PEOFESSOE  PLUCKEE  OJS'  THE  MAGNETIC  INDUCTION  OE  CEYSTALS.  579 
In  the  first  case,  the  value  of  in  the  moment  when  the  first  reversion  took  place,  in 
two  successive  observations  was  found  to  be 
in  the  second  case,  we  obtained 
561\ 
563i 
295 
300 
Mean  562 ; 
Mean  297'5 ; 
whence 
a62— 45  517 
consequently  very  near  the  value  of  sin®'4/=0'5. 
73.  The  declination  of  the  meridional  plane,  after  the  suspension  of  the  crystal, 
may  easily  be  calculated.  Let  the  number  of  degrees  through  which  the  meridional 
plane  rotates,  when  passing  from  the  position  of  unstable  equilibrium,  corresponding  to 
^=45°,  into  the  new  position  of  stable  equilibrium,  be  denoted  by  z,  whence  ^'=2:-}-45. 
Then,  according  to  (41.),  we  get 
sin  2(2-135)=?=^. 
whence 
sin^2:= 
z 
2(8-45)' 
(42.) 
In  our  first  case,  where  45  = 517,  we  obtain 
2=157-05,  a' = 180°+ 22^  3'; 
in  the  second  case,  where  ^ — 45=252-5, 
2=147-30,  ^'=180°+12°  18'. 
These  values,  according  to  an  approximative  estimation,  agree  with  observation*. 
* The  same  mode  of  experimenting  may  be  applied  to  the  general  case  of  biaxal  crystals,  by  substituting 
for  the  formula  (39.),  L=(p(a^-c=)  sin  4^  sin  4'  sin  23  ; 
denoting,  as  we  did  before,  the  angles  between  the  vertical  and  the  two  magnetic  axes  by  4 and  4'-  Wlien 
the  vertical  axis  successively  coincides  with  the  axes  of  greatest,  mean,  and  least  induction,  the  correspond- 
ing moments  of  rotation  are  ^ ^ ^ 23, 
Ijii  =<p{a,^ — cF)  sin  23, 
— c^)  cos*  w sin  23  ; 
whence,  corresponding  to  any  value  of  3, 
Li  : Lii : L^,j  = stn®  w : 1 ; cos^  w. 
Hence  we  may  determine  by  experiment  the  position  of  the  two  magnetic  axes  of  a crystal  in  the  follow- 
ing new  way,  allowing  of  great  accuracy.  Attach  the  crystal,  after  having  given  to  it  the  form  of  a sphere, 
to  the  wire  of  the  torsion-balance,  and  let  there  be  no  torsion  w'hen  the  sphere  influenced  by  the  poles  takes 
a certain  direction.  Let,  successively,  the  axis  of  greatest,  mean,  and  least  induction  be  vertical,  and  deter- 
mine m each  suspension  the  number  of  degrees  through  which  the  torsion-wire,  slowly  turned,  rotates  till 
the  reversion  of  the  sphere  takes  place.  The  smn  of  the  nwmbers  thus  obtained  in  the  first  and  the  third  case 
equals  the  number  obtained  m the  second  case.  The  first  number  divided  by  the  second  equals  sin°  w ; the 
third  by  the  second,  cos^  w ; the  first  by  the  third,  tan^  w. 
