6 
MOLECULAR  DISSYMMETRY  OF  ORGANIC  PRODUCTS. 
the  half  only  of  the  identical  parts  are  sometimes  modified  at 
the  same  time  and  in  the  same  manner.  It  is  said  in  such  case 
that  there  is  hemihedrity.  Thus,  the  cube  ought  to  be  truncated 
at  the  same  time  on  its  eight  solid  angles.  But,  in  certain 
cases  it  is  so  only  on  four.  Boracite  affords  an  instance  of  this 
kind.  Under  these  circumstances  the  modification  occurs  in 
such  wise  that  in  prolonging  the  four  truncations  in  a  way  to 
make  the  faces  of  the  cube  disappear,  we  obtain  a  regular  tetra- 
hedron. If  the  modification  were  applied  to  the  four  remaining 
angles  it  would  produce  another  regular  tetrahedron,  identical 
with  and  superposable  on  the  first,  and  differing  from  it  only  by 
its  position  on  the  cube. 
In  the  same  way  let  us  take  our  right  prism  truncated  on  the 
eight  edges  of  its  bases.  In  certain  species  the  truncation  oc- 
curs upon  half  of  the  edges  only,  and  it  also  happens  here  that 
the  truncations,  bearing  upon  edges  opposite  at  each  base  and 
crossing  at  the  two  extremities,  when  prolonged,  lead  to  a  tetra- 
hedron. There  are  two  tetrahedrons  possible,  as  for  the  cube, 
differently  placed  in  relation  to  the  prism,  accordingly  as  it  pre- 
serves such  or  such  group  of  four  truncations ;  but  here  the  two 
tetrahedrons  are  not  absolutely  identical.  These  are  symmetri- 
cal tetrahedrons.    We  cannot  superpose  them. 
These  notions  suffice  to  show  what  is  meant  by  hemihedrity, 
and  what  is  understood  by  hemihedric  faces  or  forms. 
Now,  quartz  of  which  we  just  spoke,  is  one  of  the  rare  mineral 
substances  in  which  Haiiy  found  hemihedric  faces.  The 
habitual  form  of  this  mineral,  a  regular  hexagonal  prism,  termin- 
ated by  two  pyramids  of  six  faces,  is  well  known.  It  is  clear 
that  the  trihedral  angles  situated  at  the  base  of  the  faces  of  the 
pyramid  are  identical,  and,  consequently,  if  one  of  them  bears 
a  face,  it  ought  to  be  reproduced  on  all  the  others.  This  is  true 
of  the  face  termed  rhombiferous  by  mineralogists. 
But  Haiiy  first  remarked,  in  certain  specimens,  a  face  very 
different  from  this,  which  he  designated  by  the  letter  x,  which 
falls  more  on  one  side  than  on  the  other,  without  being  double, 
as  the  law  of  symmetry  would  in  this  case  require.  Another 
very  curious  peculiarity  of  these  crystals  has  not  escaped  crys- 
tallographers.  It  is  that  the  face  x  is  inclined  sometimes  in 
one  direction  and  sometimes  in  another.    Haiiy,  who  was  fond 
