found that the stratum was visibly thicker in those crystals which showed red colour than in those which showed blue. He concluded that ‘the seat of the coloration is certainly a thin twinned stratum’ (that is to say, a homogeneous portion of crystal between a twinning and a counter-twinning), and found that ‘a single twin-plane does not show anything of the kind.’ § 45. A year or two later Lord Rayleigh entered on the subject with an exhaustive mathematical investigation of the reflection of light at a twin-plane of a crystal (_Philosophical Magazine_, September, 1888), by the application of which, in a second paper ‘On the remarkable phenomenon of Crystalline Reflection described by Prof. Stokes,’ published in the same number of the _Philosophical Magazine_, he gave what seems certainly the true explanation of the results of Sir George Stokes’ experimental analysis of these beautiful phenomena. He came very decidedly to the conclusion that the selective quality of the iridescent portion of the crystal, in virtue of which it reflects almost totally light nearly of one particular wave-length for one particular direction of incidence (on which the brilliance of the coloration depends), cannot be due to merely a single twin-stratum, but that it essentially is due to a considerable number of parallel twin-strata at nearly equal distances. The light reflected by this complex stratum is, for any particular direction of incident and reflected ray, chiefly that of which the wave-length is equal to twice the length of the period of the twinning and counter-twinning, on a line drawn through the stratum in the direction of either the incident or the reflected ray.