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arising from irregularities in the annealing process. To detect these the glass should be carefully examined by polarized light previous to being ground and polished; and by this agent the slightest defects are made appreciable.

So also glass vessels employed for domestic purposes may be advantageously tested by the same agent. The facility with which tumblers, &c. crack, sometimes spontaneously, at other times while in the hands of the glass-cutter, or when warm water is poured into them, or when exposed to a slight blow, depends on some imperfection in the annealing process. Hence, also, the reason why run glass (that is, glass made without paying the duty) is very apt to crack; for owing to the rapidity with which all the stages of its manufacture have been hurried on, it is not well made, and sufficient time has not been allowed for the annealing process.

It is probable, also, that manufacturers, or rather the mounters of electrical machines, might beneficially avail themselves of polarized light in the selection of glass cylinders and plates. Recently made cylinders, when mounted, will sometimes crack, or fly, as it is termed, without any obvious agency, owing, I presume, to some defect in the annealing process, which, perhaps, might have been previously discovered by means of polarized light.

An argument in favour of the vegetable origin of the diamond has been founded by Dr. Brewster, on the phenomena presented by this substance, when examined by means of polarized light. It is well known that various opinions have been held by different writers on the mode of formation of this mineral. All of them, however, may be included under two divisions: those which assume the diamond to be the direct produce of heat on carbonic acid or carbon, and those which ascribe it to the slow decomposition of plants. Dr. Brewster, who adopts the latter notion, met with a diamond which contained a globule of air, while the surrounding substance of the diamond had a polarizing (doubly refracting) structure, displayed by four sectors of polarized light encircling the globule. He, therefore, inferred that this air bubble had been heated, and by expansion had produced pressure on the surrounding parts of the diamond, and thereby communicated to them a polarizing structure. Now for this to have happened, the diamond must have been soft and susceptible of compression. But as various circumstances contribute to prove that this softness was the effect of neither solvents nor heat, he concluded that the diamond must have been formed, like amber, by the consolidation of vege... table matter, which gradually acquired a crystalline form by the influence of time and the slow action of corpuscular forces.

Starch grains have a laminated texture, and possess a doubly

refractive power. They are composed of concentric layers of amylaceous matter. On some part of the surface of each grain is a circular spot, called the hilum. This appears to be an aperture or transverse section of the tube or passage leading into the interior of the grain, and by which the amylaceous matter, forming the internal lamina, was conveyed. On examining the grains by the polarizing microscope, unequivocal evidence of their doubly refractive power may be obtained. At least I have found this to be the case in all the starches which I have yet examined, viz., tous les mois, potato-starch, West Indian arrow-root, sago-meal, Tahiti arrow-root (obtained from a species of Tacca), tapioca-meal, East Indian arrow-root (Curcuma angustifolia), wheat-starch, Portland arrow-root (Arum maculatum), and rice-starch. The larger grained starches form splendid objects for the polarizing microscope; tous les mois being the largest may be taken as the type of the others. It presents a black cross, the arms of which meet at the hilum.

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On rotating the analyzer the black cross disappears, and at 90° is replaced by a white cross; another, but much fainter black cross, being perceived between the arms of the white cross. Hitherto, however, no colour is perceptible. But if a thin plate of selenite be interposed beGrains of Tous les Mois viewed by the Polarizing Microscope. A. represents the tween the starch grains and the appearance when the planes of polarization of the polarizer and analyzer are at right polarizer, most splendid and angles to each other; B.when they coincide gorgeous colours make their appearance. The arms of the cross acquire the colour which the selenite plate yields in polarized light. The four spaces between the arms also appear coloured; but their tint is different to that of the cross. The colours of the first and the third spaces are identical, but different to those of the second and fourth, both of which have the same tint. At the point where the colours of the arms and of the interspaces meet, the tints blend. All the colours change by revolving the analyzer; and become complementary at every 90°. The appearances presented by potato-starch are similar to those of tous les mois. Several other starches (as West Indian arrow-root, sago-meal, Tahiti arrow-root, tapioca-meal, and East Indian arrow-root) present black and white crosses, and, when a selenite plate is used, also colours; but in proportion as the grains are small, are their appearances less distinct. I have not hitherto detected the black and white crosses in wheat-starch, Portland arrow-root, and rice-starch. Their double refractive power, however, is proved by the change they effect in the colour yielded by a plate of selenite.

A great variety of animal structures possess a doubly refracting or depolarizing structure, as a quill cut and laid out flat on glass,

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the cornea of a sheep's eye, a piece of bladder, gold-beaters' skin, human hair, a slice of a toe or finger nail, sections of bones, of teeth, &c. The crystalline lenses of animals also possess this property in a high degree, owing to their central portion being denser and firmer than the external portion. If the lens of a cod-fish be placed in a glass trough of oil or Canada balsam, it presents twelve luminous sectors separated from each other by a black cross. Even living animals present double refracting properties. The aquatic larve of a gnat, commonly called skeleton larvæ, form a very amusing exhibition. They are to be placed in water in a very narrow water-trough. In certain positions, they give no evidence of double refraction, but in others, and especially when they are exerting much muscular energy, they possess it in a very marked degree.

LECTURE III.

DOUBLY REFRACTIVE AND OTHER ALLIED PROPERTIES OF

CRYSTALS.

IN my last lecture I explained the nature and cause of double refraction; and I now proceed to examine the double refractive property of crystals, and to show how this is connected with, or related to, other properties of crystalline substances.

1. Double Refraction of Crystals. Every transparent crystalline body refracts the rays of light which are incident on it at oblique angles; and the degree of its refractive power depends on two circumstances; viz., the angle of incidence, and the nature of the crystalline substance. In these respects crystals agree with all other transparent media.

But a very large number of crystals possess the property of double refraction; and they are, therefore, called doubly refracting crystals, to distinguish them from others which have not this property, and which are denominated singly refracting crystals.

The double refraction of some crystals is immediately manifested by the production of duplicate images; either through two parallel surfaces, as Iceland spar, or through two surfaces which are more or less inclined on each other. Thus to observe the double refraction of a crystal of quartz, it is necessary to look through a pyramidal and lateral plane at the same time. By this contrivance the surface of emersion is inclined to that of admission, which causes the two pencils to emerge at different inclinations, and so become further separated as they proceed.

Many crystals, however, possess the property of double refraction in so feeble a degree that it is impossible to see, under ordinary circumstances, two images; and in such cases we are constrained to employ the polariscope to detect this property.

In every doubly refracting crystal there are one or more positions or directions in which the two images become superposed;

or, in other words, in which no double refraction exists or is evident. These directions are called the optic axes or the axes of double refraction. I have already stated that the phrase axes of No double refraction would be more intelligible. These axes may be regarded as positions of equilibrium where certain forces, which exist within the crystal and act in opposition, balance each other. In crystals of certain forms they coincide with the geometrical or crystallographical axes, whereas in crystals of other shapes they do not; but to these points I shall again have to beg your attention.

If we consider doubly refracting crystals in regard to the number of their optic axes we may divide them into two orders; one including those that possess only one axis, and another comprehending such as have two axes. The first are called uniaxial, the second biaxial crystals. As this distinction is connected with other remarkable optical peculiarities, as well as with the geometric and thermotic properties of crystals, it will be necessary to notice it a little more in detail.

a. Uniaxial Crystals.-Those crystals which have only one axis of [no] double refraction, and which, in consequence, are termed uniaxial crystals, or crystals with one optic axis, belong to the square prismatic or rhombohedric systems. In them the geometric or crystallographic axis is coincident with the optical one; that is, the line or direction in the crystal, around which the figure is symmetrically disposed, or about which every thing occurs in a similar manner on all sides, is coincident with the optic axis, or the axis around which the optical phenomena are the same in all directions. You must not, however, suppose that the axis is a single line; for there must be as many axes as there may be lines parallel to each other, so that the word is merely synonymous with a fixed direction.

In all other directions but the one called the optic axis, these crystals doubly refract; and of the two rays thus produced, one follows the ordinary laws of simple refraction, and is accordingly called the ordinary ray, while the other, being subject to an extraordinary law, is denominated the extraordinary ray.

These two rays advance with unequal degrees of velocity; the one suffering greater retardation than the other. When the ordinary ray advances more rapidly than the extraordinary one, the crystal is said to have a negative or repulsive axis of [no] double refraction; but when the ordinary ray advances less rapidly, the crystal is said to possess a positive or attractive axis In other words, when the extraordinary ray is refracted towards the axis, the crystal is said to have a positive axis; but when the ray is refracted from the axis, the crystal is said to have a negative axis. These terms are not very expressive of the property they are intended to represent. Biot used the terms

attractive and repulsive to designate the attractive or repulsive forces which he supposed to emanate from the axes of crystals. For it is obvious that if the extraordinary ray be most retarded, it will be refracted from the axis, that is, it will appear to be repelled by a force emanating from the axis; whereas, if it be the least retarded, it will be refracted towards the axis, or will appear to be attracted by a force emanating from the axis. Now it was to obviate the hypothesis which these terms involve, that Brewster substituted the words positive and negative for the terms attractive and repulsive, merely meaning to denote by them the opposition, but not the nature, of the forces.

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In uniaxial crystals the position of the optic axis is constant, whatever be the colour of the light; whereas in biaxial crystals this is not the case, as I shall presently show.

b. Of Biaxial Crystals.-A very large number of crystals, including all which belong to the right rhombic prismatic, oblique prismatic, and doubly oblique systems, have two axes of double refraction, which are more or less inclined to each other. Such crystals are, in consequence, denominated biaxial crystals, or crystals with two optic axes. In them there is no single line or axis around which the figure is symmetrical, as in uniaxial crystals; and the optic axes do not always, or even frequently, coincide with any fixed line in the crystals. Now this fact has led Dr. Brewster to believe that the optic axes are not the real axes of the crystals, but only the resultants of the real, or polarising, axes, or lines, in which the opposite actions of the two real axes compensate each other. Hence he terms them the resultant axes, or axes of no polarization, or of compensation.

The following is a list of a few biaxial crystals; and for a more extensive one I must refer my auditors to Dr. Brewster's works : Table of Biaxial Crystals.

Character of Principal Inclination of Resultant
Axes.

Axes*.

Glauberite

Negative............ 2° or 3o

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*The principal axis is, according to Dr. Brewster, the middle point between the two nearest poles of no polarization.-Phil, Tans., 1818.

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