olive oil; for these pieces, on account of their inequalities and the roughness of their surface, do not transmit the light regularly when placed in the air; but when immersed in olive oil, the oil fills up their inequalities and they become transparent; and so little reflection takes place at the common surface of the two substances that the limits of their separation are scarcely distinguishable.

It will be readily understood, also, that a body transparent in itself, may be made less transparent and even opaque, by separating its particles from each other, and introducing between them a medium, which acts very differently upon the light. This takes place, for example, when transparent liquids are made to foam by the introduction of air; for there is no doubt that the action of air and of these liquids upon the light is very different, since when their surface is covered with air a very brilliant reflection is produced. Now the air being introduced between the particles of the liquid, as many successive reflections take place as there are bubbles, or breaks in the continuity of the liquid; and all the incident light being thus turned back or dispersed among the particles of the body, this body becomes opaque; but its transparency will be restored by restoring the continuity of its parts, and this is the case with froth when by losing its air it returns to the state of water. The same phenomenon occurs in a porous stone called hydrophane, which is perfectly opaque when dry, but becomes translucent on being saturated with water, because its action upon light approaches more nearly to that of water than to that of air. Hence we see that transparency and opacity are not qualities which belong to the matter of bodies, but which depend solely on the arrangement of their particles. This will be still more strikingly confirmed, when we examine by experiment the manner in which the repulsive force begins and increases with the thickness of the body, to the limit at which it ceases to be affected by the addition of new laminæ.

DIOPTRICS.

General Laws of Simple Refraction.

31. HAVING examined the phenomena attending that portion of the incident light which is reflected at the first surface of bodies, we shall now consider the portion which penetrates them.

This, when the incidence is oblique, instead of continuing on in a straight line, deviates from its first direction; and the phenomenon is called refraction.

In all bodies, not crystallized, the refracted ray remains simple, and continues on in the plane of incidence. As to the extent of the deviation, it depends on the difference between the nature and density of the medium which the light leaves and those of the medium it enters.

If the two media are of the same nature and of equal density, the ray suffers no refraction and continues on in a straight line. If they are of the same nature but of different densities, the luminous ray on entering the more dense, is attracted towards the perpendicular to their common surface. Finally, if both the nature and density of the media are different, these two elements conspire in the result, and the ray approaches the perpendicular in that medium which exerts the strongest action upon the light. These facts we shall establish by experiment.

When a piece of money M is placed at the bottom of a vessel AB, of which the sides are opaque, it is invisible except to the Fig. 26. eye situated within the cone of direct rays RR', proceeding from it, and bounded at A and B by the edges of the vessel. But if the vessel be filled with some liquid, the piece of money becomes visible in a much more open cone, such, for example, as OSO',

although the cone of rays proceeding from M is the same as before. These rays, therefore, must be bent outward from the vessel on entering the air; and consequently they are removed farther from AN, the perpendicular to the common surface of the liquid and the air, remaining always in the vertical plane which contains the incident ray AM and the perpendicular AN.

We may take another example no less familiar. If a straight Fig. 27. stick TT is plunged obliquely into tranquil water of which the surface is AB, the stick appears to be broken at the point I where it touches the surface, and the prolonged part, although comprehended in the same vertical plane with the part which is without, seems to approach nearer to a horizontal position. To explain this phenomenon, let us suppose the eye situated at the point T', that is, at the upper extremity of the stick. If the rays from the liquid came to it in a straight line, the other extremity T'would be seen in TI produced, aud not where it really appears, at T. Now we have already remarked that we see objects in the direction of the rays which they send to the eye; since then we see the point T" above its true place, it follows that the ray T'I', which renders it visible to us, passes above T'I, and follows the broken direction T'IT, Consequently, if we draw, through the point of incidence I', the perpendicular NI'N' to the surface BB, we shall see that the luminous ray TI on passing out of the water into the air, diverges from the perpendicular as in the last example; but it still remains in the vertical plane which contains the angle of incidence.

The deviation would take place in a contrary direction, if the ray passed out of air into water, in which case it would approach the perpendicular. To prove this, take a tub of a rectangular form, the sides of which are of glass; and let ABCD represent a Fig. 28. horizontal section. Then having filled it with water, by means of a heliostat make a ray of horizontal light SI fall obliquely upon the side AB. Closing the window-shutter in order to darken the room, it will be easy to find the direction of the refracted ray IR. For we have only to move along the side opposite to the point of incidence CD, a small circle of paper or rough glass till it intercepts the emerging ray. The point R being thus found, and the line RI being drawn to the point of incidence, this line will be the direction of the refracted ray; and comparing it to the incident ray SI, we shall see that refrac

tion has made it approach the perpendicular NIÑ to the surface of incidence AB.

The phenomenon being thus established, it is important to determine the ratio which exists, for every angle of incidence, between the inclination of the incident ray to the perpendicular, and that of the refracted ray; so that, knowing the one, we may calculate directly the other. For this purpose we fix accurately the points S and R in the incident and refracted rays, and measure their distances SN, RN', from the common perpendicular NSN'; and we measure also the parts IN, IN', of this perpendicular, which are intercepted by the perpendiculars SN, RN. Having constructed the two right-angled triangles SIN, RIN', we shall know the angle SIN, formed by the incident ray with the perpendicular, which, as in reflection, is called the angle of incidence. We shall have likewise the angle RIN', formed in the interior of the liquid, by the prolongation of the same perpendicular, with the refracted ray IR. This is called the angle of refraction. We recognise the two following laws discovered by Descartes; (1.) The incident and refracted rays are always comprehended in the same plane, perpendicular to the common surface of the two media; (2.) The sine of the angle of incidence has to the sine of the angle of refraction a constant ratio for all angles of incidence, when the media are the same. This ratio is called the ratio of refraction.

This beautiful law is the fundamental principle of all dioptrics. Indeed, when the direction of the incident ray is given, as well as the position of the refracting surface, we may always deduce the direction of the refracted ray, either immediately, if the surface is plane, or if it is curved, by considering the incidence as taking place upon the tangent plane. Afterwards, if the form of the refracting medium is given, we may follow the refracted ray to the interior, and determine the point where it will meet the opposite surface, as well as the angle it will form with the tangent plane; hence we may calculate the angle of emergence, and the direction of the emergent ray.

32. The importance of this principle requires, therefore, that we should endeavour to establish it with the utmost possible exactness; we shall presently point out the method to be pursued. We shall first, however, take notice of a remarkable phenomenon which always accompanies refraction.

This phenomenon consists in a dilatation of the refracted ray in the plane of refraction, and its dispersion through an angular space, the vertex of which is at the point of incidence. This angle is then filled with rays of various colours; for if we place within it a piece of white pasteboard or of ground glass so as to intercept all the refracted light, we shall see painted upon it an oblong spectrum, in which may be distinguished all the colours of the rainbow, and arranged in the same order, the violet and red being outermost, the yellow and green in the middle. The violet rays suffer the greatest refraction, the red rays the least, the green rays less than the violet and more than the red. For the sake of brevity, I shall designate these rays by the colours they give to bodies. But it is evident that they are not in themselves either violet or green or red, and that these names express only the sensations they produce in us.

This phenomenon is called the dispersion of light; it is more sensible in the same medium in proportion as the angle of refraction is greater; and in different media, at the same angle of incidence, in proportion as the refractive power is greater. No experiments can be made on refraction without producing it, and it is for this reason that it is noticed here. But, we shall not at present, examine the phenomenon more in detail; we shall confine ourselves in what follows, to considering the refraction of the yellow or green rays, which are nearly at a middle point between the others.

33. It ought also to be mentioned that there exist substances in which light is not refracted in a single beam, but in two separate and distinct beams, each having its proper dispersion. This takes place in all bodies regularly crystallized whose primitive form cannot be geometrically reduced to a cube. One only of these follows the law of Descartes. The cause of the other is subject to a much more complicated law, which Huygen's discovered from a large class of crystals, and which has been found to apply to crystals in general. This law we shall investigate in its proper place; but at present we shall confine ourselves to the consideration of the first kind of refraction which takes place in all bodies, and is called ordinary refraction. The other kind, which is called extraordinary refraction, takes place only in certain bodies,