The dispersion of double refraction in relation to crystal structure

In a previous communication, the writer discussed the double refraction of a medium composed of similar particles arranged in rectangular order, the results being applied especially to the effects produced in colloidal solutions by mechanical stress and by a magnetic field; the present paper is the discussion of a similar problem, using a simpler method of procedure suggested by Professor Larmor. The object is to investigate to what extent it is possible to consider double refraction, whether produced artificially or occurring in natural crystals, as due simply to an æolotropic distribution of similar particles; the questions which arise when one considers whether the æolotropy occurs naturally or is produced by the action of mechanical, electric, or magnetic force are not specially considered, but the various cases are classified in the first section. In the next sections we consider a medium composed of a homogeneous assemblage of optically isotropic molecules and obtain an expression giving the dispersion of the double refraction. This is applied first to artificial double refraction produced by mechanical stress and by an electric field; then on the same basis the dispersion in quartz is examined. Certain divergences in natural crystals and especially such anomalous cases as apophylite and vesuvian lead to an extension of the theory. This is, briefly, an æolotropic distribution of optically æolotropic molecules, each of which disperses regularly; it is examined first in relation to uniaxal crystals and finally in general for biaxal crystals, and is found to contain the possibility of all the varieties of dispersion of double refraction which occur in natural crystals.