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red will vanish by degrees, till the film is colourless, then it will assume a green hue, which will increase and arrive at its maximum when the tourmaline has turned through ninety degrees; after that the green will vanish and the red will re-appear, alternating at each quadrant. Whence it appears that the tourmaline separates the light which has passed through the film into a red and a green pencil, and that in one position it absorbs the green and lets the red pass, and in another it absorbs the red and transmits the green. This is proved by analyzing the ray with Iceland spar instead of tourmaline, for since the spar does not absorb the light, two images of the sulphate of lime will be seen, one red and the other green, and these exchange colours every quarter revolution of the spar, the red becoming green and the green red, and where the images overlap, the colour is white, proving the red and green to be complementary to each other. The tint depends on the thickness of the film. Films of sulphate of lime the 0.00124 and 0.01818 of an inch respectively, give white light in whatever position they may be held, provided they be perpendicular to the polarized ray; but films of intermediate thickness will give all colours. Consequently a wedge of sulphate of lime, varying in thickness between the 0.00124 and the 0.01818 of an inch, will appear


to be striped with all colours when polarized light is transmitted through it. A change in the inclination of the film, whether of mica or sulphate of lime, is evidently equivalent to a variation in thick


When a plate of mica held as close to the eye as possible, at such an inclination as to transmit the polarized ray along one of its optic axes, is viewed through the tourmaline with its axis vertical, a most splendid appearance is presented. The cloudy spot, which is in the direction of the optic axis, is seen surrounded by a set of vividly coloured rings of an oval form, divided into two unequal parts by a black curved band passing through the cloudy spot about which the rings are formed. The other optic axis of the mica exhibits a similar image.

When the two optic axes of a crystal make a small angle with one another, as in nitre, the two sets of rings touch externally; and if the plate of nitre be turned round in its own plane, the black transverse bands undergo a variety of changes, till at last the whole richly coloured image assumes the form of the figure 8, traversed by a black cross. Substances having one optic axis have but one set of coloured circular rings, with a broad black cross passing through its centre and dividing the rings into four equal parts. When

the analyzing plate revolves, this figure recurs at every quarter revolution, but in the intermediate positions it assumes the complementary colours, the black cross becoming white.

It is in vain to attempt to describe the beautiful phenomena exhibited by innumerable bodies, all of which undergo periodic changes in form and colour when the analyzing plate revolves, but not one of them shows a trace of colour without the aid of tourmaline or something equivalent to analyze the light, and as it were to call these beautiful phantoms into existence. Tourmaline has the disadvantage of being itself a coloured substance, but that inconvenience may be avoided by employing a reflecting surface as an analyzing plate. When polarized light is reflected by a plate of glass at the polarizing angle, it will be separated into two coloured pencils, and when the analyzing plate is turned round in its own plane, it will alternately reflect each ray at every quarter revolution, so that all the phenomena that have been described will be seen by reflection on its surface.

Coloured rings are produced by analyzing polarized light transmitted through glass melted and suddenly or unequally cooled, also in thin plates of glass bent with the hand, in jelly indurated or compressed, &c. &c.; in short, all the phenomena of coloured rings may be produced, either perma

nently or transiently, in a variety of substances, by heat and cold, rapid cooling, compression, dilatation, and induration; and so little apparatus is necessary for performing the experiments, that, as Sir John Herschell observes, a piece of window→ glass or a polished table to polarize the light, a sheet of clear ice to produce the rings, and a broken fragment of plate-glass placed near the eye to analyze the light, are alone requisite to produce one of the most splendid of optical exhibitions.

It has been observed that when a ray of light, polarized by reflection from any surface not metallic, is analyzed by a doubly refracting substance, it exhibits properties which are symmetrical both to the right and left of the plane of reflection, and the ray is then said to be polarized according to that plane. This symmetry is not destroyed when the ray, before being analyzed, traverses the optic axis of a crystal having but one optic axis, as evidently appears from the circular form of the coloured rings already described. Regularly crystallized quartz, or rock crystal, however, forms an exception. In it, even though the rays should pass through the optic axis itself, where there is no double refraction, the primitive symmetry of the ray is destroyed, and the plane of primitive polarization deviates either to the right or left of the observer, by an angle proportional to the

thickness of the plate of quartz. This angular motion, or true rotation of the plane of polarization, which is called circular polarization, is clearly proved by the phenomena. The coloured rings produced by all crystals having but one optic axis are circular, and traversed by a black cross concentric with the rings; so that the light entirely vanishes throughout the space enclosed by the interior ring, because there is neither double refraction nor polarization along the optic axis; but in the system of rings produced by a plate of quartz, whose surfaces are perpendicular to the axis of the crystal, the part within the interior ring, instead of being void of light, is occupied by a uniform tint of red, green, or blue, according to the thickness of the plate. Suppose the plate of quartz to be of an inch thick, which will give the red tint to the space within the interior ring; when the analyzing plate is turned in its own plane through an angle of 17, the red hue vanishes. If a plate of rock crystal, of an inch thick, be used, the analyzing plate must revolve through 35° before the red tint vanishes, and so on; every additional 25th of an inch in thickness requiring an additional rotation of 1740, whence it is manifest that the plane of polarization revolves in the direction of a spiral within the rock crystal. It is remarkable that, in some crystals of quartz,

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