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If we employ, as the analyzer, a doulrte refracting prism, we observe two complementary disks of colour, and these may be made to cross and produce white light as before shown.

The thickness of the film of selenite determines the particular tint. If, therefore, we use a film of irregular thickness, different colours are presented by different thicknesses. A wedge-shaped piece will produce parallel bands of colours, and two wedges crossed present diagonal bands. A plano-concave film, as well as a plano-convex film, gives concentric rings of colour, the former with a black, the latter with a white, centre.

Two films superposed, do not give the colour which would arise from the mixture of the two colours, but either the colour which corresponds to the joint thickness of the films, or that which belongs to the difference of their thickness. When the two films are put together, as they lie in the crystal, the resulting colour depends on the sum of the thicknesses. But when the two films are crossed, so that similar lines in the one are at right angles to similar lines in the other, the resulting tint depends on the difference of the thicknesses. These facts admit of very beautiful, curious, and interesting illustrations. Thin films of selenite of uniform thickness are so arranged as to slide over figures also formed of films of selenite. The changes of colour effected in the tints are most striking, and to unphilosophical minds almost magical.

In the opticians' shops are met with a great variety of devices prepared with films of selenite of different thicknesses, and which constitute philosophical toys illustrative of the beforementioned facts. Gothic windows, stars, flowers, fruits, animals (butterflies, parrots, dolphins, and chameleons), and theatrical figures (Jim Crow, harlequin, &c), are some of the ingenious, and often laughable illustrations contrived by Mr. Darker.

Test of Double Refraction.—From the preceding statements then, it appears, that the polariscope becomes a very delicate test of double refraction. A very large number of crystalline, and other bodies, possess a doubly refractive property; but comparatively few of these have it in so high a degree as to present, under ordinary circumstances, the phenomenon of double images; that is, the separation of the two systems of ethereal waves is not, in general, sufficiently great to be visible to the eye. In such cases, therefore, the polariscope is of great value, since it enables us to detect the slightest degree of double refraction. Some doubly refracting bodies present, in the polariscope, most gorgeous colours, as selenite. Others, however, which possess the doubly refractive property in a much slighter degree, require the aid of a thin film of selenite, of uniform thickness. Their double refractive property then becomes evident by the change which they induce in the colour of the film. Without this, we see light or dark fringes or bands, or black or white crosses, but no colour.

Cause of Double Refraction.—Being now in possession of an exceedingly delicate test of double refraction, we are prepared to enter into an inquiry into the cause of this property.

Now we shall find that every body endowed with equal elasticity in every direction, is a single refractor. Alter its elasticity in any one direction, put it in a state of unequal tension, and immediately it acquires the property of double refraction. Hence then, double refraction may be temporarily or permanently communicated to bodies, by temporarily or permanently disturbing the equality of their elasticity in different directions.

I. Pressure produces double refraction.—In fluids (gases and liquids) pressure is equally distributed in all directions, which is obviously owing to the facility with which the molecules shift their places. Hence pressure on fluids does not communicate to them the power of double refraction.

In solids, however, matters are far otherwise. Owing to cohesion, the molecules cannot change their relative positions; and, therefore, in this form of matter unequal degrees of tension may exist in different directions: so that pressure may be communicated in any desired direction without being equally or uniformly distributed.

Now a transparent solid, as a well-annealed piece of glass, all of whose parts possess equal elasticity, is a single refractor; but if we subject such a body to the influence of a compressing force, it becomes a double refractor, and acquires neutral and doubly refracting (depolarizing) axes; the former parallel and perpendicular to the direction of pressure, the latter 45° inclined to them. Let us consider for a moment what must be the effect of pressure in any given direction. Suppose a rectangular piece of glass (fig. 20) to be subjected to pressure in the direction A B: the immediate effect will be to urge the contiguous particles nearer together in this direction, and thereby to call into action their repulsive forces. But it will also urge the particles asunder in the direction CD,—that is, in a direction perpendicular to that of the pressure, and thereby to call into operation their attractive forces. Thus then, it is obvious, that a force, which when applied to a solid, causes a condensation in the direction of the force {A B), is attended with dilatation or expansion in a direction perpendicular

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to it {CD). In the first direction the elasticity is a maximum— in the second direction it is a minimum. Incident light polarized in a plane parallel with either of these directions passes through unchanged, and these directions are called the neutral axes. But if it be polarized in a plane inclined 45° to either of these directions (that is, in the direction E F or G H) it is resolved into two systems of waves, one polarized in the direction A B, the other in the direction C D. The directions E F and GH, are, therefore, the doubly refracting or depolarizing axes. But the system polarized in the plane A B, will proceed more slowly (owing to the maximum elasticity in that direction) than the system CD (which is polarized in the direction of the minimum elasticity). Hence, at their emergence, the two systems of waves are in different phases of vibration, but they do not interfere so as to produce colours, owing to the plane of vibration of the one being rectangular or perpendicular to that of the other. When, however, we apply the analyzer, and restore these two rectangular planes to a common plane, interference takes place and colour results.

Let us now take the case of a flexed body. When I bend a cane or other solid, the convex surface is in a state of expansion or dilatation, while the concave surface is compressed. The molecules on the convex surface are urged asunder, and their attractive forces called into operation, while those on the concave surface are pressed together, and their repulsive forces brought into action. Between these two oppositely affected surfaces, there is a neutral line where equilibrium exists, and on both sides of this the degree of strain augments as we recede from the line. Now, if a well annealed, and, therefore, single refracting plate of glass be bent, and examined while in the polariscope, it will be found to have acquired, while in the bent state, double refracting properties. Two sets of coloured fringes are perceived, one on the convex or dilated side of the plate, and the other on the concave or compressed side. Between these two sets of fringes is a black line, indicating the situation where neither compression nor dilatation exists, and where, therefore, double refraction is absent.

Thus then the polariscope becomes a valuable means of detecting the existence of unequal tension or strains in transparent bodies, and Dr. Brewster has suggested its useful application to the determination of the intensity and direction of all the forces which are excited by a superincumbent load in different parts of the arch, ns also the intensity and direction of the compressing and dilating forces which are excited in loaded framings of carpentry. For these purposes, models in glass or copal are to be prepared, and the effects are rendered visible by exposing the models to polarized light. He has likewise constructed a chroviatic dynamometer for measuring the intensities of forces, founded on the facts already stated. It consists of a bundle of narrow and thick plates of glass, fixed at each end in brass caps. Then when any force is applied to a ring in the middle of the plates, the ends being fixed, the plates of glass will be bent, and the force thus produced is measured by the tints that appear on each side of the black line.

By the gradual induration, as well as by the mechanical compression and dilatation of animal jellies, fringes may be produced, as in glass.

2. Unequal heating causes double refraction.—When heat is applied to bodies, it causes them to expand or dilate. If the substance to which the heat is applied be a bad conductor, the part in contact with the heated body becomes hot, and expands before heat is communicated to the neighbouring parts. Hence the bad conductor endeavours to curve, just as when we hear a compound bar of iron and brass, a curvature is induced, owing to the unequal expansile power of these two metals, and as the brass expands more than the iron, the latter forms the inner or concave side of the curved bar, while the brass forms the outer or convex side. On this principle is constructed the compensation balance of a watch.

Glass is a bad conductor of caloric, and when a heated body is applied to it, the part in contact with this becoming hot, expands, but owing to the bad conducting quality of the medium, the surrounding parts not being influenced by the heat, do not expand, but resist the dilatation of the heated portion. In this way, therefore, the immediate effect of heat on one part of a piece of glass, is to put all the surrounding parts into a strained state, one part is expanding, and other parts are resisting the dilatation. When the difference of temperature is extreme, the violence of the strain is such that very thick pieces of glass are sometimes rent asunder.

It is very desirable that we should be acquainted with the precise mechanical condition of the glass thus partially subjected to caloric. A knowledge of this would greatly assist us in comprehending the optical phenomena. But the subject is replete with difficulties. Perhaps, some assistance may be obtained from the following considerations:—

Let A B CD (fig. 21), be a rectanB gular plate of glass, subjected to heat along its edge, A B. This portion of the glass being heated, tends to expand; but on account of its connection with other portions of the glass, cannot do D so without forcing these to participate in its augmented bulk. These, however, owing to the bad conducting power of the glass, retain their original temperature, and consequently refuse to expand, so that the stratum is subjected to compression; that is, it is prevented from acquiring that volume which is natural to it, in this heated state. The central stratum ef, is in a state of dilatation or expansion, owing to its particles being urged asunder by the tendency of the upper stratum, A B, to expand. The resistance offered to the expansion by e /, tends to produce pressure on the lower stratum C D, the particles of which will be urged together. This lower stratum C D, like the upper one A B, will then be in a state of compression. As the tension of e/is sustained at A B and C D, it will tend to send inwards the lateral columns A C and B D, dilating them at the convex portion of the bend, and compressing them at the concave portion. By these strains, therefore, the rectangular plate of glass will assume a figure concave on all its edges.

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It is obvious then, from the unequal states of tension of the different parts of a piece of glass thus partially heated, that it ought to acquire doubly refracting properties, and the polariscope shows that it does so. In this state, the glass exhibits distinct neutral and doubly refracting (depolarizing) axes, the neutral ones being parallel and perpendicular to the direction in which the heat is propagated. The black fringes, sometimes called lines, of no polarization, indicate the neutral axes, or those portions of the glass which are destitute of the property of double refraction.

It deserves especial notice that fringes make their appearance iri the part of the glass most distant from the heated body, before they have received any sensible accession of heat, and which, therefore, must depend on the state of strain into which they are thrown by the effect of the heat on the other parts of the mass, in the way I have already endeavoured to explain.

Dr. Brewster has suggested the construction of two kinds of chromatic thermometers, for measuring changes of temperature by the production of coloured fringes, exhibited by glass plates when exposed to heat; for " every tint in the scale of colours has a corresponding numerical value, which becomes a correct measure of the temperature of the fluid." In the one instrument, the tints originate immediately from the changes of temperature; in the other, they are produced by the difference of pressures upon the glass, occasioned by the difference of expansions arising from changes of temperature. I must refer you to his paper in the Philosophical Transactions for 1816, for details respecting them.

3. Unequal cooling causes double refraction.—If a piece of

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