CERUSSITE CRYSTALS FROM BROKEN HILL AND MULDIVA. 291 



on the goniometer. To discover the twin relations of two 

 or more segments it is sufficient to determine the relative 

 positions of the zone [cb] in the various segments; this 

 zone is fortunately the best developed, and, in most cases 

 an average of several measurements can be obtained. The 

 orientation is most conveniently given by fixing the relative 

 positions of the normals to o in each segment, that is by 

 comparing <f> of the individuals with reference to a * first 

 meridian.' 



For twins on m the angle between the b pinacoids is 

 62° 46' or 117° 14' (180° - 62° 46'), for twins on r, 57° 18' 

 or 122° 42'. It will be noticed that these angles approach 

 60°, the means being 60° 2' and 119° 58' respectively. Now 

 Ooldschmidt and Hubrecht found (loc. cit.) that the angles 

 between the twinned segments do not in every case con- 

 form to the theoretical requirements, but show a slight 

 divergence, so that the angle between the two segments 

 approaches more nearly to 60°, that is the angle between 

 w doublets decreases and between r doublets increases. 

 Goldschmidt sees in this a proof that the zone planes are 

 planes of force (Kraftebene), and the face-normals directions 

 of force (Kraftrichtungen), which endeavour to place 

 themselves in parallelism much as the magnetic needle 

 places itself in the magnetic meridian. Thus Goldschmidt 

 says (loc. cit., p. 583): — "By mutual diversion the meridians 

 [c b] of the separate individuals of a polyet approach the 

 positions 0°, + 60°, + 120°, + 180°. The group approxi- 

 mates to hexagonal symmetry." Hubrecht (loc. cit., p. 149) 

 puts the matter very clearly and concisely, "This diver- 

 gence [Ablenkung] was regarded as an argument in favour 

 of the view that face-normals are directions of force which 

 bind the particles together and unite crystals in parallel or 

 twin position, that moreover zone planes are to be regarded 

 as planes of force, and that such directions of force and 

 planes of force influence one another when they have nearly 



