English translation of “Mémoire sur la double réfraction que les rayons lumineux éprouvent en traversant les aiguilles de cristal de roche suivant les directions parallèles à l’axe” (9 December 1822), in which Fresnel coins the terms linear polarization, circular polarization, and elliptical polarization, and reports a direct refraction experiment showing that optical rotation is circular birefringence. There were two versions of the experiment. In the first version, one extremely obtuse isosceles quartz prism was approximately achromatized by two glass half-prisms. In the second version, for improved achromatism and a wider separation of the two images, the two glass half-prisms were replaced by quartz half-prisms whose chirality was opposite to that of the first prism.