450 PROCEEDINGS OF THE AMERICAN ACADEMY. 



on (120), the radial zone containing the forms v, r, and R is, in twin 

 position, almost coincident in direction with the positive orthodome 

 zone, and the three forms named correspond in position to the domes 

 w, u, and y. 



Twinned on m (120), 



w (101) 



v (T22) twin 



u (201) 



r (T21) twin 



y (401) 



R (241) twin 



If on the other hand the twinning is on (320), the above-named 

 pyramid zone occupies in twin position nearly the same direction as 

 before, but the forms correspond to the negative domes f and e. 



Twinned on F (320), 



The same relation exists for twinning on (120) between the pyra- 

 mids t (122) and x (121) and the domes f and e : and for twinning on 

 (320) between t and x and the domes w and u. Hence in twinned 

 crystals any of these pairs of faces usually appears as a single face, 

 which, however, reflects a double or (owing to vicinals) a multiple 

 signal. The face can, however, sometimes be seen to be made up of two 

 very slightly inclined portions separated by an oblique line, the trace 

 of the composition face v (Figures 8 and 9). 



The measurements obtained on twinned crystals were too variable to 

 decide between the two laws where the angular differences were so 

 slight ; but it was found that the pyramid series v, r, and R occurred 

 repeatedly in twin position with the dome series w, u, and y, and since 

 the negative dome corresponding to y and the positive pyramid corre- 

 sponding to R were not found on our crystals and are not known for 

 the mineral, it seems necessary to conclude that the twinning is on 

 the first law or m (120). 



A second case of approximate superposition of zones by twinning is 

 in the case of the radial zone containing the pyramids £, s, 8, /a, q, and Y, 



