and  the  Magnetic  Relations  of  the  Heavenly  Bodies.        359 
3.  The  coefficient  of  friction  a  between  the  liquid  and  the 
solid  crust, 
then  we  have,  as  in  the  above  work,  pp.  54  &  55,  for  the  less  of 
velocity  dv  by  the  motion  of  a  liquid  particle  into  higher  latitudes, 
dv  =  Aavk  sin  (j)  cos  <p  dcf> ; (1) 
where  A  signifies  a  constant  determined  by  the  nature  of  the 
body,  and  vl  the  linear  velocity  of  a  point  on  the  solid  crust  at 
the  equator. 
Hence  the  velocity  which  a  particle  loses  going  from  the 
equator  to  lat.  6  is 
c* . 
Aavx  1    sin  <j>  cos  <f>  d<fi. 
Jo 
The  remaining  component  of  velocity  v{  will  be 
t><=t>1--£-Ssina0,       .......    .(2) 
if  we  assume  the  original  velocity  of  the  particle  at  the  equator 
to  have  been  equal  to  the  velocity  of  the  solid  crust. 
Now  the  velocity  of  a  particle  in  the  solid  crust  lat.  <j>  will 
be 
ve=vlcos(f> (3) 
Putting 
ka 
and  subtracting  (3)  from  (2),  we  have 
v{— i?e=t;1[l  —  (cos  <j)-\-p  sin2  </>)]     .     .     (4) 
This  expression  represents  the  law  according  to  which  the  differ- 
ence in  linear  velocity  of  the  inner  glowing  streams  (v§)  and  the 
solid  crust  (ve)  varies  with  the  latitude.  But  this  difference  is 
evidently  nothing  else  than  the  relative  velocity  of  the  glowing 
liquid  with  respect  to  the  earth's  crust. 
The  constant  p  will  always  have  a  mean  value  considerably 
less  than(l);  so  that  the  above  expression  will  generally  increase 
with  increasing  latitude  and  have  a  maximum  value  at  the  poles. 
As,  according  to  the  developed  theory,  the  magnetic  appear- 
ances on  the  surface  of  the  earth  are  only  effects  of  the  streaming 
movement  in  the  liquid  nucleus,  the  magnetic  phenomena  must 
increase  in  intensity  with  increasing  latitude.  It  follows  from  this 
that  the  peculiarities  of  magnetic  disturbances  characterized  as 
above  by  Lamont  must  be  much  more  intense  in  higher  latitudes, 
and  can  generally  only  consist  in  a  decrease  of  the  intensity  of 
the  current,  as  this  was  supposed  to  be  the  case  in  the  above 
