PEOFESSOE  PLOCKEE  ON  THE  MAGNETIC  INDUCTION  OE  CEYSTALS.  665 
whence,  in  the  general  case,  a®,  j3®,  y®  being  the  angles  between  the  vertical  axis  of  rota- 
tion and  the  three  semi-axes  A,  B,  C, 
K^= Kf  cos^  a® + Kl  cos^  jS® + K^,  cos^  y®. 
The  time  corresponding  to  one  oscillation  round  A,  B,  C being  denoted  by  0^  0^^  0^^,, 
we  have 
' <8  ■ b^-c^ 
<p 
A^  + C^ 
0 =-j^T  — • —2 T’ 
M A2  + B2 
m r 0 p cP  — 
Eemembering  the  relations  (10.),  we  find,  by  division, 
^ m 
@*  A2+C2  . ^ 
g2  Q2  ■ ^ 
(27.) 
0; 
@2  A^-l-B® 
1^-WTc^ 
/ 
and  likewise,  according  to  (17.), 
©2 
• tan^ 
(28.) 
K"  K"  . , . ,, 
=^»sin-4/sin'4/'. 
(29.) 
@2  K2  a^-C^  K2 
■v//  and  ”4/'  being,  as  before,  the  angles  between  the  vertical  axis  of  rotation  and  the  two 
magnetic  axes. 
45.  Eliminating,  finally,  a from  any  two  of  the  three  equations  (28.),  we  obtain 
A2+B2  , B2  + C2  A2  + C2 
@2  @2  ©2 \ V 
///  ! n 
46.  With  regard  to  the  magnetic  induction  of  crystals,  the  following  geometrical  con- 
siderations will  not  appear  -without  some  interest. 
The  auxiliary  ellipsoid,  whose  equation  in  rectangular  coordinates  is 
«V+Sy-fc^z^=l,  ....  (3.) 
may  be  replaced  by  another  one  represented  by 
iP"  2^ 
(^1-) 
The  new  ellipsoid,  whose  axes  are  a,  h,  c,  may  be  called  the  Jirst  auxiliary  ellipsoid ; the 
elhpsoid  hitherto  made  use  of,  the  second  auxiliary  one.  The  two  ellipsoids  are  polar 
surfaces  with  regard  to  a concentric  sphere  whose  radius  equals  unity.  The  two  mag- 
netic axes  hitherto  defined  to  be  the  two  perpendiculars  to  the  circular  sections  of  the 
second  auxiliary  ellipsoid,  may  be  defined  also,  -with  regard  to  the  first  auxihary  ellipsoid, 
to  be  the  axes  of  the  circumscribed  circular  cylinders.  The  resulting  couple  ^ 
