7,2


DESCRIPTIVE   MINERALOGY


Twins  are  very  common.  In  many  cases  it  is  difficult  to  positively
recognize  the  twinning.  This  can,  however,  be  done  by  means  of  the  opti-
cal or  pyro-electric  properties,  as  also  by  the  etch-figures.  Four  of  the
more  important  twinning  laws  may  be  referred  to.  (i)  Common  or  Dau-
phine  law,  sometimes  also  called  the  Swiss  law.  Here  two  right-  or  left-
handed  crystals  so  interpenetrate  that  the  positive  rhombohedron  of  the  one
individual  coincides  with  the  negative  of  the  other.  This  interpenetration
causes  a  face  of  the  trigonal  trapezohedrons  to  appear,  in  the  case  of  two
right-handed  crystals,  in  the  upper  right  hand  corner  of  each  one  of  the  prism
faces  (a).  When  two  left-handed  crystals  interpenetrate  the  trigonal  trap-
ezohedron  face  (.r)  is  to  be  observed  in  the  upper  left  hand  corner,  Figure
39.  This  can  be  explained  by  the  rotation  of  either  one  of  the  indi-


FIG.  39.
FIG.  40.
viduals  through  180°  about  the  c  axis.  Such  twinned  crystals  are  not
symmetrical  to  a  twinning  plane  but  rather  to  a  twinning  axis,  which  in
this  case  is  the  crystallographic  c  axis.  (2)  Brazilian  law.  A  right-  and  a
left-hand  crystal  of  the  same  sign  interpenetrate  so  that  the  twinned  crys-
tal is  symmetrical  to  a  plane  parallel  to  a  face  of  the  prism  of  the  second
order,  Figure  40.  Such  twins  are  in  reality  supplementary  twins  for  they
possess  the  symmetry  of  the  ditrigonal  scalenohedral  class.  This  law  is
often  observed  on  amethyst  crystals  from  Brazil,  hence,  the  name,  Brazilian
law.  (3)  Prism  of  the  first  order  acts  as  the  twinning  plane.  Here,  right-
and  left-hand  crystals  interpenetrate.  The  twinned  crystal  is  symmetrical,
not  only  to  the  prism  of  the  first  order,  but  also  to  the  basal  pinacoid.
