﻿PREFACE. 
  

  

  IX 
  

  

  • 
  * 
  

  

  am 
  r* 
  

  

  o 
  the 
  crest 
  of 
  a 
  sea 
  wave 
  and 
  the 
  point 
  of 
  maximum 
  rarefaction 
  to 
  the 
  trough, 
  

   The 
  wave 
  length 
  becomes 
  then 
  the 
  distance 
  o 
  to 
  o, 
  or 
  the 
  length 
  of 
  the 
  complete 
  

   undulation 
  is 
  analogous 
  to 
  the 
  length 
  of 
  sea 
  waves 
  measured 
  from 
  crest 
  to 
  crest. 
  

  

  16. 
  It 
  is 
  to 
  be 
  noticed 
  that 
  the 
  points 
  of 
  maximum 
  condensation 
  or 
  rarefaction 
  

   are 
  those 
  of 
  junction 
  of 
  the.semiphases 
  of 
  movement 
  towards 
  and 
  away 
  from 
  the 
  

   normal 
  position 
  of 
  the 
  molecule 
  ; 
  that 
  of 
  greatest 
  condensation 
  is 
  where 
  this 
  point 
  is 
  

   passed 
  in 
  the 
  phase 
  of 
  motion 
  in 
  the 
  same 
  direction 
  as 
  the 
  wave 
  is 
  travelling, 
  that 
  of 
  

   greatest 
  rarefaction 
  where 
  the 
  same 
  point 
  is 
  being 
  passed 
  in 
  the 
  opposite 
  phase 
  of 
  

   motion. 
  It 
  may 
  also 
  be 
  noticed 
  that 
  the 
  tracts 
  which 
  are 
  in 
  this 
  latter 
  phase 
  are 
  

   longer 
  than 
  those 
  in 
  the 
  former, 
  the 
  difference 
  being 
  four 
  times 
  the 
  amplitude. 
  

  

  17. 
  As 
  has 
  already 
  been 
  remarked 
  waves 
  of 
  this 
  nature 
  can 
  be 
  transmitted 
  

   through 
  fluids 
  as 
  well 
  as 
  solids 
  ; 
  in 
  the 
  latter 
  they 
  travel 
  faster 
  than 
  any 
  other 
  

   form 
  of 
  elastic 
  wave. 
  It 
  is 
  waves 
  of 
  this 
  nature 
  which, 
  if 
  the 
  period 
  is 
  not 
  too 
  small 
  

   or 
  too 
  great, 
  become 
  sensible 
  as 
  sound. 
  

  

  18. 
  Waves 
  of 
  elastic 
  distortion.— 
  Another 
  form 
  of 
  elastic 
  waves 
  is 
  due 
  to 
  the 
  

  

  rigidity 
  of 
  the 
  substance 
  through 
  which 
  it 
  is 
  

   transmitted, 
  or 
  to 
  that 
  form 
  of 
  elasticity 
  which 
  

   ** 
  causes 
  a 
  substance 
  to 
  resist 
  a 
  change 
  of 
  its 
  original 
  

  

  shape, 
  by 
  the 
  action 
  of 
  an 
  external 
  force, 
  and 
  to 
  

   regain 
  it 
  when 
  this 
  is 
  removed. 
  These 
  waves, 
  

   which 
  are 
  necessarily 
  confined 
  to 
  solids, 
  and 
  

   cannot 
  be 
  transmitted 
  by 
  fluids, 
  are 
  known 
  as 
  

   waves 
  of 
  elastic 
  distortion 
  or 
  distortional 
  naves. 
  

   In 
  them 
  the 
  motion 
  of 
  the 
  wave-particle 
  is 
  still 
  in 
  

   a 
  straight 
  line 
  backwards 
  and 
  forwards, 
  but 
  this 
  

   line 
  lies 
  at 
  right 
  angles 
  to, 
  instead 
  of 
  along, 
  the 
  

   direction 
  in 
  which 
  the 
  wave 
  path 
  is 
  travelling, 
  the 
  

   displacement 
  being 
  alternately 
  to 
  one 
  side 
  and 
  the 
  

   other 
  of 
  the 
  normal 
  position 
  of 
  the 
  wave-particle; 
  

   hence 
  these 
  waves 
  are 
  sometimes 
  distinguished 
  as 
  

   transverse. 
  The 
  motion 
  of 
  the 
  wave-particle 
  may, 
  

   in 
  fact, 
  be 
  likened 
  to 
  the 
  motion 
  of 
  the 
  bob 
  of 
  a 
  

   pendulum, 
  the 
  direction 
  of 
  travel 
  of 
  the 
  wave 
  being 
  

   vertically 
  up 
  or 
  down. 
  This 
  form 
  of 
  wave 
  motion 
  

   is 
  represented 
  diagram 
  matically 
  in 
  fig. 
  iv. 
  The 
  

   figures 
  opposite 
  the 
  dots 
  having 
  the 
  same 
  signi- 
  

   ficance 
  as 
  in 
  fig. 
  ii, 
  the 
  amplitude 
  is 
  the 
  distance 
  

   o 
  to 
  4, 
  and 
  the 
  period 
  is 
  the 
  time 
  taken 
  to 
  travel 
  

   through 
  the 
  complete 
  cycle. 
  As 
  before, 
  there 
  are 
  two 
  principal 
  phases 
  of 
  the 
  move- 
  

   ment, 
  in 
  two 
  opposite 
  'directions, 
  and 
  these 
  are 
  divided 
  each 
  into 
  two 
  semi 
  phases 
  

   according 
  as 
  it 
  is 
  towards 
  or 
  away 
  from 
  the 
  normal 
  position 
  of 
  the 
  particle. 
  The 
  

   wave 
  length 
  is 
  the 
  distance 
  between 
  two 
  points 
  where 
  the 
  wave-particle 
  is 
  at 
  the 
  

   same 
  extremity 
  of 
  its 
  displacement 
  at 
  the 
  same 
  instant, 
  these 
  extremes 
  corres- 
  

   ponding 
  to 
  the 
  crests 
  and 
  trough 
  of 
  a 
  gravitational 
  wave. 
  

  

  19. 
  Elastic 
  surface 
  undulations.— 
  When 
  waves 
  of 
  either 
  of 
  the 
  last 
  two 
  

   kinds 
  after 
  travelling 
  through 
  the 
  interior 
  of 
  a 
  body 
  reach, 
  its 
  surface, 
  they^ 
  might 
  

   produce 
  disturbances 
  of 
  form 
  which 
  would 
  simulate 
  the 
  surface 
  undulations 
  of 
  

  

  Fig. 
  iv. 
  Diagram 
  of 
  movement 
  

   of 
  wave-particle 
  during 
  one 
  com- 
  

   plete 
  undulation 
  of 
  a 
  distortional 
  

   wave. 
  

  

  