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.