The following laws were discovered by Stokes: 

(1) If one of the crystalline plates be turned round in its own plane, without alteration of the angle of incidence, the peculiar reflection vanishes twice in a revolution, viz., when the plane of incidence coincides with the plane of symmetry of the crystal. [Shown.]

    (2) As the angle of incidence is increased, the reflected light
    becomes brighter and rises in refrangibility. [Shown.]

    (3) The colors are not due to absorption, the transmitted light
    being strictly complementary to the reflected.

(4) The colored light is not polarized.  It is produced indifferently, whether the incident light be common light or light polarized in any plane, and is seen whether the reflected light be viewed directly or through a Nicol’s prism turned in any way. [Shown.]

(5) The spectrum of the reflected light is frequently found to consist almost entirely of a comparatively narrow band.  When the angle of incidence is increased, the band moves in the direction of increasing refrangibility, and at the same time increases rapidly in width.  In many cases the reflection appears to be almost total.

[Illustration:  FIG. 1 GENERAL SCHEME
               FIG. 2 DETAIL OF LAZY-TONGS]

In order to project these phenomena a crystal is prepared by cementing a smooth face to a strip of glass whose sides are not quite parallel.  The white reflection from the anterior face of the glass can then be separated from the real subject of the experiment.

A very remarkable feature in the reflected light remains to be noticed.  If the angle of incidence be small, and if the incident light be polarized in or perpendicularly to the plane of incidence, the reflected light is polarized in the opposite manner. [Shown.]

Similar phenomena, except that the reflection is white, are exhibited by crystals prepared in a manner described by Madan.  If the crystal be heated beyond a certain point the peculiar reflection disappears, but returns upon cooling. [Shown.]

In all these cases there can be little doubt that the reflection takes place at twin surfaces, the theory of such reflection (Phil.  Mag., Sept., 1888) reproducing with remarkable exactness most of the features above described.  In order to explain the vigor and purity of the color reflected in certain crystals, it is necessary to suppose that there are a considerable number of twin surfaces disposed at approximate equal intervals.  At each angle of incidence there would be a particular wave length for which the phases of the several reflections are in agreement.  The selection of light of a particular wave length would thus take place upon the same principle as in diffraction spectra, and might reach a high degree of perfection.

In illustration of this explanation an acoustical analogue is exhibited.  The successive twin planes are imitated by parallel and equidistant disks of muslin (Figs. 1 and 2) stretched upon brass rings and mounted (with the aid of three lazy-tongs arrangements) so that there is but one degree of freedom to move, and that of such a character as to vary the interval between the disks without disturbing their equidistance and parallelism.