366 Prof. Lewis, On the [May 14, 



Miller's A, , and his a becomes Miller's C. 1 But whilst Naumann gives 

 ao = 48° 14', ob (cleav.) = 50° 10'; Miller has oA, (cleav.) = 48° 14', 

 OC = 50° 10'. Now as Miller clearly follows Naumann's orientation 

 he has fallen into error in thus transposing these angles. Atten- 

 tion was called to this transposition by Prof. Weisbach in a paper 

 on Miargyrite published in Pogg. Ann. cxxv., 1865, in which he 

 gives Miller's new planes without any criticism which would con- 

 nect them with this transposition. Now, if Miller, as seemed 

 probable, had obtained his planes by measurement, it follows 

 that his zone [C£hr~Kx] will be incorrectly or correctly placed 

 according as C is or is not the cleavage plane. It will be 

 coincident with Naumann's zone [bfdst] if the plane C be that 

 which Miller found to be the cleavage plane. In this case his 

 statement that A is the cleavage plane would be simply due to a 

 misapprehension that this plane was still Naumann's b. Starting 

 with Miller's data, the determination of the crystals presents con- 

 siderable difficulty, for the angles in the common prominent zone 

 [bfdst] are liable to such great variations as to render the discrimi- 

 nation of this zone from Miller's [%hrM.%y] often very uncertain. By, 

 however, attending to the physical character of the faces and the 

 traces of cleavage, when they could be perceived, I found that all 

 the crystals measured by me (about twenty in number) led to the 

 result, that the zone [bfdst] was the one always present, and that in 

 no case was [£hrM.xy] prominent. It seemed certain, moreover, that 

 Weisbach's suggestion, that a transposition of the angles ao and 

 bo had been made by Miller, was correct. In this case then the 

 zone [CtfirMxy] given by Miller is simply the common zone 

 [bfdst], which has acquired the position given it by the trans- 

 position of Naumann's planes a and b. Moreover the zone [vzkty] 

 will also change its position with the same transposition, and these 

 planes will have for indices v (013) = Weisbach's /?, z (187), h (124), 

 y (211) instead of those given by Miller. A further consequence 

 of this error is that all the angles not in the zone of symmetry, 

 calculated by Miller, will be incorrect, and this might serve to 

 conceal the divergence in some of the observed angles from their 

 values as given by calculation. A search through Prof. Miller's 

 manuscript books was rewarded with the discovery of the actual 

 measurements of a crystal which justify the conclusion arrived at. 

 He finds 50° 20' to be the angle between o and the cleavage plane, 

 to which he has attached the letter c. He also gives a rough 

 drawing of the crystal projected on the plane of symmetry, which is 

 sufficiently characteristic to render its identification easy, but the 



1 I employ capital letters in the early part of this paper to distinguish Miller's 

 letters, whenever they are liable to confusion with those of others. In the 

 actual discussion of my own observations, capitals, when used, represent planes for 

 which no other suitable lettering exists. 



