560  PEOFESSOE  PLOCKEE  ON  THE  MAGNETIC  INDTJCTION  OF  CETSTALS. 
33.  By  means  of  the  formulae  (9.)  and  (11.) — (13.),  we  can  determine  the  position  of 
the  influenced  ellipsoid,  if  by  the  angles  a and  (p  its  horizontal  section  be  fixed,  with  regard 
to  any  of  its  three  principal  planes.  The  two  axes  of  the  elliptic  section  of  the  auxiliary 
ellipsoid  iu  the  same  horizontal  plane,  determined  both  by  X,  will  point  axially  and 
equatoriaUy.  The  same  two  axes  may  be  found  also  by  the  most  simple  geometrical 
construction. 
34.  Let  the  axis  ^ fall  on  OA,  the  axis  i on  OC ; let  OQ  and  OQ!  (fig.  24)  be  the 
two  magnetic  axes  lying  in  the  plane  containing  OA  and  OC,  therefore  AQ=AQ'=2y. 
Fig.  24. 
Let  DMD'  be  the  horizontal  plane,  AD  being  « and  MDC=(p;  let  P be  the  pole  of  this 
plane,  whence  OP  the  vertical  axis  of  suspension.  Let  OE  be  the  projection  of  OA  on 
the  horizontal  plane,  OR  and  OR'  the  projections  of  the  two  magnetic  axes  OQ  and  OQ'. 
Let  OK  and  OK'  in  the  same  plane  be  the  traces  of  the  two  cucular  sections  of  the 
auxiliary  ellipsoid,  and  OM  and  OM'  the  two  semi-axes  of  the  horizontal  elliptic  section, 
pointing  axially  and  equatoriaUy. 
The  two  semidiameters  (OK  and  OK')  in  which  any  eUiptical  section  of  the  eUipsoid 
is  intersected  by  its  two  circular  sections,  are  both  equal  to  the  mean  semi-axis  The  two 
semidiameters  (OR  and  OR')  of  the  same  elliptical  section,  perpendicular  to  OK  and 
OK',  are  likewise  equal  to  one  another.  Hence  we  shaU  find  the  two  axes,  OM  and 
OM',  of  this  section,  here  supposed  horizontal,  by  bisecting  the  angle  RR'  and  its 
supplementary  angle. 
