572  PEOPESSOE  PLtiCKEE  THE  MAGNETIC  EN'DrCTIOX  OP  CETSTAES. 
one  of  the  formulee  (ll.)-(13.),  or  of  the  fomaulse  (18.),  (19.).  EeciprocaUy,  a being 
determined,  we  may  calculate  the  position  of  the  crystal  in  any  given  suspension,  by 
means  of  (9.)  and  (11)-(13.),  or  of  (14.)  and  (15.). 
3rd.  Let  the  spherical  crystal  be  successively  suspended  along  any  two  diameters, 
previously  determined  within  it  with  regard  to  its  axis  of  induction,  and  let  us  take  in 
both  cases  the  number  of  oscillations  it  performs  in  a given  time,  when  brought  a little 
out  of  its  position  of  stable  equilibrium.  From  the  two  numbers  thus  obtained  we  can 
easily  calculate  the  value  of  ca  (34.),  most  easily  when  the  crystal  was  suspended  along 
any  two  of  its  axes  of  induction  (33.). 
58.  By  determining  for  any  crystal  the  value  of  the  angle  a in  the  three  different 
ways,  we  are  enabled  to  verify  the  theory  we  have  put  foi-ward.  Such  a verification, 
however,  is  immediately  supplied  by  the  equation  (36.),  which  maybe  expressed  thus : — 
The  sum  of  the  squares  of  the  numbers  of  oscillations  which  a sphere  turned  out  of  a 
crystalline  substanee  performs  in  a given  thne,  when  successively  suspended  along  the  great- 
est and  least  axis  of  induction,  equals  the  square  of  the  number  of  oscillations  performed 
when  suspended  along  the  mean  axis  of  induction. 
59.  Among  the  crystals  I was  able  to  provide,  the  most  proper  to  be  used  in  order  to 
verify  the  proposed  theory  of  the  magnetic  induction  of  crystals  was  formiate  of  cop- 
per, which  I crystallized  myself.  After  some  trials,  I succeeded  in  getting  tuimed,  by 
M.  Fessel,  out  of  a fine  crystal  of  this  salt,  a perfectly  homogeneous  sphere  0-39  of  an 
inch  in  diameter.  A great  circle  traced  on  its  varnished  surface  marked  the  cleavage 
plane  of  the  crystal.  [In  order  to  verify,  after  experiment,  the  position  of  this  plane, 
the  sphere  was  cloven  by  means  of  the  heat  produced  in  the  focus  of  a burning  lens.] 
The  sphere  was  supported  by  a small  circular  ring  of  very  tliin  mica,  attached  by  three 
thin  silk  threads  to  the  double  cocoon-fibre  of  the  torsion-balance.  The  distance  of  the 
pointed  poles,  the  extremities  of  large  iron  pieces  put  on  the  fiat  poles  of  the  large 
electro-magnet,  from  each  other,  was  about  1'58  of  an  inch. 
60.  The  sphere  was  first  placed  on  the  ring,  with  its  cleavage  plane  horizontal,  in 
order  to  determine  the  symmetrical  plane,  this  plane  being  m our  case  vertical  and 
forced  by  the  power  of  the  magnetic  poles  into  the  axial  position.  After  ha'^ing  traced 
on  the  surface  of  the  sphere  the  symmetrical  plane  thus  obtained,  we  placed  it  on 
the  ring,  with  this  plane  horizontal.  The  two  points,  marked  on  the  new  great  cii-cle, 
pointing  axially  and  equatorially,  indicated  the  direction  of  the  greatest  and  least  axis  of 
magnetic  induction,  the  mean  axis  being  perpendicular  to  the  symmetrical  plane.  The 
two  principal  planes  perpendicular  to  the  symmetrical  plane  were  likewise  marked  on 
the  surface  of  the  sphere  by  great  circles,  one  of  which,  passing  through  the  least  and 
mean  axis,  is  nearly  coincident  with  the  cleavage  plane,  the  angle  between  the  two  planes 
being  nearly  3°. 
61.  1st.  We  tried  first  to  determine  directly  the  position  of  the  two  magnetic  axes 
within  the  symmetrical  plane,  by  turning  the  sphere,  when  infiuenced  by  the  poles, 
around  the  mean  axis,  the  symmetrical  plane  remaining  always  vertical.  But  here  we 
observed  that  the  passage  from  the  axial  position  of  the  symmetrical  plane  to  the  equa- 
