Abstract
Before treating of the subject before me, I must describe its history. At a soirée of the Royal Society on April 25, 1877, I showed a number of specimens illustrating a new class of optical properties, applicable to the identification of minerals. These greatly interested the late Sir G. G. Stokes, Bart., and led to a considerable amount of correspondence between us ; and he communicated a paper to the Royal Society on the mathematical part of the subject, and I sent a short one on my apparatus and observations. This was admitted to be very imperfect, since the crystals examined, though showing the general facts perfectly well, had not been cut so as to be suitable for such quantitative measurements as could be compared with Stokes's theoretical determinations.

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