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  XXXIV. 
  On 
  the 
  Pressure 
  of 
  Vibrations. 
  

   By 
  Lord 
  Rayleigh, 
  F.R.S.* 
  

  

  THE 
  importance 
  of 
  the 
  consequences 
  deduced 
  by 
  Boltz- 
  

   maim 
  and 
  W. 
  Wien 
  from 
  the 
  doctrine 
  of 
  the 
  pressure 
  

   of 
  radiation 
  has 
  naturally 
  drawn 
  increased 
  attention 
  to 
  this 
  

   subject. 
  That 
  sethereal 
  vibrations 
  must 
  exercise 
  a 
  pressure 
  

   upon 
  a 
  perfectly 
  conducting, 
  and 
  therefore 
  perfectly 
  reflecting, 
  

   boundary 
  was 
  Maxwell's 
  deduction 
  from 
  his 
  general 
  equations 
  

   of 
  the 
  electromagnetic 
  field 
  ; 
  and 
  the 
  existence 
  of 
  the 
  pres- 
  

   sure 
  of 
  light 
  has 
  lately 
  been 
  confirmed 
  experimentally 
  by 
  

   Lebedew. 
  It 
  seemed 
  to 
  me 
  that 
  it 
  would 
  be 
  of 
  interest 
  to 
  

   inquire 
  whether 
  other 
  kinds 
  of 
  vibration 
  exercise 
  a 
  pressure, 
  

   and 
  if 
  possible 
  to 
  frame 
  a 
  general 
  theory 
  of 
  the 
  action. 
  

  

  We 
  are 
  at 
  once 
  confronted 
  with 
  a 
  difference 
  between 
  the 
  

   conditions 
  to 
  be 
  dealt 
  with 
  in 
  the 
  case 
  of 
  sethereal 
  vibrations 
  

   and, 
  for 
  example, 
  the 
  vibrations 
  of 
  air. 
  When 
  a 
  plate 
  of 
  

   polished 
  silver 
  advances 
  against 
  waves 
  of 
  light, 
  the 
  waves 
  

   indeed 
  are 
  reflected, 
  but 
  the 
  medium 
  itself 
  must 
  be 
  supposed 
  

   capable 
  of 
  penetrating 
  the 
  plate 
  ; 
  whereas 
  in 
  the 
  corre- 
  

   sponding 
  case 
  of 
  aerial 
  vibrations 
  the 
  air 
  as 
  well 
  as 
  the- 
  

   vibrations 
  are 
  compressed 
  by 
  the 
  advancing 
  wall. 
  In 
  other 
  

   cases, 
  however, 
  a 
  closer 
  parallelism 
  may 
  be 
  established. 
  Thus 
  

   the 
  transverse 
  vibrations 
  of 
  a 
  stretched 
  string, 
  or 
  wire, 
  may 
  

   be 
  supposed 
  to 
  be 
  limited 
  by 
  a 
  small 
  ring 
  constrained 
  to 
  

   remain 
  upon 
  the 
  equilibrium 
  line 
  of 
  the 
  string, 
  but 
  capable 
  

   of 
  sliding 
  freely 
  upon 
  it. 
  In 
  this 
  arrangement 
  the 
  string 
  

   passes 
  but 
  the 
  vibrations 
  are 
  compressed, 
  when 
  the 
  ring 
  

   moves 
  inwards. 
  

  

  We 
  will 
  commence 
  with 
  the 
  very 
  simple 
  Fig. 
  1. 
  

  

  problem 
  of 
  a 
  pendulum 
  in 
  which 
  a 
  mass 
  C 
  is 
  

   suspended 
  by 
  a 
  string. 
  B 
  is 
  a 
  ring 
  con- 
  

   strained 
  to 
  the 
  vertical 
  line 
  AD 
  and 
  capable 
  

   of 
  moving 
  along 
  it 
  ; 
  BG 
  = 
  l, 
  and 
  6 
  denotes 
  

   the 
  angle 
  between 
  BC 
  and 
  AD 
  at 
  any 
  time 
  t. 
  

   If 
  B 
  is 
  held 
  at 
  rest, 
  BC 
  is 
  an 
  ordinary 
  pen- 
  E 
  

  

  dulum, 
  and 
  it 
  is 
  supposed 
  to 
  be 
  executing 
  A 
  

  

  small 
  vibrations; 
  so 
  that 
  # 
  = 
  ©cosrc£, 
  where 
  / 
  

  

  n 
  2 
  =g/l. 
  The 
  tension 
  of 
  the 
  string 
  is 
  approxi- 
  / 
  

  

  mately 
  W, 
  the 
  weight 
  of 
  the 
  bob 
  ; 
  and 
  the 
  / 
  

  

  force 
  tending 
  to 
  push 
  B 
  upwards 
  is 
  at 
  time 
  t 
  c/ 
  

   W(l 
  — 
  cos 
  6). 
  Now 
  this 
  expression 
  is 
  closely 
  O 
  c 
  

  

  related 
  to 
  the 
  potential 
  energy 
  of 
  the 
  pendulum, 
  for 
  which 
  

  

  V 
  = 
  WZ(l-cos0). 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

  

  