﻿K S. Dana — Crystallization of Native Copper. 423 





axis with the edge of the plane normal to this diagonal, and 

 that of the macrodiagonal axis is the twinning-axis, normal to 

 the twinning-plane. 



With respect to these axes the isometric forms met with on 

 these copper twins group themselves as in the following table; 

 the different forms into which the single isometric form sepa- 

 rates are indicated, as in the preceding table, by subscript 

 accents. 





Isometric. 



Ortho- 

 rhombic. 



Isometric. 



Ortho- 

 rhombic. 



Cube 



a 



j 100 

 1 010 



Ill Octahedron 



111 



jlll 

 / 111 



014 

 014 





a, 



001 



012 





fill 



212 



Dodecahedron 



d 



110 

 110 



011 

 100 



0i 



Jill 

 ]111 



[ill 



212 

 212 

 212 





dn 



j 101 



103 





3111 



•jlll 



010 





I 011 



103 



On 



010 





dm 



j 101 



121 











I 011 



121 













etc. 











Tetrahexahedrons 



k 



520 



377 



h 



410 



355 





h 



520 



133 



fa 



410 



533 





Ku 



502 



539 



h n 



401 



436 





"'in 



502 



571 



fan 



401 



452 





«TV 



205 

 etc. 



218 



fay 



1 



104 

 stc. 



157 





e 



210 



133 



e n 



201 



214 





6 t 



210 



311 



6jy 



201 



102 



230 

 133 



It will be seen from the table that the brachypinacoid 

 (010, i-i), is formed by one of the octahedral planes (o n 111), the 

 macropinacoid (100, i-l) by a dodecahedral plane (d I} 110); 

 also one of the planes of the tetrahexahedron e is a prism 



(em 201 = 230, i-f). 



All of the planes given in the above list play an important 

 part in these twins. The transformation from the isometric 

 symbol (hjiji^) to that of the corresponding orthorhombic form 

 (P1P2P3) is easily accomplished by aid of the equations : 



p 1 =hi — h 2 p^=h 1 +h 2 —h 3 p3=hi+h 2 + 2h 3 



The way in which these twin crystals are developed will be 

 clear from the following descriptions. One specimen of rare 

 beauty and perfection consists of a group of elongated pris- 

 matic forms, the longest about 1J inches in length. In each of 

 them the extremity is formed by a smooth and symmetrically 

 developed pyramid of the form just described, while the 

 elongation in the direction of the diagonal of the twinning-face 

 is somewhat obscure. Figure 33 represents* one of the 



* In the drawing of figures 33, 34, 35, 3(5, 37, 38, 51, 52, 53, 54, the writer has 

 had the assistance of Mr. J. H. Emerton. 



