Mr. L. Fletcher's Crystallographic Notes. 185 



by talc. A crystal presenting the habit shown in fig. 6, was 

 found to be a spinel-like twin of the combination (10 0) 

 (3 10) (7 4 0) shortened along that trigonal axis which is at 

 right angles to the twin-plane. The following are some of the 

 angles obtained: — 





Observed. 



Calculated. 



100.310 . 



. 18° 24' : 18° 33' : 18° 16' 

 19° 27' : 18° 51' 



18° 26' 



740.470 . 



29° 59' : 30° 14' 



30° 30' 



740.310 . 



. 11° 48' : 11° 30' : 11° 0' 



11° 19' 



301.310 . 



26° 4' 



25° 50J 



074.301 . 



81° 10' about 



80° 58' 



We have seen above that both these new forms also occur 

 on native copper. 



III. Gold. 



The forms already described as occurring on native gold 

 are : — 



(10 0) (110) (111) (210) (410) (211) 

 (311)" (811) (421) (19 11 1). 



The form (3 2 1) has been observed by Lang* on an artificial 

 crystal. The forms (4 10) (81 1) were first observed by 

 Lewis f. The forms (2 1 1), (4 2 1), (1 9 11 1)% have not 

 been observed on any crystals in this collection. To the list 

 of observed forms must now be added (3 1 0). 



A specimen from Beresowsk in the Urals presents the 

 habit shown in fig. 7, and proves to be a spinel-like twin of 

 the combination (310) (10 0) having no reentrant angles. 

 Eight different angles between a cube-face and an adjacent 

 face of the tetrakishexahedron gave values varying between 

 16° and 19°, and having 18° for mean, the calculated angle 

 being 18° 26'; 310.310, observed 24 £°, calculated 25° 50^'. 



Some crystal-sprays from various localities in the Philip- 

 pines proved to be composed of small crystals presenting the 

 known form (3 1 1) and occasionally twinned about the octa- 

 hedron-plane. 



IY. Bismuth. 



The crystals of this mineral are generally very indistinct. 

 The following forms are given by Miller : — (1 11) cleavage, 



* Philosophical Magazine, 1863, vol. xxv. p. 435. 

 t Ibid. 1877, vol. iii. p. 456. 



X See a paper by Helmhacker in Tschermak, Mineral, Mitiheil, 1877, 

 p. 12. 



