20         The  Rev.  T.  K.  Abbott  on  the  Theory  of  the  Tides. 
where  the  constant  c  retains  the  same  value  as  in  the  potential  oj 
two  electrical  particles. 
But  even  if  it  should  hereafter  result  from  more  accurate  ex- 
perimental results  that  it  is  not  permissible  thus  to  ascribe  the 
same  value  to  the  constant  c  in  the  case  of  ponderable  particles, 
the  possibility  would  always  remain  of  assigning  to  the  constant 
c  a  still  greater  value  for  ponderable  particles ;  and  this  could 
easily  be  taken  so  great  that  any  sensible  disagreement  with 
experiment  would  completely  vanish. 
[To  be  continued.] 
II.  Further  Notes  on  the  Theory  of  the  Tides. 
By  the  Rev.  T.  K.  Abbott,  Trinity  College,  Dublin*. 
IN  the  demonstrations  given  in  two  previous  papers  in  this 
Magazine  (January  1870  and  February  1871),  we  have  sup- 
posed the  water  to  be  limited  to  an  equatorial  canal,  the  moon 
also  being  in  the  equator.  It  is  desirable  to  consider  what  mo- 
difications will  be  introduced,  first,  by  supposing  the  earth  to  be 
uniformly  covered  with  water,  and,  secondly,  by  taking  into  ac- 
count the  moon's  declination. 
It  will  save  repetition  if  we  state  once  for  all  certain  general 
principles  which  we  shall  have  to  employ.  First,  suppose  an 
accelerating  force  acts  alternately  in  opposite  directions,  the 
effect  (measured  by  velocity)  increases  as  long  as  the  force  acts 
in  either  direction,  and  therefore  the  velocity  in  that  direction 
is  greatest  at  the  moment  that  the  force  changes  its  direction. 
Secondly,  the  velocity  (diminishing  under  the  counteraction  of  the 
new  force)  continues  to  be  in  the  same  direction  until  this  counter 
force  has  undone  all  the  work  done  in  that  direction  by  the  pre- 
vious force.  When  the  circumstances  are  alike  in  both  direc- 
tions, this  will  be  when  the  force  has  done  half  its  work.  This 
is  precisely  the  case  of  the  common  pendulum.  Thirdly,  in  the 
case  before  us,  the  water  rises  when  the  particles  behind  are 
moving  faster  than  those  before.  The  rate  of  rise  is  greatest 
when  this  difference  is  greatest;  but  as  the  effect  is  cumula- 
tive, the  whole  amount  of  the  rise  is  greatest  at  the  moment 
when  the  difference  =  0,  and  is  about  to  change  to  the  oppo- 
site. Fourthly,  as  in  2,  this  difference  ceases  to  increase  (i.  e. 
is  greatest)  when  the  force  (or  difference  of  forces)  producing  it 
ceases  to  act ;  but  it  is  not  reduced  to  0  until  the  opposite  force 
has  done  half  its  work.  At  this  moment  the  accumulation  is 
greatest.  Fifthly,  in  the  case  which  we  are  now  considering, 
the  effective  force  depends  on  the  form  of  the  surface,  and  vice 
*  Communicated  by  the  Author. 
