﻿Wave- 
  Resistance 
  of 
  a 
  Ship. 
  107 
  

  

  middle 
  body. 
  The 
  neglect 
  of 
  friction 
  is 
  probably 
  of 
  little 
  

   consequence. 
  The 
  eddying 
  water 
  close 
  to 
  the 
  side 
  will 
  no 
  

   doubt 
  slightly 
  alter 
  the 
  virtual 
  shape 
  of 
  the 
  ship, 
  but 
  the 
  

   change 
  in 
  the 
  inclination 
  of 
  the 
  virtual 
  tangent 
  plane, 
  on 
  

   which 
  the 
  wave-making 
  depends, 
  will, 
  almost 
  certainly, 
  be 
  

   very 
  small. 
  Further, 
  the 
  effect 
  of 
  viscosity 
  in 
  destroying 
  

   the 
  waves 
  produced 
  by 
  the 
  bow 
  will 
  modify 
  to 
  some 
  extent 
  

   the 
  interaction 
  of 
  bow 
  and 
  stern 
  waves; 
  but, 
  seeing 
  that 
  it 
  

   is 
  the 
  waves 
  of 
  length 
  comparable 
  with 
  that 
  of 
  the 
  ship 
  which 
  

   chiefly 
  give 
  rise 
  to 
  the 
  resistance, 
  the 
  effect 
  must 
  be 
  small. 
  

   The 
  conclusion 
  is, 
  therefore, 
  that 
  the 
  course 
  followed 
  by 
  

   W. 
  Froude, 
  of 
  considering 
  frictional 
  resistance 
  and 
  wave- 
  

   resistance 
  separately 
  and 
  adding 
  the 
  two, 
  w 
  r 
  ill 
  probably 
  give 
  

   a 
  close 
  approximation 
  to 
  the 
  truth. 
  

  

  A 
  summary 
  of 
  the 
  experimental 
  work 
  on 
  this 
  question, 
  as 
  

   well 
  as 
  a 
  sketch 
  of 
  the 
  theoretical 
  work 
  of 
  Russell, 
  Rankine, 
  

   and 
  the 
  two 
  Froudes, 
  is 
  given 
  in 
  White's 
  interesting 
  ' 
  Manual 
  

   of 
  Naval 
  Architecture' 
  (1894), 
  chap. 
  xi. 
  Recent 
  mathe- 
  

   matics 
  on 
  the 
  subject 
  has 
  been 
  devoted 
  chiefly 
  to 
  explaining, 
  

   in 
  a 
  general 
  way, 
  the 
  interesting 
  wave-patterns 
  observed, 
  but 
  

   exception 
  must 
  be 
  made 
  of 
  the 
  papers 
  of 
  Sir 
  W. 
  Thomson 
  

   (Lord 
  Kelvin), 
  Phil. 
  Mag. 
  (1886-7), 
  in 
  which 
  the 
  critical 
  

   speed 
  of 
  a 
  canal 
  boat, 
  examined 
  experimentally 
  long 
  before 
  

   by 
  Russell, 
  was 
  mathematically 
  discussed. 
  Reference 
  may 
  

   be 
  made 
  to 
  Lamb's 
  i 
  Hydrodynamics 
  ' 
  (1895) 
  , 
  chap, 
  ix., 
  and 
  to 
  

   Sir 
  W. 
  Thomson's 
  ' 
  Popular 
  Lectures 
  on 
  Navigation 
  ' 
  (1891), 
  

   p. 
  450, 
  for 
  the 
  discussion 
  of 
  wave-patterns. 
  

  

  None 
  of 
  these 
  writers 
  has, 
  however, 
  considered 
  the 
  waves 
  

   produced 
  by 
  an 
  actual 
  ship, 
  and 
  the 
  present 
  paper 
  is 
  intended 
  

   to 
  supply 
  the 
  necessary 
  investigation. 
  The 
  formula 
  obtained 
  

   for 
  the 
  wave-disturbance 
  is 
  rather 
  complex, 
  but 
  that 
  for 
  the 
  

   resistance 
  is 
  much 
  simpler, 
  as 
  the 
  most 
  complicated 
  term 
  

   in 
  the 
  former 
  represents 
  a 
  local 
  disturbance 
  not 
  leading 
  to 
  

   any 
  resistance 
  in 
  an 
  in 
  viscid 
  liquid. 
  There 
  will 
  therefore 
  be 
  no 
  

   difficulty 
  to 
  those 
  who 
  have 
  the 
  necessary 
  apparatus 
  in 
  making 
  

   comparisons 
  with 
  experiment. 
  As 
  to 
  general 
  results, 
  for 
  

   deep 
  w 
  r 
  ater 
  the 
  theory 
  leads 
  to 
  a 
  resistance 
  which 
  increases 
  

   with 
  the 
  velocity, 
  in 
  an 
  oscillating 
  manner, 
  to 
  a 
  maximum 
  

   and 
  then 
  decreases 
  to 
  zero 
  as 
  the 
  velocity 
  is 
  indefinitely 
  in- 
  

   creased. 
  That 
  the 
  resistance 
  is 
  an 
  oscillating 
  function 
  of 
  the 
  

   velocity 
  has 
  been 
  experimentally 
  found 
  by 
  Mr. 
  W. 
  Froude 
  

   and 
  his 
  son 
  *, 
  to 
  whom 
  also 
  we 
  owe 
  the 
  general 
  explanation 
  

   in 
  terms 
  of 
  the 
  interference 
  of 
  bow 
  and 
  stern 
  waves. 
  But 
  the 
  

  

  * 
  " 
  On 
  the 
  Leading 
  Phenomena 
  of 
  the 
  Wave-making 
  Resistance 
  of 
  

   Ships," 
  Trans. 
  Inst. 
  Naval 
  Architects, 
  1881. 
  

  

  