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  XLVIII. 
  On 
  the 
  Resistance 
  due 
  to 
  Obliquely 
  Moving 
  Waves 
  

   and 
  its 
  dependence 
  upon 
  the 
  Particidar 
  Form 
  of 
  the 
  Fore-part 
  

   of 
  a 
  Ship, 
  By 
  Lord 
  Rayleigh, 
  OJ/., 
  F.R'.S.'' 
  

  

  1 
  SUPPOSE 
  that 
  everyone 
  is 
  familiar 
  with 
  the 
  system 
  o£ 
  

   oblique 
  waves 
  advancing 
  in 
  echelon 
  from 
  the 
  bow 
  of 
  a 
  

   ship 
  which 
  travels 
  through 
  smooth 
  water. 
  What 
  is 
  not 
  so 
  

   easily 
  observed 
  from 
  on 
  board 
  is 
  the 
  corresponding 
  wave- 
  

   profile, 
  i. 
  e, 
  the 
  deviation 
  of 
  the 
  water-surface 
  at 
  the 
  side 
  of 
  

   the 
  ship 
  from 
  the 
  position 
  which 
  it 
  would 
  occupy 
  in 
  a 
  state 
  

   of 
  rest. 
  Sketches, 
  both 
  of 
  the 
  whole 
  system 
  of 
  waves 
  and 
  of 
  

   various 
  wave-profiles 
  have 
  been 
  given 
  by 
  W. 
  and 
  R. 
  E. 
  

   Froude 
  f, 
  and 
  the 
  influence 
  of 
  the 
  various 
  components 
  of 
  the 
  

   wave-sj-stem 
  in 
  contributing 
  to 
  the 
  aggregate 
  wave-resistance 
  

   has 
  been 
  discussed. 
  Attention 
  has 
  perhaps 
  tended 
  to 
  concen- 
  

   trate 
  upon 
  the 
  directly 
  advancing 
  waves 
  — 
  those 
  whose 
  crests 
  

   are 
  perpendicular 
  to 
  the 
  ship's 
  motion 
  — 
  and 
  upon 
  the 
  remark- 
  

   able 
  interaction 
  between 
  the 
  systems 
  originating 
  at 
  the 
  bow 
  

   and 
  stern. 
  But, 
  apart 
  from 
  its 
  interesting 
  geometrical 
  

   features, 
  the 
  oblique 
  part 
  of 
  the 
  wave-system 
  also 
  impresses 
  

   an 
  observer 
  with 
  its 
  mechanical 
  importance 
  as 
  probably 
  

   contributing 
  in 
  no 
  mean 
  degree 
  to 
  the 
  total 
  wave-making 
  

   resistance. 
  

  

  From 
  the 
  time 
  of 
  my 
  first 
  acquaintance 
  with 
  drawings 
  of 
  

   wave- 
  profiles 
  I 
  have 
  been 
  struck 
  with 
  their 
  significance 
  as 
  

   indicating 
  that 
  the 
  usual 
  form 
  of 
  bow 
  (and 
  perhaps 
  of 
  stern) 
  

   is 
  not 
  well 
  adapted 
  to 
  minimise 
  the 
  forces 
  of 
  resistance. 
  At 
  

   the 
  stem 
  and 
  immediately 
  behind, 
  the 
  water 
  is 
  raised 
  above 
  

   the 
  normal 
  level, 
  and 
  this 
  elevation 
  is 
  undoubtedly 
  the 
  

   principal 
  feature. 
  The 
  additional 
  pressure 
  thence 
  arising 
  

   operates 
  normally 
  upon 
  the 
  skin 
  of 
  the 
  ship, 
  and 
  the 
  com- 
  

   ponent 
  in 
  the 
  fore-and-aft 
  direction 
  acting 
  stern 
  wards 
  holds 
  

   the 
  ship 
  back. 
  It 
  is, 
  I 
  suppose, 
  in 
  order 
  to 
  diminish 
  the 
  force 
  

   here 
  operative 
  that 
  the 
  bows 
  of 
  many 
  ships 
  are 
  made 
  holloio, 
  

   i. 
  e. 
  with 
  a 
  curvature 
  concave 
  outwards. 
  But 
  the 
  question 
  

   does 
  not 
  stop 
  here. 
  If 
  we 
  follow 
  the 
  wave-profile, 
  we 
  find 
  

   that 
  somewhat 
  further 
  back 
  the 
  water 
  falls 
  to 
  the 
  normal 
  

   level 
  and 
  farther 
  back 
  still 
  to 
  a 
  level 
  below 
  the 
  normal, 
  that 
  

   in 
  fact 
  there 
  is 
  a 
  succession 
  of 
  waves 
  of 
  elevation 
  and 
  

   depression 
  of 
  gradually 
  diminishing 
  importance 
  as 
  w^e 
  recede 
  

   from 
  the 
  bow. 
  As 
  regards 
  the 
  force 
  acting 
  upon 
  the 
  ship 
  in 
  

   the 
  fore-and-aft 
  direction, 
  we 
  know 
  that 
  at 
  any 
  point 
  it 
  is 
  the 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

  

  t 
  Naval 
  Arch. 
  Trans. 
  1881 
  ; 
  or 
  see 
  Kelvin, 
  Proc. 
  Mech. 
  Eng., 
  Aug. 
  

   1887 
  ; 
  also 
  Lamb's 
  Hydrodynamics, 
  3rd 
  ed. 
  p. 
  414. 
  

  

  