6    .  Lord  Kelvin  on 
sponds,  in  each  of  figs.  26,  27,  29,  to  &  =  243'89,  and 
tt6  =  1-0251  .  lO"3  .X.  This  makes  by  (98)  and  (97)  A  =  ±\, 
and  li  =  7r.  Fig.  30  represents  the  curve  of  fig.  29  at  the 
maximum,  in  the  neighbourhood  of  0,  on  a  greatly  magnified 
scale  :  about  1720  times  for  the  abscissas,  and  39  times  for 
the  ordinates. 
§  74.  Fig.  26  shows,  on  the  right-hand  side,  the  water 
slightly  heaped  up  in  front  of  the  travelling  forcive,  which  is 
a  distribution  of  downward  pressure  whose  middle  is  at  0. 
On  the  left  side  of  0,  we  see  the  water  surface  not  differing 
perceptibly  from  a  curve  of  sines  beyond  half  a  wave-length 
rearwards  from  0.  A  small  portion  of  a  wave-length  of  true 
curve  of  sines  in  the  diagram  shows  how  little  the  water's 
surface  differs  from  the  curve  of  sines  at  even  so  small  a 
distance  from  0  as  a  quarter  wave-length. 
It  must  be  remembered  that  in  reality  the  water  surface  is 
everywhere  very  nearly  level;  and  in  considering,  as  we 
shall  have  to  do  later,  the  work  done  by  the  forcive,  we  must 
interpret  properly  the  enormous  exaggeration  of  slopes  shown 
in  the  diagrams.  It  is  interesting  to  remark  that  the  static 
depression,  k,  which  the  forcive  if  at  rest  would  produce,  is 
about  87  times  the  elevation  actually  produced  above  0  by 
the  forcive,  travelling  at  the  speed  at  which  free  waves, 
of  the  wave-length  shown  in  the  diagrams,  travel.  It  is 
interesting  also  to  remark  that  the  limitation  to  very 
small  slopes  is  not  binding  on  the  static  forcive  curve.  Thus 
for  example,  a  distribution  of  static  pressure,  everywhere 
perpendicular  to  the  free  surface,  producing  static  depression 
exactly  agreeing  with  fig.  25,  would,  if  caused  to  travel  at  a 
speed  for  which  the  free-wave-length  is  very  large  in  com- 
parison with  b,  produce  a  disturbance,  represented  by  fig.  26 
with  waves  of  moderate  slopes  :  and,  as  said  in  §  69  above, 
would  produce  no  disturbance  at  all  if  the  speed  of  travelling 
were  infinitely  great. 
§  75.  Fig.  27  is  interesting  as  showing  the  waveless  dis- 
turbance produced  by  two  equal  and  similar  forcives  with 
their  middles  at  distance  equal  to  half  the  wave-length.  This 
disturbance  is  essentially  symmetrical  in  front  and  rear  of 
the  middle  between  the  two  forcives.  By  dynamical  con- 
siderations of  the  equilibrium  of  downward  pressures,  we  see 
that  the  area  of  fig.  27  (portion  above  line  of  abscissas  being 
reckoned  as  negative)  must  be  exactly  equal  to  2  A,  the 
sum  of  the  areas  of  the  two  forcives,  representing  their 
integral  amount  of  downward  pressure.  This  area,  being 
2irbk,  with  the  numerical  data  of  §73,  is  numerically  J>X  ; 
that  is  to  say  a  rectangle  whose  length  is  ^\,  and  breadth 
