MOLECULAR  DISSYMMETRY  OP  ORGANIC  PRODUCTS. 
5 
constitution.  In  quartz  the  phenomenon  results  from  the  mode 
of  aggregation  of  the  crystalline  particles. 
These  are  the  physical  precedents,  if  I  may  so  express  myself, 
of  the  researches  with  which  I  propose  to  entertain  you.  Here 
are  their  mineralogical  precedents. 
II. 
Hemihedrity*  is  assuredly,  among  the  peculiarities  of  crys- 
tallization, the  one  which  is  the  easiest  to  seize  in  its  external 
manifestation  :  consider,  for  example,  a  species  of  mineral  crystal- 
lizing in  the  cubic  form.  This  form,  as  all  know,  may  surround 
different  kinds  of  determinate  forms  by  the  law  of  symmetry,  a 
law  so  natural  that  it  is,  so  to  speak,  a  physical  axiom.  The 
expression  of  this  law  is,  that  a  form  being  given,  all  others 
compatible  with  it  may  be  obtained  by  a  contrivance  which  would 
consist  in  modifying,  truncating,  as  Rome'  de  Lisle  said,  at  the 
same  time  and  in  the  same  manner  the  identical  parts.  The 
identical  edges  are  those  which  are  at  the  intersection  of  faces 
respectively  identical,  mutually  catting  at  the  same  angle;  and 
solid  identical  angles,  those  which  are  formed  by  dihedral  angles 
respectively  equal  and  similarly  placed.  For  example,  in  the 
cube  there  is  but  one  kind  of  solid  angles  and  one  kind  of  edges. 
Let  one  of  the  solid  angles  be  truncated  by  a  face  equally  in- 
clined to  the  three  faces  of  the  solid  angle,  and  the  seven  other 
angles  should  be,  at  the  same  time,  by  a  face  of  the  same  na- 
ture. This  is  observed  in  alum,  in  galena,  and  generally  in  all 
cubic  species. 
Let  us  consider  a  right  prism  with  a  rhomb  base.  The  eight 
edges  of  the  bases  are  identical.  If  one  is  truncated,  the  seven 
others  should  be,  and  in  the  same  manner.  The  four  vertical 
edges  are  of  another  kind.  Generally  they  will  not  be  truncat- 
ed at  the  same  time  as  those  of  the  bases,  and  if  they  are,  it 
will  be  differently. 
These  examples  alone  will  suffice  to  explain  the  law  of  symme- 
try and  its  application. 
Nothing  is  more  simple  than  to  have  a  clear  idea  of  hemi- 
hedrity. Experiment  has  long  since  shown,  Haiiy  was  ac- 
quainted with  the  most  celebrated  instances,  that,  in  a  crystal, 
*  Umisus,  half  ;  edron  side. 
