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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 (N. 213). Substances with one optic axis have but one set of coloured circular rings, with a broad black cross passing through its centre, 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 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 obviated 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 through thin plates of glass bent with the hand, jelly indurated or compressed, &c. &c. In short, all the phenomena of coloured rings may be produced, either permanently 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 Herschel says, 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.
Pressure produces remarkable changes in the optical properties of crystals. Compression, perpendicular to the axis, transforms a crystal with one optic axis into one with two. A slice of
quartz and one of beryl, both cut perpendicularly to their axis, were compressed thus by MM. Moignot and Soleil, They found that the single system in the quartz, which is a positive crystal, was doubled in the direction of the compression, while in the beryl, which is a negative crystal, the duplication was perpendicular to the compression. In the quartz the axis of the double system coincided with the line of pressure, but in the tourmaline, which is a negative crystal, the line which joins the centres of the rings was perpendicular to the pressure.
If a positive crystal be compressed in the direction of its axis the tint of the rings descends, and that of a negative crystal rises. But if the crystals be dilated in the direction of their optic axis, the tints in positive crystals rise, and negative descend.
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 forms of the coloured rings already described. Regularly crystallized quartz, 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 (N. 214). 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 170, 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, the plane of polarization revolves from right to left, and in others from left to right, although the crystals themselves differ apparently only by a very slight, almost imperceptible, variety in form. In these phenomena the rotation to the right is accomplished according to the same laws, and with the same energy, as that to the left. But if two plates of quartz be interposed, which possess different affections, the second plate undoes, either wholly or partly, the rotatory motion which the first had produced, according as the plates are of equal or unequal thickness. When the plates are of unequal thickness, the deviation is in the direction of the strongest, and exactly the same with that which a third plate would produce equal in thickness to the difference of the two.
M. Biot has discovered the same properties in a variety of liquids. Oil of turpentine, and an essential oil of laurel, cause the plane of polarization to turn to the left, whereas the syrup of sugar-cane, and a solution of natural camphor, by alcohol, turn it to the right. A compensation is effected by the superposition or mixture of two liquids which possess these opposite properties, provided no chemical action takes place. A remarkable difference was also observed by M. Biot between the action of the particles of the same substances when in a liquid or solid state. The syrup of grapes, for example, turns the plane of polarization to the left as long as it remains liquid; but, as soon as it acquires the solid form of sugar, it causes the plane of polarization to revolve towards the right, a property which it retains even when again dissolved. Instances occur also in which these circumstances are reversed.
A ray of light passing through a liquid possessing the power of circular polarization is not affected by mixing other fluids with the liquid-such as water, ether, alcohol, &c.—which
do not possess circular polarization themselves, the angle of deviation remaining exactly the same as before the mixture. Whence M. Biot infers that the action exercised by the liquids in question does not depend upon their mass, but that it is a molecular action exercised by the ultimate particles of matter, which depends solely upon the individual constitution, and is entirely independent of the positions and mutual distances of the particles with regard to each other. These important discoveries show that circular polarization surpasses the power of chemical analysis in giving certain and direct evidence of the similarity or difference existing in the molecular constitution of bodies, as well as of the permanency of that constitution, or of the fluctuations to which it may be liable. For example, no chemical difference has been discovered between syrup from the sugar-cane and syrup from grapes. Yet the first causes the plane of polarization to revolve to the right, and the other to the left; therefore some essential difference must exist in the nature of their ultimate molecules. The same difference is to be traced between the juices of such plants as give sugar similar to that from the cane, and those which give sugar like that obtained from grapes.
If chlorate of soda be dissolved in water, the liquid has no circular polarization; but if the solution be allowed to crystallize, some of the crystals turn the light to the right and others to the left. Now, if all those of one kind be gathered together and dissolved a second time, the liquid will have no circular polarization; but if crystals be allowed to form, some will turn the light to the right and others to the left, although only one kind was dissolved.*
It is a fact established by M. Biot, that in circular polarization the laws of rotation followed by the different simple rays of light are dissimilar in different substances. Whence he infers that the deviation of the simple rays from one another ought not to result from a special property of the luminous principle only, but that the proper action of the molecules must also concur in modifying the deviations of the simple rays differently in different substances.
One of the many brilliant discoveries of M. Fresnel is the pro
*M. Marbach of Breslau.
duction of circular and elliptical polarization by the internal. reflection of light from plate-glass. He has shown that, if light polarized by any of the usual methods be twice reflected within a glass rhomb (N. 169) of a given form, the vibrations of the ether that are perpendicular to the plane of incidence will be retarded a quarter of a vibration, which causes the vibrating particles to describe circles, and the succession of such vibrating particles throughout the extent of a wave to form altogether a circular helix, or curve like a corkscrew. However, that only happens when the plane of polarization is inclined at an angle of 45° to the plane of incidence. When these two planes form an angle either greater or less, the succession of vibrating particles forms an elliptical helix, which curve may be represented by twisting a thread in a spiral about an oval rod. These curves will turn to the right or left, according to the position of the incident plane.
The motion of the ethereal medium in elliptical and circular polarization may be represented by the analogy of a stretched cord; for, if the extremity of such a cord be agitated at equal and regular intervals by a vibratory motion entirely confined to one plane, the cord will be thrown into an undulating curve lying wholly in that plane. If to this motion there be superadded another similar and equal, but perpendicular to the first, the cord will assume the form of an elliptical helix; its extremity will describe an ellipse, and every molecule throughout its length will successively do the same. But, if the second system of vibrations commence exactly a quarter of an undulation later than the first, the cord will take the form of a circular helix or corkscrew, the extremity will move uniformly in a circle, and every molecule throughout the cord will do the same in succession. It appears, therefore, that both circular and elliptical polarization may be produced by the composition of the motions of two rays in which the particles of ether vibrate in planes at right angles to one another.
Professor Airy, in a very profound and able paper published in the Cambridge Transactions, has proved that all the different kinds of polarized light are obtained from rock crystal. When polarized light is transmitted through the axis of a crystal of quartz, in the emergent ray the particles of ether move in a circular helix; and when it is transmitted obliquely so as to