544  PEOFESSOE  PLCCEIEE  ON  THE  IVIAGNETIC  INDHCTION  OF  CETSTALS. 
directions,  and  not  solely  along  peculiar  ones.  Hence  nearly  two  years  ago  I finally 
abandoned  an  hypothesis  against  which  serious  doubts  had  for  a long  time  arisen.  For 
the  hypothesis  of  one  or  two  axes  acted  upon  by  the  magnet,  I substituted  another  similar 
hypothesis.  In  the  case  of  uniaxal  crystals,  I now  conceived  an  ellipsoid  of  revolution, 
consisting  of  an  amorphous  paramagnetic  or  diamagnetic  substance,  and  having  within 
the  crystal  its  principal  axis  coincident  with  the  principal  crjstallographic  axis.  It  is 
easy  to  verify,  that  both  crystal  and  eUipsoid,  the  poles  of  the  magnet  not  being  too 
near  one  another,  will  be  directed  between  them  exactly  in  the  same  way.  In  the 
generalization,  an  elhpsoid  with  three  unequal  axes,  having  vdthin  the  crystal  a deter- 
mined direction,  must  be  substituted  for  the  eUipsoid  of  revolution.  In  this  hypothesis 
too,  we  meet  with  magnetic  axes.  In  the  case  of  uniaxal  crystals,  the  direction  I 
formerly  denoted  by  “magnetic  axis”  may  also  be  defined  as  the  direction  within  the 
crystal  round  which  there  is  no  extraordinary  magnetic  action.  In  the  general  case  we 
get  two  such  directions,  which  we  shall  also  caU  “ magnetic  axes”  using  this  name  in  a 
difierent  sense  from  that  in  which  it  was  employed  before.  A crystal  suspended  along 
either  of  the  two  magnetic  axes  is  acted  upon  Uke  an  amorphous  body. 
According  to  observation,  a crystal  under  favourable  chcumstances  is  directed  in  the 
same  way  as  the  smallest  of  its  fragments.  Hence,  according  to  our  new  hypothesis, 
the  direction  which  each  of  its  particles  would  take,  when  freely  osciUating  under  the 
influence  of  a magnet,  may  be  regarded  as  determined  by  an  auxiliary  eUipsoid.  A 
quite  analogous  case  is  that  of  an  amorphous  eUipsoid  of  iron,  for  instance,  with  three 
unequal  axes,  acted  upon  by  an  infinitely  distant  pole.  Here  also,  according  to  Pois- 
son’s theory,  we  meet  with  an  auxiliary  eUipsoid  upon  which  the  pointing  of  the  given 
one  depends.  The  mode  of  verifying  the  existence  of  such  an  auxiUary  eUipsoid,  as 
well  as  the  laws  immediately  resulting  from  it,  is  exactly  the  same  in  both  cases.  This 
double  verification  had  the  fullest,  I may  say,  an  unexpected  success.  I first  proceed  to 
the  investigation  of  the  case  of  Poisson’s  elhpsoid.  Starting  from  a beautiful  theorem 
lately  published  by  Professor  Beee,  I was  enabled  to  deduce  immediately  the  analjtical 
expressions,  which  subsequently  I verified  in  the  experimental  way.  I think  this  inquiiy, 
in  which  too  I enjoyed  Professor  Beee’s  valuable  cooperation,  wUl  contribute  to  fami- 
liarize experimentalists  more  and  more  with  the  admirable  theory,  too  long  neglected, 
of  the  French  mathematician. 
The  curious  magnetic  phenomena  I first  observed  in  crystals  ten  years  ago  being 
thus  supported  by  an  analytical  theory,  and  the  numerical  results  derived  Horn  this 
theory  confirmed  by  new  series  of  experiments,  I take  the  Uberty  to  lay  before  the 
Royal  Society  an  account  of  my  researches.  According  to  the  theory  of  the  magnetism 
of  crystals  I now  propose,  the  magnetic  induction  within  a crystal  is,  like  the  elasticity 
of  the  luminiferous  ether,  determined  by  means  of  an  auxiliary  eUipsoid,  which  in  both 
cases  is  similarly  placed  within  the  crystal.  In  both  cases  there  ai’e  two  fixed  dhections 
within  it,  the  two  optic  axes  along  which  there  is  no  double  refraction,  and  the  two 
magnetic  axes^  round  which  there  is  no  extraordinary  magnetic  induction.  By  means  of 
