of Minerals in the Thin Section. 323 



by Biot* by which the directions of extinction for any section 

 of a birefracting mineral can be found. Some ten years before 

 Biot announced this general rule, Mains f had found that the 

 light waves emerging from a calcite rhomb were plane polar- 

 ized and that for any given section of calcite the lines of 

 extinction were parallel and at right angles with the trace of 

 the plane containing the optic axis and the normal to the sec- 

 tion ; in other words, the orthogonal projection of the optic 

 axis on any given section of a uniaxial mineral determines its 

 lines of extinction which are parallel with and normal to this 

 projection line. By modifying the wording of this rule 

 slightly, it is possible, as Biot proved experimentally and Fres- 

 nel^: demonstrated theoretically, to make it of general appli- 

 cation to all birefracting substances; thus, the directions of 

 extinction of a biaxial mineral § cut after any section are par- 

 allel to the traces, on that section, of the planes bisecting the 

 angles between the two planes containing the normal to the 

 section and the optic axes (or optic binormals) ; in other words, 

 the lines bisecting the angles between the lines of orthogonal 

 projection of the optic binormals on any given section of a 

 biaxial mineral are the directions of extinction for that section 

 for the particular color of light employed. It should be noted 

 that this rule applies to optic phenomena within the crystal 

 itself, and that for oblique incidence of light, as in convergent 

 polarized light, the apparent angles observed in air must be 

 reduced to true angles by means of the average refractive 

 index of the mineral in question ; by the formula sin V= 



— ^ — , E being the observed angle, Y the required true angle, 



and /3 the mean refractive index of the mineral. 



The above methods of projection, together with the Biot- 

 Fresnel rule of construction for finding the directions of 

 extinction on any plane, constitute the basis on which several 

 of the methods described below rest. With practice, these 

 projections become working models for the observer and aid 

 him very materially in grasping and picturing the optical 

 phenomena presented by different minerals under varying 

 conditions. 



* Biot, J. B., Mem. de l'Acad. de l'Inst. de France, iii, 228, 1820. 



f Malus, E. L. , Theorie de la double refraction de la lumiere dans les sub- 

 stances cristallisees, Mem. pres a l'Inst. Sc. math, et phys., ii, 303, 1811. 



^Fresnel, Second Memoire sur la double refraction, Pogg. Ann., xxiii, 

 542, 1831. 



§ The uniaxial minerals may for the moment be considered the limiting 

 case of biaxial minerals for which 2V = 0. 



