368 Prof. Lewis, On the [May 14, 



the angles in the zone of symmetry. There are also one or two 

 stereographic projections which show that Miller had at one time 

 contemplated a change in the parametral plane. In one case d is 

 tried as (111), and in another /3 (Miller's v) as (110). Miller seems 

 to have made the observations given in the note-book in the summer 

 of 1848, and as the crystal there described is labelled C I should 

 expect that the loose papers bear the same date. In this case 

 Miller must have felt too little confidence in the results of his own 

 observations to justify an alteration of Naumann's elements, and 

 has contented himself with giving the planes which he believed to 

 be new. The plane e (212) does not seem to have been observed 

 by him. A plane given by Miller on crystal A in zone [dst], and 

 making an angle of 16° 5' with a (100) falls between (11 11) and 

 (10 11). The former is inclined to a at an angle of 15° 3925', the 

 latter at one of 17° 6'"5. 



In Weisbach's paper in 1865 the axial system previously 

 adopted is exchanged for one in which o and c become the ortho- 

 pinakoid and base. The object aimed at in this change is to be 

 able to represent the form #(313) as a prism. It has, however, 

 serious disadvantages which more than compensate any advantage 

 so obtained, and does not seem justified by the importance of the 

 form (313). The zone [og] is generally a much striated and 

 curved zone, the angles in which are rarely capable of even 

 approximate determination. The planes x are those which are 

 generally most largely developed, and they were very preponderant 

 in the crystals measured by Miller. The planes ft (013) are fre- 

 quently very largely developed, as are also the planes £(213). 

 Naumann's orientation places the well-marked plane A and the 

 zones [Adst] in prominent positions which show the development 

 well ; and both the development of the more complicated crystals 

 and the simplicity of the indices is decidedly in favour of retaining 

 the axial system first selected. The letters employed to designate 

 the faces have been much confused, and it is not possible to find a 

 lettering free from objection. I have tried to retain as far as 

 possible the lettering used by the various writers. The letters 

 z, k are used to denote the planes (137), (124) in their correct 

 positions, and several of the letters applied by Miller in the zone 

 [ct] have been transferred to new planes as they no longer refer to 

 any known planes. 



Whilst completing the calculations involved in the determina- 

 tion of the elements I received through the kindness of Professor 

 Groth a copy of the proof-sheets of a paper on the mineral by 

 Prof, vom Rath. 



Prof, vom Rath has in this paper deduced elements from 

 the spherical triangle ss^ ; and has given no weight to any other 



