286 Wright — Optical Character of Birefr acting Minerals. 



The figures 1-6, used to illustrate the methods, were obtained 

 in part by graphical and in part by mathematical means based 

 on the law of Fresnel, that the planes of polarization for rays 

 traveling in any direction bisect the angles between the planes 

 containing the ray and the two optic axes respectively ; in 

 other words, the directions of extinction for any face bisect 

 the angles between the projections of the optic axes on the face. 



Plates cut perpendicular to the acute hisectrix. 



For birefracting minerals in which 2E is less than 80°, the 

 methods ordinarily described in text-books are applicable and 

 satisfactory. Both optic axes appear then in the held, and the 

 optical character can be ascertained in convergent polarized 

 light by observing the change in position of the lemniscatic 

 interference curves in alternate quadrants on the insertion of a 

 quartz wedge or a plate showing the interference-color red of 

 the first order, or a quarter-undulation mica plate. The 

 numerical value of 2E can also be measured on the same sec- 

 tion by the Bertrand-Mallard* method described below. For 

 minerals whose 2E is greater than 80°, a method described by 

 Michel Levyf for determining whether the section is perpen- 

 dicular to the obtuse or the acute bisectrix can be used to 

 advantage. It consists in observing the angle of revolution of 

 the stage from the position where the black achromatic curves 

 of the interference figure form across to that at which they are 

 tangent to a given circle (usually field of the microscope). 

 From this angle 2E can be determined, and from it in turn 

 the true optic axial angle (2V), if the medium index of refrac- 

 tion of the substance be known. 



It can be proved both mathematically and graphically that 

 the dark achromatic hyperbolas, which form during the revolu- 

 tion of the stage, pass through the traces of the optic axes and 

 recede from the field along the diagonals of the principal 

 planes of the nicols. ' Practically, the course of procedure is to 

 find a plate cut perpendicular to the bisectrix, to record the 

 angle of revolution of the stage from the point where the dark 

 hyperbolas intersect to that at which they are tangent to a given 

 circle within the field of vision. From this angle the corre- 

 sponding axial angle in air can be obtained by using fig. la, 

 provided the Mallard constant of the microscope has been pre- 

 viously determined. If the medium refractive index of the 

 mineral is also given, it is possible to convert 2E into 2V by 

 means of fig. lb. 



* E. Bertrand in Mallard, Miner, physique, 11, 418. E. Mallard, Sur la 

 mesure de l'angle des axes optiques. Bull. Soc. miner., 1882, page 77 et seq. 

 f Michel Levy, Mineraux des Roches, 94-95. 



