PEOrESSOE  PLiiCKEE  ON  THE  MAGNETIC  INDUCTION  OE  CEYSTALS.  567 
In  the  general  case,  where  the  influenced  ellipsoid  is  free  to  rotate  round  its  centre, 
construct  the  planes  touching  the  sphere  in  the  points  K and  K',  in  which  it  is 
intersected  by  the  radius  vector  OM  passing,  when  prolonged,  through  the  infinitely 
distant  magnetic  pole ; and  let  the  conjugate  poles  of  these  planes,  with  regard  to  the 
first  auxiliary  ellipsoid,  be  E and  E'.  Then  EOE'  is  a diameter  of  the  ellipsoid  of  induc- 
tion; its  projection  SOS'  on  any  plane  perpendicular  to  OM  (containing,  for  instance, 
the  centre  O)  represents  the  absolute  moment  of  rotation  (putting  p=l),  and  the 
line  within  the  same  plane,  perpendicular  to  the  projection  SOS',  is  the  instantaneous 
axis  of  rotation. 
49.  In  order  to  verify  the  results  emanating  from  Poisson’s  theory,  I appealed  to 
the  known  ability  of  M.  Fessel  of  Cologne,  to  turn,  out  of  a homogeneous  piece  of 
soft  iron,  two  ellipsoids  with  unequal  axes,  the  position  of  the  centres  and  the  length 
of  the  diameters  of  one  set  of  their  circular  sections  having  been  previously  calculated. 
The  ratio  of  the  squares  of  the  three  axes  in  both  ellipsoids  was  fixed  as  follows : — 
0^=400:160:100. 
According  to  this  ratio,  both  sets  of  circular  sections  were  perpendicular  to  each  other, 
as  were  also  the  diameters  perpendicular  to  both  sets  of  circular  sections.  The  longest 
axis,  2A,  of  the  first  ellipsoid  was  3T6  inches ; the  second  ellipsoid  had  only  half  the 
dimensions  of  the  fir’st. 
50.  1st.  The  first  ellipsoid  was  attached  at  the  extremities  of  its  longest  axis  2 A to  the 
inside  of  a graduated  thin  ring  of  brass,  the  shortest  axis  2C  coinciding  also  with  a dia- 
meter of  the  ring.  The  ring  was  attached  to  the  torsion-balance.  We  made  use  of 
a great  horseshoe-electro-magnet  placed  vertically,  and  excited  by  twelve  of  Geove’s 
elements.  The  diameter  of  the  fiat  poles  was  about  4 inches,  the  distance  between 
their  centres  10‘24.  The  ellipsoid  was  brought  into  such  a position  that  its  centre 
lay  in  the  vertical  plane  passing  through  the  centres  of  the  two  poles,  at  a distance  of 
30‘74  inches  from  the  point  midway  between  them,  nearly  4T  inches  below  the  hori- 
zontal plane  touching  both  poles.  A dipping-needle,  having  its  centre  similarly  placed 
within  the  same  vertical  plane,  and  by  means  of  a counterpoise  pointing  horizontally 
when  the  current  was  interrupted,  pointed  horizontally  too  when  the  current  was 
closed. 
When  suspended  with  its  longest  axis  2A  vertical,  the  ellipsoid  set  its  mean  axis  2B 
axially ; when  with  its  shortest  axis  2C  vertical,  the  same  mean  axis  2B  pointed  equato- 
rially.  Therefore,  as  the  vertical  axis  of  suspension  passes  within  the  principal  plane  AC, 
i.  e.  within  the  middle  plane  of  the  ring,  from  the  fii’st  position  to  the  second,  there  ought 
to  be  found  a position  where  the  mean  axis  2B  passes  fr’om  the  axial  into  the  equatorial 
line.  Accordingly  we  got  the  two  magnetic  axes  of  the  ellipsoid,  equally  distant  on 
both  sides  from  the  longest  axis  2A,  and  two  suspensions  corresponding  to  each  axis  and 
coiTecting  each  other. 
MDCCCLVIII.  4 F 
