PEOrESSOE  PLiiCKEE  ON  THE  MAGNETIC  INDUCTION  OF  CETSTALS.  575 
them  with  such  a face  horizontal,  and  were  enabled  to  observe  with  accuracy  the  angle 
between  the  equatorial  line  and  an  edge  of  the  primitive  octahedron,  the  line  of  inter- 
section of  the  horizontal  face  and  the  cleavage  plane.  This  angle  was  found  to  be  2^°. 
The  same  value  of  the  angle  was  obtained  as  well  by  different  natural  crystals  as  by  a 
circular  plate  turned  out  of  a fine  crystal,  on  whose  base,  lying  in  the  face  above  men- 
tioned, the  dii’ection  of  the  edge  was  marked  by  a line,  along  which,  moreover,  was 
attached  a long  and  very  thin  filament  of  glass,  indicating  more  distinctly  the  pointing 
of  the  ciy-stal. 
Let  ABDC  (fig.  26)  be  the  symmetrical  plane  containing  the  two  axes  of  greatest  and 
least  induction  OX,  OZ;  AEBF  the  cleavage  plane  perpendicular  to  the  symmetrical  plane, 
and  containing  the  mean  axis  OY;  and  lastly,  PQSK  the  horizontally-suspended  face  of 
the  primitive  octahedron,  intersecting  ABDC  in  OS  and  AEBF  in  the  edge  PQ.  The 
equatorial  and  the  axial  line  OT  and  O V lie  in  the  horizontally-oscillating  face  PQSR ; 
the  measured  angle  POT  equals  2|°.  According  to  M.  Heussee’s  measures,  the  inclina- 
tion of  the  face  PQSE  to  the  cleavage  plane  is  51°  31',  and  from  his  above-quoted  angles 
(art.  17)  we  derive  QOB=44°  51'.  Hence,  considering  the  rectangular  spherical  triangle 
determined  by  OQ,  OS,  OB,  we  get 
QOS=57°  59',  BOS=41°  35i',  <p=56°  17', 
denoting  by  (p  the  angle  between  the  face  in  question  and  the  symmetrical  plane.  The 
angle  ZOB  within  the  sjunmetrical  plane  being  3°  (art.  19),  we  get 
a=XOS=BOS+93°=134°  35^', 
and  in  hke  manner 
X=VOS=POT+90°-QOS=34°  31'. 
Starting  from  these  values  of  the  angles  (p,  a and  X,  we  obtain,  by  means  of  the  formulae 
(9.)  and  (12.),  or  (18.)  and  (19.), 
fi;  = 25°  3'* 
64.  After  ha\ing  expounded  the  general  theory  of  the  magnetic  induction  of  crystals, 
* Hitherto  we  have  only  determined,  by  various  methods,  the  value  of  the  angle  «,  and  thus  obtained  a 
linear  relation  between  the  three  axes  of  the  ellipsoid  of  induction.  If,  by  considerations  exceeding  the 
limits  of  this  paper,  we  should  be  enabled  to  get  the  ratio  itself  of  these  axes,  we  could  hence  deduce  the  form 
of  the  magnetic  particles  of  the  examined  crystal,  supposing  that,  in  fact,  these  particles  are  similar  ellip- 
soids, similarly  directed,  aE  induced  by  the  magnetic  pole,  but  not  sensibly  inducing  each  other.  Mr.  W. 
Thomson,  however,  has  published  a curious  theorem,  according  to  which  a body  of  any  exterior  shape  is 
influenced  by  an  infinitely  distant  pole  like  a certain  ellipsoid  whose  axes  are  to  be  determined  in  each 
case.  Hence  an  infinite  variety  of  forms  corresponds  to  a known  ellipsoid  of  induction.  Again,  each  physical 
condition  of  crystals  leading  to  our  ellipsoid  of  magnetic  induction  has,  to  the  present  time,  independently 
of  Poisson’s  hypothetical  views  on  matter,  the  same  claim  to  be  the  law  of  nature.  We  may  generally  con- 
ceive an  amorphous  substance  to  consist  of  equal  particles,  pointing  in  all  different  directions,  which  by  the 
act  of  crystallization  become  directed  in  the  same  way.  But  I think  it  probable  we  shall  obtain  the  same 
results  by  admitting  spherical  particles,  which,  according  to  their  different  proximity  along  different  direc- 
tioDs  within  the  crystal,  will  equally  lead,  by  their  mutual  induction,  to  three  axes  of  induction ; thus  each 
such  particle  may  possibly  be  acted  upon  in  the  same  way  as  our  ellipsoidal  particles. 
MDCCCLVIII.  4 G 
