576  PEOFESSOE  PLtiCKEE  ON  THE  JtHlGNETIC  IXDUCTIOX  OF  CETSTALS. 
we  may  easily  apply  it  to  the  case  where  the  auxiliary  ellipsoids  are  ellipsoids  of  revolu- 
tion, and  therefore  the  two  magnetic  axes  coincident  along  the  same  line.  The  crystals 
in  this  case  are  to  be  called  uniaxal.  We  may  distinguish  too  positive  and  negative 
uniaxal  crystals.  In  positive  crystals  (f=lf,  and  therefore  ^=0 ; in  negative  crystals 
and  therefore  (y=90°.  The  induction  in  both  cases  may  be  as  well  a diamag- 
netic as  a paramagnetic  one. 
65.  Since  the  two  axes  of  the  horizontal  section  of  the  first  auxiliary  ellipsoid  point 
axially  and  equatorially,  as  they  do  in  the  general  case,  the  position  of  a uniaxal 
crystal,  when  suspended  between  the  two  poles  along  any  of  its  diameters,  is  imme- 
diately obtained.  Here  the  axis  of  revolution,  i.  e.  the  magnetic  axis  of  the  crystal, 
when  projected  on  the  horizontal  plane,  is  one  of  these  two  axes,  the  other  being  the 
intersecting  line  of  the  equatorial  plane  of  the  elhpsoid  and  the  horizontal  plane.  If 
the  crystal  be  positive,  this  intersecting  hne  is  coincident  with  the  shorter  axis  of  the 
elliptical  section  within  the  horizontal  plane;  if  it  be  negative,  with  the  longer  axis. 
Hence  a paramagnetic  crystal,  when  positive,  sets  its  magnetic  axis  in  the  axial, 
when  negative  in  the  equatorial  plane  of  the  electro-magnet.  In  diamagnetic  crystals, 
when  positive,  the  magnetic  axis  is  forced  into  the  equatorial,  when  negative  into  the 
axial  plane.  In  order  to  give  a true  description  of  this  fact,  you  may  say,  in  all  cases  the 
magnetic  axis  of  the  crystal  is  either  attracted  or  repelled  by  the  poles. 
This  law  can  easily  be  verified  in  a most  distiirct  way  by  a great  number  of  paramag- 
netic and  diamagnetic,  positive  arrd  negative  crystals.  I think  it  therefore  not  necessary 
to  refer  here  to  new  experiments. 
66.  In  most  cases  the  magnetic  axis  is  known,  if  not,  it  can  easily  be  found  by 
suspending  the  crystal  along  any  two  vertical  axes.  Mark  in  both  suspensions  if  the 
crystal  be  positive  and  paramagnetic,  or  negative  and  diamagnetic,  on  its  suiTace  the 
axial  plane,  if  it  be  positive  and  diamagnetic,  or  negative  and  paramagnetic,  the  equato- 
rial plane ; in  both  cases  the  line  of  intersection  within  the  crystal  of  the  two  planes 
marked  on  its  surface  is  the  magnetic  axis. 
67.  The  law  of  the  small  oscillations  of  the  crystal,  which  agam,  for  simphcity,  we 
suppose  of  a spherical  form,  when  suspended  between  the  poles  along  any  vertical  axis, 
is  represented  by  the  former  equations  (33.)  and  (35.),  now  simplified  thus: 
0 1 , 
5tp(a^—c^)  sin  4/^  ' 
0j=0sin-4/, (38.) 
denoting  by  0 the  time  of  one  oscillation,  if  the  angle  between  the  magnetic  axis  and 
the  vertical  axis  of  suspension  equal  \j^,  and  0o  the  time  of  one  oscillation  if  4’= 90°,  i.  e. 
if  the  magnetic  axis  oscillate  horizontally. 
68.  Remembering  a former  observation,  according  to  which  sulphate  of  uon,  although 
belonging  to  the  clinorhombic  system,  ranges  among  uniaxal  crystals,  having  its  mag- 
netic axis  within  the  symmetrical  plane,  I selected  this  salt  to  verify  the  last  formula.  I 
