On the laws of polarization and double refraction in regularly crystal­lized bodies. By David Brewster, LL. D. F. R. S. and Edin. In a letter to the Right Hon. Sir Joseph Banks, Bart. G. C. B. P. R. S

Abstract

In the different inquiries which the author has already laid before this Society, his attention was often directed to the phenomena of regular crystals; but he only lately succeeded in reducing under a general principle all those complex appearances which result from the combined action of more than one axis of double refraction. In this paper Dr. Brewster gives a general view of the present state of our knowledge respecting the double refraction and polarization of light, and afterwards traces the steps which led him to the discovery of the general law. He began his researches by the examination of 165 crystals, in 145 of which he discovered the property of double refraction. In 80 he was able to ascertain whether they had one or more axes; and by examining the tints which they exhibited at va­rious angular distances from the axes, whence the forces emanate, he has been led to a general principle, which embraces all the phenomena and extends to the most complex as well as to the most simple de­velopment of the polarizing forces. This general principle, says Dr. Brewster, is in no respect an empyrical expression of the facts which it represents, nor is it supported by any empyrical data. Founded on the principles of mechanics, it is a law rigorously physical, by which we are enabled to calculate all the tints of the coloured rings, and all the phenomena of double refraction, with as much accuracy as we can compute the motions of the heavenly bodies. The faculty of depolarization, explained by the author in a former paper, has been considered as sufficient indication of two separate images; and upon this principle it has been stated that all crystals are doubly refractive whose primitive form is neither the cube nor the regular octohedron: but this is incorrect; for some of these crystals possess a doubly refracting structure in a high degree. Ad­mitting the statement, however, it could not have been used as a rule for determining whether a crystal refracts doubly or singly; for it is more difficult to detect the primitive form than to examine the optical properties. Tungstate of lime, for instance, would have been reckoned a crystal without double refraction, when Haüy believed its primitive form to be the cube, although it is highly doubly refractive.