ON THE OPTICAL CHARACTERS OF THE VERTICAL 

 ZONE OF AMPHIBOLES AND PYROXENES: AND ON 

 A NEW METHOD OF DETERMINING THE EXTINC- 

 TION ANGLES OF THESE MINERALS BY MEANS OF 

 CLEAVAGE PIECES. 



By K. A. Daly. 



Presented by John E. Wolff, December 14, 1898. Received December 15, 1898. 



It is evident that, in an optical examination of monoclinic minerals 

 with coincident optical and crystallographic planes of symmetry, the 

 angle of extinction on (010) is a highly important datum, for it is indis- 

 pensable to a knowledge of the shape and orientation of the ellipsoid of 

 elasticity. The difficulty of preparing sections in the plane of symmetry 

 of amphiboles and pyroxenes, and the practical impossibility of doing so 

 in the case of very small crystals, lead the student of these species to 

 revert to those good natural sections, cleavage plates, and inquire as to 

 the relation subsisting between the extinction on sections parallel to (010) 

 and that on prismatic cleavage flakes. This relation is not simple, and 

 it was long ago demonstrated that, accepting Fresnel's optical theorem, 

 the extinction on (110) is dependent in a complex way on the angle of 

 extinction on (010) and on the optical angle. Michel Levy made it clear 

 that, for pyroxenes, the extinction on (110) would always be less than 

 on (OlO), since the latter is the maximum possible value of extinction 

 read against cleavage cracks on any section in the vertical zone. On 

 the otlier hand, it was shown for the negative amphiboles that among 

 the infinite number of possible sections made by a plane revolving in 

 the vertical zone from (010) to (100), there is one which has the highest 

 value of extinction in that zone, and that this value decreases as the 

 revolving plane moves toward (010) or (100).* It is interesting to 

 determine whether an amphibole with this property of showing a max- 

 imum of extinction for positions of the rotating plane between (010) 

 and (100) could have an extinction-angle on (110) greater than that on 



* Fouque and Michel Levy, Mineralogie Micrographique, p. 368. 



