Mr. L. Fletcher's Crystaltographic Notes. 291 



images are perfectly smooth and bright, and remarkably dif- 

 ferent in aspect from the two dull and striated faces o o 2 . 



A further example is presented by a specimen (probably 

 from the Trevannance mine, St. Agnes) shown in fig. 12, 

 which the symmetry to the combination-plane and the extreme 

 difference between the smooth and the deeply-striated tetra- 

 hedra render most convincing. The angle between these 

 striations is so very definite that it can be measured with fair 

 accuracy by means of a microscope; it Avas determined to be 

 120f°, the angle calculated according to Naumann's law 

 being 120° 28', and according to Haidinger's law 119° 31 / . 



Finally, we may refer to fig. 8, representing a Cornwall 

 specimen (now in the Museum) figured in 1825 by Haidinger 

 himself in his memoir on the Regular Composition of Crys- 

 tallised Bodies. Here the predominant form of each individual 

 is a hemiscalenohedron ; and this in each pair is symmetrically 

 disposed to the plane of composition. Although this speci- 

 men is symmetrical in its habit, the planes s are so striated 

 and rounded that it was found impossible to assign to them 

 a definite symbol; they lie, however, in the zone defined by 

 the symbol [112], and approximate to {312}. 



We conclude, therefore, that there is no doubt of the actual 

 existence of a kind of twin-growth which it is not possible to 

 represent by a single rotation through two right angles from a 

 position of parallel orientation of one of the individuals to the 

 other — that for the representation of this growth an additional 

 rotation is requisite, but that the simplest mode of represen- 

 tation is the one which regards the two individuals as symme- 

 trical to a plane. 



EXPLANATION OF PLATE VI. 

 (To accentuate the differences in twin-growths according to the laws of 

 Haidinger and Naumann, figs. 1-7 are drawn for a parametral angle 42^° 

 instead of 44° 34|'.) 



Fig. 1. Stereographic projection of the poles of {ll l}, and of the same 



twinned ahout T T, the normal to (101). 

 Fig. 2. The octahedron abed* py 8 {ill}. 



Fig. 3. The octahedron a x b x e x a\ * 1 P 1 y x S 1 {l 1 l}, parallel to the last. 

 Fig. 4. The same turned through two right angles round T T the normal 



to (1 1). 

 Fig. 5. Twin-growth of {l 1 1}. according to Haidinger's law. 

 Fig. 6. The same, viewed from the opposite side. 

 Fig. 7. Twin-growth of {l 1 1}, according to Naumann's law. 

 Fig. 8. Twin-growth, with faces s of a hemiscalenohedron or disphenoid 



(Haidinger, Edin. J. of Sc. 1825). 

 Fig. 9. Twin-growth of {ill}- {0 01} {101} {2 01} (Haidinger, 



Edin. J. of Sc. 1825). 

 Fig. 10. A similar twin-growth. 



Fig. 11. A twin-crystal from Pool mines, near Kedruth. 

 Fig. 12. A twin-crystal, probably from Trevannance mine. St. Agnes. 

 * U2 



