PALACTIE. — CRYSTALLOGRAPHY OF LEADHILLITE. 449 



Twinning. — The crystals are often twinned, the twinning plane 

 being regarded as the prism m (120) according to the usual twinning 

 law of the species. Three types of twins may be recognized : (1) con- 

 tact twins of the aragonite type with a face of the twinning plane m as 

 composition plane, seen chiefly in cleavage flakes under the microscope ; 

 (2) contact or lamellar twins, the composition face parallel to a face of 

 v (T22), (see Figures 8 and 9) ; (3) interpenetration twins in which the 

 faces in normal position and those in twin position are mingled without 

 any apparent system and can only be distinguished by measurement 

 and projection. 



The gnomonic projection is particularly useful in the study of such 

 complex twin crystals of this general type where the twin plane is nor- 

 mal to the plane of projection. The projection points of a face and its 

 twin then lie symmetrically on either side of the trace of the twin 

 plane, that is, equidistant from the trace and on a perpendicular to it. 

 This test can be quickly and easily applied in the projection to any 

 face concerning which there is doubt as to whether it is in normal or 

 twin position, and the rule was adopted, after much study in the special 

 case of these crystals, that the position of a face should be accepted as 

 correct, which, tested in this way, gave the simplest indices. 



It was noted in applying this test that the prism F (320) is almost 

 at right angles to m (320 A T20 = 89° 32'), and this relation leads to a 

 certain amount of ambiguity in the interpretation of the twinning. 

 The prism F has been recorded as the twin plane of lamellar twins of 

 leadhillite due to elevation of temperature, but it is not found in 

 the form series of the mineral. Since their planes are so nearly at 

 right angles, twinning on m and on F will produce closely similar effects, 

 and the decision in favor of the former law is somewhat arbitrary, 

 as may be judged from the following statement of the respective 

 relations. 



The most striking effect of twinning by either law is the practical 

 superposition of certain faces lying in radial zones. If the twinning be 

 vol. xliv. — 29 



