to it (CD). In the first direction the elasticity is a maximumin 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 C D (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, as 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 chro

matic 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 C D (fig. 21), be a rectanBgular 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 f, 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 ef 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.

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 in 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

hot glass of uniform temperature be unequally cooled, as by placing one of its edges on a cold mass of iron, it acquires doubly refracting properties, and when examined by polarized light, presents fringes, &c. similar to those observed in glass unequally heated. It is obvious, however, that as the physical condition produced by cold is diametrically opposite to that caused by heat, so the structure of the corresponding parts of the two glasses (the one which has been cooled, and the other which has been heated) must be opposite.

4. Unannealed glass is a double refractor.-If glass be suddenly cooled after having been melted, it possesses certain remarkable properties, which unfit it for ordinary use. Sometimes it splits or flies to pieces in the act of cooling; or if it fail to do this, a very moderate change of temperature, a slight external force, a scratch, or a slight fracture, is sufficient to cause it to crack and fly to pieces. The glass tears called Rupert's drops, or hand-crackers, and the proofs, or philosophical phials, are familiar illustrations of this kind of glass. In order to prevent it acquiring this remarkable condition, glass, after being fashioned, is submitted to the process called annealing, that is to very slow cooling in the annealing oven or lier. Glass which has undergone this process is said to be annealed, while that which has not is termed unannealed. But the so-called unannealed glasses sold by the opticians are in fact annealed glasses, which have been reheated until they begin to soften, then cooled by placing them on the ashes beneath the furnace, and afterwards ground and polished.

The optical properties of unannealed glass are very remarkable. To comprehend them let us consider the mechanical condition of the glass. When a mass of red-hot and soft glass is exposed to a cool air, its external portion becomes cold and rigid, while the inner parts are still hot and soft. After a short time, however, the latter solidify and cool, but are prevented from contracting themselves into the smaller bulk which is natural to them in their cooled state, by the rigid crust, which acts like an arch or vault, and keeps them distended, but which is to a certain extent strained and drawn somewhat inwards by the tension exercised on it by the internal parts. It is obvious then that the different parts of a mass of unannealed glass are unequally and differently strained; the internal being in a state of distention or dilatation, the external in that of compression. So that the state of the different parts, and the distribution of the forces, will be almost exactly similar to those already described, in the case of annealed glass which has been unequally heated. "The analogy between the cases," says Sir John Herschel, "would be complete, if, instead of supposing the

annealed plate heated at one edge only, the heat were applied to all the four simultaneously, by surrounding it with a frame of hot iron."

There is one very important point in reference to these unannealed glasses, to which I must beg your attention; I refer now to the circumstance that in them, the polarizing (doubly refracting) structure depends entirely on the external form of the glass plate, and on the mode of aggregation of its particles. This will be very obvious by observing the different shapes of the fringes respectively presented by square, circular, oval, rectangular, and other shaped plates. The circular and square plates have only one axis of [no] double refraction; whereas the oval and rectangular plates have two axes. By dividing and subdividing these plates, the doubly refractive property is not only greatly diminished, but sometimes even destroyed, if the portion be very small. Moreover, it is distributed in a new manner, according to the shape of the fragment. The dissected unannealed glasses, sold in the opticians' shops, beautifully illustrate the dependence of the form of the coloured fringes on the external shape of the glass. Thus the pattern produced by one circular piece of unannealed glass, is very different to that of a circle formed by joining four segments.

In these particulars, the unannealed plates of glass differ very widely from doubly refracting crystals. The fringes and colours, presented by the latter, are unaltered by the changes we may effect in the external form of the crystal-the smallest fragment producing the same system of fringes as the largest; and, provided the thickness remains the same, the polarizing force suffers no diminution by the reduction in size.

We are then constrained to infer that the optical properties of crystals are those of their integrant molecules; while those of the unannealed glasses depend on the mode of arrangement of the molecules, and on the external form of the mass.

The effects produced by superposing similarly shaped pieces of unannealed glass are striking, and, at first, surprising; but, on consideration, may be easily understood. If they be symmetrically superposed, similar points being laid together, the tints will be equal to the sum of the separate tints :-but, if superposed crosswise, the resulting tints will be the difference of the separate tints. This may be conveniently shown by causing an unannealed glass bar to rotate in front of another unannealed bar.

Applications. These facts respecting the properties of unannealed or imperfectly annealed glasses, admit of some valuable practical applications. To the optician it is of the highest importance that the glass, of which lenses and prisms are made, should possess uniform density, and be free from all defects