822 PROCEEDINGS OP THE AMERICAN ACADEMY. 



tinction was read in this position against the cleavage trace, at an angle 

 with the latter of just 20° (average of ten readings). Substituting this 

 value and the value of extinction on (110) in equation (12), I obtained 

 15° 3' as the corresponding value of p. This very close correspondence 

 with the determination of p by the use of the oriented sections is not 

 less than accidental, but the example clearly shows that cleavage pieces 

 may be made to yield information concerning the value of extinction on 

 the plane of symmetry as useful for practical purposes as that derived 

 from a section in that plane. 



A second example was found in a hornblende, which was given me for 

 examination by Professor J. E. Wolff of Harvard University. It occurs 

 associated with much pyroxene and biotite in the classic coarse theralite 

 of Theralite Peak in the Crazy Mountains. Optical study of the horn- 

 blende in the numerous slides which have been made of the rock is 

 difficult, on account of the scarcity of the mineral in large individuals. 

 It would be quite impossible to make oriented sections even if the grains 

 could be freed from the much more abundant pyroxene, with which they 

 are commonly intergrown. Apart from the absolute small amount of 

 the hornblende present in the rock and from the fact of intergrowth with 

 another silicate, this seemed to be a particularly unfavorable case for the 

 application of our method, in that the absorption is strong, and errors in 

 6' and 0" should appear rather larger than characterize readings on such 

 an amphibole as Zillerthal actinolite, for example. The rock was pul- 

 verized and, after some search, suitable cleavage pieces were discovered 

 in the powder, and manipulated as in the last example. This time, the 

 curve of extinctions was examined on four points besides that at the 

 position (010); namely, at the positions, 42:^°, 47J°, 771°, and 82^°. 

 Extinctions were read for these at respective values of 29°, 29° 30', 31°, 

 and 30°. The cleavage position gave 34°. The average value of p now 

 determined by substituting the readings in the general equation is 28° 5'. 

 Now, I was fortunate enough to find in one of the thin sections a longi- 

 tudinal section of the hornblende, evidently in the vertical zone since the 

 cleavage cracks were rigorously parallel to one another, and very near 

 the plane (010), inasmuch as there was practically no trace of a hyper- 

 bola in convergent light. Careful reading of the extinction afforded 

 an astonishingly close approximation to the value of p just determined, 

 viz. 28°. It is possible that the true angle is half a degree or more 

 greater or less than that, but the calculated value is in any case near that 

 observed in* the rock -slide. It may be noted in passing that this is a 

 rather remarkable hornblende, from the fact that its extinction angle is 



