578  PEOFESSOE  PLOCKEE  ON  THE  ilAGNETIC  IXDrCTIOX  OF  CETSTALS. 
were  obKged  to  recur  to  the  formula  (24.),  expressing  the  moment  of  rotation  (L)  round 
any  vertical  axis, 
— 5'^)  sin  2^=ip(a^—(f)  sin^  '4^  sin  2^ (39.) 
In  this  formula  the  angle  between  the  vertical  gi’eat  circle  of  the  sphere  passing  through 
the  magnetic  axis  and  the  axial  plane  is  denoted  by  and  the  angle  taken  on  the  same 
great  circle  between  the  magnetic  and  the  vertical  axis  by  Denoting  the  value  of 
the  moment  corresponding  to  -4/= 90°,  where  the  magnetic  axis  is  vertical,  by  Lo,  we 
obtain 
L=Losin^-4/ (^0-) 
The  angle  -ip  remaining  the  same,  the  maximum  of  L corresponds  to  S-=45°;  denoting 
this  maximum  by  L®,  we  get 
L=L®sin2^ (41.) 
71.  The  sphere  of  crystallized  bismuth  was  placed  on  a ring  of  very  thin,  not  pain- 
magnetic,  copper  Avire,  attached  by  three  silk  threads  to  the  platinum  Avire  of  the  torsion- 
balance.  The  centre  of  the  sphere  was  brought  into  the  middle  point  between  the  two 
poles,  its  marked  meridional  great  circle  remaining  always  veilical. 
When  the  equatorial  great  circle  was  horizontal,  there  was  no  sensible  direction ; the 
torsion-wire  being  turned  through  any  angle,  the  sphere  rotated  roimd  its  vertical  axis 
through  the  same  angle.  When  the  equatorial  circle  was  more  and  more  inclined,  the 
dhecting  power  emanating  from  the  poles,  ^.  e.  the  moment  L,  increased  till  the 
equatorial  plane  became  vertical,  and  therefore  the  magnetic  axis  horizontal.  Let  us 
consider  in  a more  special  way  this  last  case,  corresponding  to  ^4'  = 90°5  and  the  case 
corresponding  to  -4/ =45°.  In  all  cases  the  marked  meridional  plane  points  axially:  so 
it  did  in  our  two  cases  most  exactly,  after  it  had  been  brought  by  means  of  the  torsion- 
balance  into  that  position  Avhile  the  current  Avas  interrupted.  The  cuiTent  being  esta- 
blished, by  turning  the  platinum  Avire  the  meridional  circle  Avas  brought  out  of  the  axial 
position.  If  the  number  of  degrees  through  which  the  wire  rotated  be  and  the  dech- 
nation  of  the  meridional  plane  of  the  sphere  from  the  axial  position  the  number 
^ indicates  the  value  of  the  moment  of  rotation  in  the  corresponding  position 
of  the  crystal.  The  number  of  degrees  (§ — S^)  corresponding  to  diiferent  values  of  -p/. 
but  to  the  same  declination  S-  of  the  meridional  plane  of  the  crystal  from  the  axial 
position,  is  proportional  to  sin^-4/.  In  our  two  cases  these  corresponding  numbers  are 
in  the  ratio  of  2 : 1.  It  was  confirmed  by  experiment. 
72.  While  in  the  first  suspension  the  torsion-Avire  was  sloAAdy  turned,  the  angle  of 
declination  more  and  more  increased ; but  finally,  just  Avhen  it  reached  45°,  correspond- 
ing to  a certain  value  of  the  crystalline  sphere  was  suddenly  driAen  into  a nearly 
opposite  position  of  stable  equilibrium.  A similar  reversion  took  place  after  a rotation 
of  the  wire  of  the  torsion-balance  in  the  same  sense  through  180°  more,  and  so  on.  In 
our  second  case,  Ave  got  the  same  phenomena,  Avith  this  difference  only ; that  the  first 
reversion  took  place  when  the  torsion-A\dre  Avas  turned  through  a smaller  number  of 
degrees.  In  both  cases  we  made  use  of  twelve  of  Grove’s  elements. 
