314 PROCEEDINGS OP THE AMERICAN ACADEMY. 



all amphiboles so far as known, except pargasite and a very few other 

 varieties ; with these exceptions, each has a maximum in a section far 

 removed from the plane of symmetry. A striking example is to be found 

 in an interesting amphibole rich in ferrous oxide from Philipstad, Sweden. 

 It has a pronounced zonal structure ; all the zones extinguish together in 

 (010) at 15° 9', but at different angles on (110), the latter varying from 

 21° to 17°, corresponding to different and unusually small optic angles 

 in the respective zones of from 50° to 60°. 



Plates I., II., and III. represent diagrammatically the variation which 

 may be observed in the behavior of certain negative amphiboles that 

 have such maxima of extinction, — namely, those with optical angles of 

 50°, 60°, 70°, and 80°, and each characterized by extinctions on (010) 

 of 10° (Plate I.), 15° (Plate IL), and 20° (Plate III.). The abscissa rep- 

 resents the angle of rotation of the section out of the plane of symmetry, 

 the ordinate indicates the corresponding angle of extinction. Arrow- 

 heads show which plane of the vertical zone possesses the maximum 

 extinction peculiar to each curve, and also the value of that maximum. 

 The diagrams clearly show that the maximum extinction observable in a 

 rock-slide examined for one of these amphiboles would be far from repre- 

 senting the extinction-angle on (010), and data regarding extinctions and 

 pleochroism derived from the study of thin sections would be worthless, if 

 not controlled by this principle. For the sake of comparison, the anal- 

 ogous curves for amphiboles with 2 V= 90° and p respectively equal to 

 10°, 15°, and 20°, appear in the plates. It will be seen that there is no 

 position of maximum extinction between (010) and (100).* 



Now, among the i^ossible positions of the movable plane, there is one 

 which surpasses all others in interest except that of the plane of sym- 



(010) and (100) just equal to that on (010) may be found from the following un- 

 publislied formula by Dr. A. C. Lane of Houghton, Mich. : — 



1 — cos- p — cos'2 V 



sin X — — — — > 



cos- V — cos- p 



where x is the angle made with (100) hy the required section. 



* It is characteristic of all the curves, that the angle of extinction changes very 

 slowly in passing out from (010). This is important in the study of rock-slides, 

 since a section may be removed several degrees (even 30° when the optical angle is 

 large) out of the plane of symmetry, and but small error would be made in using 

 its value of extinction as equivalent to that on (010). It would, in that case, be 

 only necessary to be sure that the section is really in tlie vertical zone, as ascer- 

 tained by the parallelism of cleavage cracks. That it is near tlie position (010) 

 can, of course, be proved by the absence of a well defined hyperbola in con- 

 vergent light. 



