DALY. — AMPHIBOLES AND PYROXENES. 317 



rock-forming pyroxenes and amphiboles which, owing to the small size 

 of the crystals or their very friable nature, it is extremely difficult, if 

 not impossible, to cut in the directions necessary to obtain p and 2 V. 

 On the other hand, good cleavage flakes are almost always to be had, and 

 it is by the use of these that I propose the following method of finding 

 the extinction on the clinopinacoid of an amphibole or pyroxene. 



A perfectly flat cleavage piece, thick enough to give the greatest pos- 

 sible definiteness to the position of extinction and showing clearly marked 

 cleavage cracks, is laid on an object-glass with the broadest face down. 

 It is then carefully mounted on the stage of a two-circle FedorofF table. 

 With the vertical circle set at zero, the stage of the table is turned so 

 as to bring the cleavage cracks of the specimen into a position parallel 

 to the axis of the vertical circle.* This axis should be parallel to the 

 principal section of either polarizer or analyzer. By taking the average 

 of a number of good readings, the extinction angle is now obtained. 

 Following this operation, the vertical circle is turned in such a direction 

 that the plane of symmetry of the crystal is more oblique to the polarized 

 ray and by an angle nearly approaching that at which the specimen 

 would begin to slide on the object glass. I have found that 15° is a con- 

 venient amount of rotation, and that angle will be used in the following 

 discussion. Extinction is again read in this new orientation with the 

 greatest possible care. 



We have in this way determined two special angles of extinction (0' 

 and 6"), corresponding to two jjlanes in the vertical zone, which are at 

 different angles (C and C" = C + 15°) to (010). It is now possible 

 in a simple way to eliminate a and 13, and thus permit of the determina- 

 tion of p directly from 6' and 6". To this end, we have the following 

 series of transformations, which I owe to Mr. J. K. Whittemore of 

 Harvard University. 



Substituting in (2) the special values of and C, we have, 



- ., (tan a — tan B) cos C" 



(3) tan 2 6' = ^, "^ ^-^7/ ; and 



^ ^ 1 -f tan a tan )8 cos^ 6" ' 



(4) tan 2 6 



Then 



(5) 



(tan a — tan ft) cos C 



1 + tan a tan /3 cos" C" 



tan 2 p 1 + tan a tan /? cos'^ C" 



tan 2 (^' ~ (1 -f tan a tan /3) cos C 



* The Nachet form of the table or the simpler model by Fuess is best for the 

 purpose. 



