ated by the calculating of the average value. The reason of 

 the choosing of /"{04l) for the formation of the fundamental 

 angle is that this face is upon the whole far more developed 

 than e{02l}. The average deviation from the mean value of 

 the angle (041): (041) is thus 6', while for (021): (021) it is 12'. 

 To be sure this advantage i somewhat counteracted by the 

 fact that e(02l} forms an angle with è{010} nearer to 45° 

 than the angle formed by f{Oi\)-, so that an alteration of 1' 

 of the angle (041): (041) will be about corresponding to an 

 alteration of 1,2' of the angle (021) : (021); but this difference 

 is not so large that it can outweigh the difference in accuracy 

 between the two angles. 



In the zone [010, 101 j the vicinal faces are especially pro- 

 minent. P{lOl} is almost always replaced by two vicinal faces 

 forming a reentrant, very obtuse angle with each other; possibly 

 the face itself is never really found, which, however, on account 

 of the want of a fixed starting point for the measuring, it is 

 impossible to prove. The angle between the two vicinal faces is 

 exceedingly varying, and may in some cases grow to about 2° 

 but as we can in no case be sure that the faces on both sides 

 belong to one and the same form, il is impossible to determine 

 their indices, as, moreover, these indices must always be very 

 large ^). This fact is exactly the same with regard to w(30l}. 

 As to o(lll}, it seems in about half the cases to have been 

 replaced by a vicinal face lying about 15' near to (lOl); but 

 many others may otherwise also be found. The existence of 

 this vicinal face is most distinctly seen by an examination of 

 the values of the angle (041): (111). As will be seen from the 

 table of angles the calculated value is 46° 44', while the value 

 found is on an average 46° 49'. The separate values found 

 show, however, a very particular feature in grouping very nearly 

 round the two angles 46° 44' and 46° 53^/2'. The same feature 



Comp. Max Bauer: Beiträge zur Mineralogie, VI Reihe; Neues Jahr- 

 buch, 1890, 1. Band. 



