Of other papers in which he dealt with this and kindred branches of physics may be mentioned "Observations with a Rigid Spectroscope," "Heating of a Disc by Rapid Motion in Vacuo," "Thermal Equilibrium in an Enclosure Containing Matter in Visible Motion," and "Internal Radiation in Uniaxal Crystals."
In Biot's earlier experiments the beam of light employed was nearly parallel: the phenomena of rings and brushes that are seen with a conical pencil of light were discovered by Sir David Brewster in the case of uniaxal crystals in 1813 and in that of biaxal crystals in 1815.
(Reference should be made to the article Crystallography for illustrations, and for applications of these phenomena to the determination of crystal form.) With an uniaxal plate perpendicular to the optic axis, the curves of constant retardation are concentric circles and the lines of like polarization are the radii: thus with polarizer and analyser regulated for extinction, the pattern consists of a series of bright and dark circles interrupted by a black cross with its arms parallel to the planes of polarization and analysation.
Then with an uniaxal plate perpendicular to the optic axis, the black cross is replaced by two lines, on crossing which the rings are discontinuous, expansion or contraction occurring in the quadrants that contain the axis of the quarter-wave plate, according as the crystal is positive or negative.
This consists of two plates of an uniaxal crystal of equal thickness, cut at the same inclination of about 45° to the optic axis and superposed with their principal planes at right angles.
Again, a system of rings, similar to those of an uniaxal plate perpendicular to the axis, may be produced with a glass cylinder by transmitting heat from its surface to its axes by immersion in heated oil, and glass that has been raised to a red heat and then cooled rapidly at its edges gives in polarized light an interference pattern of a regular form dependent upon the shape of the contour.
In general a stream of plane-polarized light undergoes no change in traversing a plate of an uniaxal crystal in the direction of its axis, and when the emergent stream is analysed, the light, if originally white, is found to be colourless and to be extinguished when the polarizer and analyser are crossed.
A similar rotary property is possessed by other uniaxal crystals, such as cinnabar and the thiosulphates of potassium, lead and calcium, and as H.
Airy extended Fresnel's hypothesis to directions inclined to the axis of uniaxal crystals by assuming that in any such direction the two waves, that can be propagated without alteration of their state of polarization, are oppositely elliptically polarized with their planes of maximum polarization parallel and perpendicular to the principal plane of the wave, these becoming practically plane polarized at a small inclination to the optic axis.
As regards the course - of the streams on refraction into the crystal, it is found that it is determined by the Huygenian law (see Refraction, § Double); as, however, the two streams in the direction of the axis have different speeds, the spherical and the spheroidal sheets of the wavesurface do not touch as in the case of inactive uniaxal crystals.
This refractive index should be equal to the greatest index of the plate, and with a biaxal plate the mean axis of optical symmetry should be parallel to its faces and in the normal section of the prisms, while with an uniaxal plate the optic axis should be in a plane perpendicular to this normal section.