58G  PEOFESSOE  PLOCKEE  ON  THE  MAG]STETIC  IXDrCTIOX  OF  CRYSTALS. 
intersecting  this  plane  along  OX,  which  may  be  the  axis  of  greatest  or  least  induction. 
The  angle  is  to  be  measured  from  OX. 
In  the  third  case  we  have 
tan  tan  
The  two  axes  are  situated  in  the  plane  ZOY  perpendicular  to  the  plane  XOZ,  and  in- 
tersecting this  plane  along  OZ,  which  may  be  the  axis  of  the  greatest  or  least  induction. 
The  angle  co  is  to  be  measured  from  OZ. 
In  the  preceding  paper  I gave  only  the  formulae  of  the  fii’st  case,  where  I supposed  OX 
to  be  the  axis  of  greatest  induction.  From  this  formula  the  others  are  easily  deduced. 
The  magnetic  axes  of  a crystal,  either  paramagnetic  or  diamagnetic,  not  examined 
before,  whose  primitive  form  is  a right  prism  with  a rhombic  base,  may,  for  instance, 
immediately  be  found  by  means  of  these  formulae.  In  this  case,  let  the  axes  OX,  OY 
and  OZ  coincide  with  the  crystallographic  axes  in  any  order  whatever ; cut  by  pai'allel 
planes,  whose  inclination  to  these  axes  is  known,  a plate  out  of  the  crystal ; let  this  plate 
oscillate  horizontally  between  the  two  poles  of  the  magnet,  and  mark  on  its  suiTace  a line 
pointing  either  axially  or  equatorially.  Thus  the  angles  (p,  a,  and  being  determined. 
and  d,  as  well  as  tan  rj  tan  rj,  can  be  easily  calculated.  The  sign  and  the  value  of  the  last 
expression  shows  by  which  of  the  last  three  equations  the  angle  u is  to  be  calculated, 
and  immediately  indicates  in  which  of  the  three  principal  planes  the  two  magnetic  axes 
are  situated. 
The  position  of  the  optic  axes  may  be  found  hy  the  very  same  formulae.  If  we  make 
use  of  the  former  plate,  the  angles  9 and  a remain  the  same,  the  angle  X only  varies,  and 
is  to  be  determined  by  means  of  a convenient  polarizing  apparatus. 
The  optic  axes  relative  to  different  colours  being  dispersed  in  the  same  principal  plane, 
and  even  passing  in  certain  cases  from  one  principal  plane  to  another,  we  cannot  be 
surprised  that  the  optic  and  magnetic  axes  are  differently  directed,  and  placed  either  in 
the  same  or  in  different  planes.  In  ferridcyanide  of  potassium,  for  instance,  the  axis  of 
the  right  prism  is  the  axis  of  the  greatest  optic  elasticity  and  of  the  least  magnetic 
induction ; the  longer  diagonal  of  the  base  is  the  axis  of  the  least  elasticity  and  mean 
induction ; the  shorter  diagonal  the  axis  of  the  mean  elasticity  and  greatest  induction. 
Therefore  the  two  principal  planes,  containing  the  optic  and  the  magnetic  axes,  inter- 
sect each  other  along  the  axis  of  the  prism.  In  the  case  of  sulphate  of  zinc,  the  axis  of 
the  prism  is  the  axis  of  the  mean  optic  elasticity  and  of  the  greatest  diamagnetic  induc- 
tion; the  longer  diagonal  of  the  rhombic  base  is  the  axis  of  the  least  elasticity  as  well  as 
of  the  least  induction ; the  shorter  diagonal  is  the  axis  of  the  greatest  elasticity  and  the 
mean  induction.  Accordingly  the  two  optic  axes  lie  in  the  base  of  the  prism,  the  two 
magnetic  axes  in  the  plane  passing  through  the  axis  of  the  prism  and  the  longer 
diagonal  of  its  base.  In  the  case  of  formiate  of  copper,  the  mean  axis  of  paramagnetic 
induction  and  that  of  optic  elasticity  are  both  perpendicular  to  the  symmetric  plane  of 
the  crystal ; therefore  the  two  optic  axes  and  the  two  magnetic  ones  lie  in  this  plane. 
