570  PEOFESSOE  PLtiCKEE  0:N'  THE  JVIAaXETIC  IXDrCTIOX  OF  CEYSTALS. 
differs  from  the  first  by  only 
0-111, 
i.  e.  nearly.  This  error  falls  within  the  limits  of  the  errors  of  obserration. 
The  equation  (30.)  being  thus  verified,  we  obtain,  according  to  (28.), 
, /T459 
tan  dj—  \ / ? 
V 4301 
whence 
iy=30°  13'. 
This  value  of  the  angle  u agrees  very  well  with  the  value  concluded,  in  a less  exact 
way,  from  the  first  series  of  observations 
III.  Theory  of  the  magnetic  induction  of  crystals,  and  its  erpentnental  verification. 
53.  The  results  we  obtained  in  the  preceding  section  remain  unchanged  as  long  as  the 
dimensions  of  the  influenced  body  may  be  neglected,  with  regard  to  the  distance  of  the 
pole,  ^.  e.  as  long  as  within  the  influenced  body  the  lines  of  magnetic  force  are  sensibly 
parallel.  The  formulse  therefore  we  deduced  from  Poissox’s  theory,  relating  to  a finite 
ellipsoid  influenced  by  an  infinitely  distant  pole,  may  be  immediately  applied  to  the 
infinitely  small  particle  of  a crystal  at  a finite  distance  from  the  inducing  pole.  If  the 
particle  be  placed  between  two  opposite  poles,  we  may  substitute  for  the  two  poles  a 
single  one  of  double  intensity. 
54.  Let  us  then  conceive,  as  we  did  before,  the  crystal  to  consist  of  an  infinite  number 
of  influenced  small  ellipsoids,  not  sensibly  acting  on  each  other.  Evei-}"  such  ellipsoid 
will  furnish  a moment  of  rotation  represented  by 
2 tan 
I and  r being  determined  by  the  auxiliary  ellipsoid.  The  resulting  moment  of  rotation 
will  be  represented  by  the  integral 
extended  to  the  entire  mass  of  the  crystal.  If  we  admit  that  all  particles  of  a crystal- 
ized  mass  are  of  the  same  form  and  similarly  directed,  f and  r become  constant,  whence 
the  resulting  moment, 
2(p  sin  ^ 
* We  may  regard  here  the  above-described  experiments  as  a sufficient  verification  of  the  results  ema- 
nating from  Poisson’s  theory,  in  the  case  of  an  ellipsoid  of  iron  influenced  by  a distant  pole.  A more 
complete  verification  of  this  theory  lies  beyond  the  limits  of  this  paper.  The  ellipsoid  of  u’on  may  be 
replaced  by  a similar  one  of  cobtilt  or  nickel ; according  to  theory,  the  angle  (2w)  between  the  two  axes  will 
be  found  to  be  a different  one.  We  may  derive  from  experiment  tbe  value  of  Poisson’s  constant  Tc 
(art.  24,  note),  and  compare  the  value  of  the  magnetic  induction  with  gravitation.  Whatever  may  be  the 
interest  connected  with  tliese  questions,  they  must  be  reserved  to  another  series  of  experunents  ; the  more 
so,  as  our  horseshoe-electro-magnet — whose  two  poles  induce  a distant  ellipsoid  in  opposite  sense,  along 
du’ections  which  are  to  be  previously  determined  by  observation— is,  for  such  researches,  to  be  replaced  by 
a system  of  two  cylindric  electro-magnets  having  a common  axis. 
