370 Prof. Lewis, On the [May 14, 



very large, and we obtain somewhat flat crystals in which planes g 

 &c. in the zone [opg] are fairly conspicuous. The zones [cist] in 

 these crystals have less prominence than in other types (Figs. 9 

 and 10). (6) Crystals of the habit of Kenngottite in which a large c 

 plane is associated with minor planes which lie either in the zones 

 [dst] or in [opg]. Fig. 11 is a representation of a crystal of the 

 latter kind which seems to be rare. (7) Small crystals with o, b 

 well developed, and planes g forming a prism. The plane a in the 

 best instance I have observed (given in Fig. 12) becomes a triangle 

 bounded by the zones [dst], which are inconspicuous, and c was 

 absent. 



As is well known the faces in the zones [aoc] and [dst] are all 

 much striated, the latter in the direction parallel to their common 

 intersections. The plane a has two sets of striations parallel to the 

 intersections with the adjacent d planes and sometimes striations 

 parallel to [ao]; and it in consequence always gives an image from 

 which radiate the branches of a four or six-rayed cross. The 

 plane o gave very good images in a few cases, but the plane c 

 generally gave two images. The plane £ is one common to several 

 of the crystals examined by me, and is a well developed face: 

 it gives reliable though not perfect images. Of Miller's zone [£7<>'^| 

 only the plane h has been found associated with those common to 

 [aoc] and [dst]. 



I have retained the axial system adopted by Naumann and 

 Miller. The axial elements as obtained by direct observation are 

 too little reliable to be of much use, and the best angles are such 

 as are ill adapted for obtaining them by calculation. I have 

 brought into the determination of these elements all the angles 

 which seemed fairly reliable, where the process of calculation did 

 not seem to reduce the value to that of a poor observation. The 

 angles so employed amounted to thirty-six. It is naturally ex- 

 tremely difficult to attach weights to the observations in a satis- 

 factory manner, but an attempt has been made to do this in the 

 case of the best angles. Owing to the peculiar development of 

 Miargyrite crystals, the spherical triangles one has to use are 

 of the worst description for purposes of calculation, and great care 

 has been necessary to prevent multiplying, to a serious extent, the 

 errors which necessarily must exist in the angles used. Whilst 

 examining these errors and variations, I noticed some peculiar 

 discrepancies which seem not uncommon. On crystal (No. 7), 

 which seems well developed and which gives good reflexions, the 

 angles st, tco, oax, on measurement were found to be 13° 51'"), 

 17° 24', 9° 10'- 5. The two latter agree well with those calculated from 

 the elements, but the first ought to be 14 16'"33. Now criticism 

 of the possibility of these four planes including these angles 

 between them and having a constant anharmonic ratio leads to the 



