PEOFESSOE  PLUCKEE  ON  THE  MAGNETIC  INDUCTION  OF  CETSTALS.  571 
The  moment  therefore  is  the  same,  as  if  the  crystal,  whatever  may  he  its  exterior  form,  were 
transformed  into  an  amorphous  ellipsoid  of  the  same  mass. 
55.  A imite  amorphous  ellipsoid,  attached  to  any  vertical  axis,  when  influenced  by 
an  infinitely  distant  pole  falhng  within  the  horizontal  plane,  will  be  directed  in  the 
same  way  as  a similar  ellipsoid  rotating  round  its  vertical  diameter.  Having  therefore 
a series  of  such  ellipsoids  attached  one  to  another  and  rotating  round  a common  axis, 
each  of  them  will  be  forced  into  the  same  position  of  equilibrium  as  when  rotating  alone. 
Hence  a crystal  too,  oscillating  between  the  two  poles,  is  directed,  whatever  may  be  its 
shape,  like  one  of  its  ultimate  particles,  ^.  e.  like  the  above-mentioned  ellipsoid. 
56.  Therefore,  in  the  case  of  the  magnetic  induction  of  crystals,  the  same  analytical 
formulae  subsist,  which,  in  the  preceding  section,  we  derived  in  the  case  of  an  influenced 
amorphous  ellipsoid  by  means  of  auxiliary  elhpsoids.  All  former  formulae  concerning 
the  direction  of  the  crystal  remain  unchanged.  With  regard  to  the  formulae  bearing 
upon  the  law  of  its  oscillations,  we  shall  suppose  the  oscillating  crystal  to  be  always  of  a 
spherical  form ; then  the  moment  of  inertia,  corresponding  to  any  vertical  axis,  is  equal 
to  fMR^,  denoting  the  mass  of  the  crystal  by  M and  its  radius  by  E,.  Accordingly,  the 
formulae  (26.),  (28.),  (29.),  (30.)  are  to  be  replaced  by 
_ MRV  1 
5<p(a^— c^)  sin  \J/ sin  rf/'  ' 
(33.) 
@ @ 
v_/,.  . W,j 
— ^ =sin  Of,  = cos 
0 
0 
0 
-^=tan^. 
(34.) 
I ^iii 
0^  = 02  sin  -x//  sin  4/' . ( 35 .) 
^+^=@2 
In  all  these  formulae,  we  suppose  known,  as  we  did  before,  the  direction  of  the  three 
axes  2a,  2h,  2c  of  the  first  ellipsoid,  ^.  e.  the  direction  of  the  axes  of  greatest,  mean,  and 
least  induction.  The  angle  between  the  two  magnetic  axes  is  always  denoted  by  2ou, 
The  time  of  one  oscillation  is  denoted  by  0^  0^^  and  0^  in  the  cases  where  the 
crystal,  of  a spherical  form,  successively  oscillates  round  its  axes  of  greatest,  mean,  and 
least  induction,  and  round  any  diameter  determined  by  the  two  angles  x//' 
between  it  and  the  two  magnetic  axes. 
57.  The  first  question  we  here  meet  with,  is  to  determine  for  any  crystalline  substance 
the  constants,  especially  oj,  upon  which  depends  the  position  of  the  crystal,  when 
suspended  between  the  poles,  and  the  law  of  its  oscillations. 
1st.  We  may,  as  shown  in  the  case  of  ferridcyanide  of  potassium,  sulphate  of  zinc, 
and  formiate  of  copper,  find  by  experiment,  within  the  crystal,  the  two  magnetic  axes, 
remembering  that  the  crystal,  when  suspended  along  one  of  them,  is  not  acted  upon  in 
an  extraordinary  way,  not  at  all  acted  upon  when  its  form  is,  for  instance,  that  of  a 
sphere. 
2nd.  Any  one  suspension  of  the  crystal  along  a vertical  axis,  fixed  with  regard  to  the 
axes  of  induction,  is  sufiicient  to  determine  the  angle  oj,  and  hence  the  position  of  the 
two  magnetic  axes.  We  may  for  this  purpose  make  use  of  the  formula  (9.),  and  any 
