The  Rev.  T.  K.  Abbott  on  the  Theory  of  the  Tides.         23 
rotation  northward,  and  daring  the  other  half  southward,  and  in 
each  case  is  an  elevating  force,  which,  as  before,  has  its  greatest 
effect  90°  from  the  moon.  At  all  places  whose  latitude  is  less 
than  the  moon's  declination  there  is  a  permanent  accumulation. 
In  the  circle  abed  this  component  is  directed  towards  the  north 
at  a  and  towards  the  south  at  c,  the  points  of  change  being 
where  the  great  circles  from  M  touch  abed.  This  gives  rise  to 
a  north  and  south  oscillation.  The  southerly  force  being  the 
greater,  there  will  be  a  residual  depression  of  the  water  in  this 
region.  The  depressing  force,  however,  varies,  being  greatest  at 
a  and  at  c*,  while  the  elevating  force  is  greatest  where  the  tan- 
gents from  M  meet  the  circle.  Hence,  by  4  and  5,  the  tide  will 
be  lowest  at  the  latter  points  and  high  at  the  former.  Combi- 
ning this  with  the  former  result,  the  effect  of  both  components 
together  will  be  to  give  high  water  at  a. 
It  is  not  necessary  to  enter  into  a  detailed  examination  of  the 
state  of  things  at  intermediate  places.  It  is  not  difficult  to  see 
that,  as  long  as  the  moon's  declination  is  small,  there  will  be  an 
accumulation  effected  by  the  meridional  component  extending 
from  the  equator  to  about  lat.  45°,  and  that,  as  the  moon's  decli- 
nation increases,  the  accumulation  becomes  less  at  the  equator  and 
greater  towards  45°.  If  the  declination  were  exactly  45°,  there 
would  be  no  accumulation  at  the  equator,  but  two  elevated  rings 
at  lat.  45°.  With  a  greater  declination  these  rings  would  ap- 
proach the  poles ;  and  obviously,  if  the  moon  were  at  the  pole, 
the  ocean  would  take  the  form  of  a  prolate  spheroid. 
The  places  of  high  water  at  any  latitude,  as  far  as  this  is  due 
to  the  meridional  component,  would  be  easily  found;  but  the 
proportionate  effect  of  the  meridional  and  equatorial  components 
depends  partly  on  the  latitude  and  partly  on  the  moon's  decli- 
nation ;  and  it  does  not  come  within  the  scope  of  the  present 
paper  to  solve  this  problem.  It  is  sufficient  to  observe  that  the 
importance  of  the  meridional  component  increases  with  the  de- 
clination as  well  as  with  the  latitude.  If  the  moon  were  at  the 
pole  this  force  would  be  alone ;  and  whatever  the  declination,  it 
alone  produces  an  effect  at  the  pole. 
*  If  the  moon's  declination  were  greater  than  22°  30',  c  might  be  less 
than  45°  from  M,  in  which  case  the  force  there  would  be  an  elevating  one. 
Again,  at  a  place  whose  latitude  was  greater  than  22°  30'  and  less  than  the 
moon's  declination,  the  moon's  least  nadir  distance  (=/N)  would  be  greater 
than  45°,  and  the  force  depressing. 
