Sir Isaac Newton ascertained in this way, by direct measurement, that air at and below a thickness of half a millionth of an inch ceases to reflect light, and at and above a thickness of seventy-two millionths of an inch it reflects all the rays of the spectrum. Between these two limits it reflects the various orders of colours set down in the table.

Water at and below a thickness of three-eighths of a millionth of an inch ceases to reflect light; at and above fifty-eight millionths it reflects white.

And glass transmits all light at a thickness of one-third of a millionth of an inch, and reflects all at and above fifty-millionths of an inch (61).

§ 242. That alternating motion of light to which these phenomena must be referred, and which, as we have already observed, must be as real as the motion of translation itself, is an essential condition of the undulatory hypothesis. It has been accounted for less happily, upon the hypothesis of emission, by conditions superadded to the original conception of the luminiferous particles, that the poles of the latter present themselves alternately in opposite directions, so that they are thereby endued with, what Sir Isaac Newton designated as, fits of easy reflection and transmission; the different duration of which in the differently coloured rays may account for the phenomena which we have been discussing.

(61) The arrangement of the lenses is here shown, with the coloured concentric rings arising from the thin film of air inclosed

between them: and in the annexed figure they are exhibited in section; the proportion of the curvatures being much exaggerated, in order to show the gradual increase in the thickness of the film.

§ 243. The law of ordinary refraction, which we have hitherto considered, is very far from general, and it only obtains where the refracting medium belongs to one or other of the following classes:

1. Gases or vapours.

2. Liquids.

3. Bodies solidified from the liquid state so suddenly, as not to admit of regular crystalline arrangement, such as glass, jelly, gums, resins, &c.

4. Crystallized bodies of the tessular system, or that class which may be supposed to be constructed

of spherical particles, such as the regular cube, octohedron, &c.

In uncrystallized bodies, whose structure is indefinite, we may suppose that the action upon light is the same in every direction, from a system of compensation which takes place amongst their molecules: in crystallized bodies of the tessular system, the same equality of action arises from the regular molecular structure which confers upon them three precisely similar axes.

These solid bodies even cease to belong to this class when they are forcibly compressed or dilated either by mechanical force or the unequal action of heat. All other bodies, such as salts, crystallized minerals, all animal and vegetable bodies in which there is a tendency to regularity of structure,—as horn, quill, mother-of-pearl, &c.,—act upon light in its passage through them in a very different manner. They divide the refracted portion into two distinct pencils, each of which pursues a rectilinear course within the medium, according to its own peculiar law.

§ 244. The best exemplification of this mode of refraction is to be found in a substance called Iceland spar, of the rhombohedric system of crystallization. It is perfectly transparent and colourless, and susceptible of a high polish. It may be cleaved or broken into solids of a rhombohedral form, and the natural faces are generally even and perfectly polished (§ 112).

If we take a rhombohedron of this substance, and look at a small illuminated object through it, or a line of light passing through a slit in an opaque plate, or a black line upon a sheet of paper, in certain positions, two images of the object will appear; and upon turning the rhombohedron round in its own

plane, so as to make a complete revolution, the two images will assume a regular movement with regard to each other, and one will fall upon the other, or coincide with it, twice in the revolution; and it will be easy to ascertain that these coincidences take place in two positions of the spar, which are directly opposite to each other. The maximum separation occurs at the two intermediate points of the revolution, and the distance is proportioned to the thickness of the rhombohedron (62).

Hence it appears that a ray of light, in passing through Iceland spar, is split into two by some force residing in the crystal.

§ 245. Now, the line which joins the obtuse angles of such a rhombohedron is designated as the axis of the crystal, (§ 124,) and it is also the optic axis of the mineral. Whenever a ray of light passes along this axis, or the principal section or plane, of the crystal in which it is contained, (and which may be conceived to include an infinite number of the similar axes of the primitive molecules of which it is composed,) it passes whole and undivided; and if two artificial planes be ground

(62) If we place the rhombohedron, as in the annexed figure, above a sharp line, the line will appear doubled, as m n, p q; or a dot will be doubled, as e o. If we cause a pencil of light, R r, to fall upon the surface of the crystal, it will be separated into two rays, To, re, which will respectively emerge at o and e, in the directions

od, e e', parallel to R r. The same phenomena will occur by making the ray Rr fall at the same incidence, and in the same direction relatively to the summit A, upon any point of the faces. The plane A CBD is called the principal section of the crystal, and the axis, or the line which may be drawn from the solid angle A to the angle B, is contained in it.

parallel to one another, and perpendicular to the axis, an object will appear single when viewed perpendicularly through them. In this direction the ray of light is equally related on all sides to the crystalline forces, and hence, as in all directions of the tessular system, there is only one image. In all other directions the ray will be divided into two, one of which follows (nearly) the laws of ordinary refraction, and may be denominated the ordinary ray; the other varies from those laws, inasmuch as in general its plane of refraction does not coincide with the plane of incidence, and the sines of incidence and refraction cease to have a constant relation to each other: it is distinguished as the extraordinary ray. The sines of incidence and refraction, however, of the extraordinary ray, are always constant in the same substance at the point of greatest deviation, which happens when the ray passes along a plane at right angles to the axis of the crystal; and in certain substances, the index of refraction of the extraordinary ray is sometimes greater, and sometimes less, than the index of refraction of the ordinary ray. Hence, crystals have been distinguished as repulsive and attractive, or negative and positive crystals.

There are crystals of other substances, again, which present two optic axes, along which a ray of light can penetrate without being divided: but the position of these cannot conveniently be determined with regard to the crystallographical axis.

§ 246. If the rays of light which have been separated by passing through a crystal of Iceland spar, be made to pass through another crystal placed similarly to the first, there will be no further subdivision of the light; the two images will be merely separated to a greater distance from the increased thickness through which the rays pass. If, again, the two crystals be so placed that the principal sections are at right angles to each other, there will be still but two images; but the ray ordinarily refracted in the first, will become extraordinary in the second, and the extraordinary ray will become the ordinary: but at all intermediate positions of the two crystals there will be a subdivision of each ray, and consequently four images. These four images will be of equal intensity when the principal sections of the two crystals are at an angle of 45° to each other; at all other angles one or other of the images diminishes in intensity as the principal sections approach to a perpendicular or parallel position.

Each ray emerging, then, from a crystal of Iceland spar, is only subject to a further division in particular positions of a second crystal; whereas natural light is always divided into two portions of equal intensity. Each ray has suffered a physical change, its nature has been altered; it is not acted upon by the force of the second crystal as natural light would be, but requires that the force be applied in a particular direction relatively to the modification it has received from the first crystal.

§ 247. This physical change has been called polarization, a term which must be taken to indicate "opposite properties in opposite directions, so exactly equal, as to be capable of accurately neutralizing one another*." There are many crystallized minerals which, when cut into parallel plates, are sufficiently transparent to allow abundance of light to pass through them with perfect regularity, which, upon its emergence, is found to have acquired the peculiar modification here in question. One of the most remarkable of these is the tourmaline. If we take a well-polished plate of this mineral of moderate thickness, cut from a crystal of a brown colour in a direction parallel to the axis of the prism, a candle may be seen through it as through a plate of coloured glass; and no change will be observed upon turning it round. If another similar plate be interposed between the first plate and the eye, and turned slowly round in its own plane, the candle will appear and disappear alternately at every quarter revolution of the plate; passing through every gradation of brightness, from the maximum to a total, or nearly total, evanescence, and then increasing again by the same degrees as it diminished before. If we attend to the position of the second plate with respect to the first, we shall find that the maximum of illumination takes place when the axis of the second plate is parallel to that of the first.

§ 248. If we examine the two pencils of light after separation by a crystal of Iceland spar, by means of a plate of tourmaline, we shall readily perceive that the ordinary image (that which is not deviated from the axis of the crystal) acquires its greatest intensity when the axis of the tourmaline is perpendicular to the principal section of the rhombohedron, and that it becomes extinct in the opposite direction. When the axis of the tourmaline lies in the principal section itself, the extra

* WHEWELL.