of the exquisite colours of the sea. Near shore, or in shoal water, another cause sometimes comes into play, viz., fine solid particles suspended in the water. When such particles, whether in air or in water, are ex ceedingly small, they may produce colours due to their minuteness alone, and not to their own colour nor to the absorptive properties of the medium. This, however, is a question of physical optics. In general, even the most highly coloured opaque or translucent solids, such as painted wood or stained paper, are visible by scattered light whatever portion of the spectrum falls on them. This is very well seen with highly coloured paper-hangings, when illuminated by homogeneous light, such as that of a sodium flame (a Bunsen flame, into which is thrust a platinum wire dipped in strong brine). The red, orange, and yellow parts usually appear very bright under such treatment, the blue parts appearing but slightly illuminated. The colour of all is, of course, that of the incident light. It appears, therefore, that some of the light is scattered from the surface. It is by this, for instance, that the blue parts are feebly visible. But that which is scattered from the portions coloured red, orange, &c., must come mainly from under the surface. An excellent proof of this is furnished by mixing, in Mixture proper proportions, a yellow and a blue powder, or yellow of P S and blue paints. It is commonly imagined that the green ments - colour which is thus produced is a mixture of blue and yellow. Far from it ! When a disk divided into alternate sectors, coloured with the same blue and yellow pigments, is made to rotate rapidly in its own plane, it of course produces on the eye the true result of a mixture of these Mixture blue arid yellow colours. This depends for its exact tint of on the pigments employed, and on the angles of the sectors, cc but is usually a faint pink or a muddy purple, utterly different from the green produced by mixing the powders or the paints. Helmholtz was the first to point out the true source of the green. It is the one colour which is not freely absorbed either by the yellow or by the blue pig ment. For the scattered light by which the mixture is seen comes chiefly from below the surface, and has thus suffered absorption by each of the component powders. The yellow powder removes the greater part of the blue, indigo, and violet rays ; the blue, the greater part of the reds, oranges, and yellows. Thus the light which finally escapes is mainly green. For the accurate study of the absorptive power of a solid Exact or liquid medium, it is necessary to compare the spectrum study of of white light which has passed through a plate or layer of ^ ^ !1> it with a normal spectrum. This is easily effected by placing the absorbing medium (if a fluid, it must be in a
