﻿29G 
  PROFESSOR 
  WILLIAM 
  THOMSON 
  ON 
  THE 
  

  

  Hence 
  the 
  total 
  quantity 
  of 
  heat 
  emitted 
  will 
  be 
  the 
  excess 
  of 
  this 
  above 
  the 
  

   amount 
  previously 
  found 
  to 
  be 
  absorbed 
  when 
  the 
  mechanical 
  effect 
  is 
  all 
  ex- 
  

   ternal 
  ; 
  and 
  therefore 
  we 
  have 
  

  

  u== 
  HX 
  7sdv+pu 
  - 
  p 
  ^}'lf 
  u 
  d 
  -Tt 
  dv 
  • 
  ■ 
  C/). 
  

  

  Whatever 
  changes 
  of 
  temperature 
  there 
  may 
  actually 
  be 
  of 
  the 
  air 
  in 
  or 
  near 
  the 
  

   orifice, 
  this 
  expression 
  will 
  give 
  rigorously 
  the 
  total 
  quantity 
  of 
  heat 
  emitted 
  by 
  

   that 
  portion 
  of 
  tube 
  which 
  contains 
  the 
  orifice 
  and 
  the 
  whole 
  of 
  the 
  second 
  spiral 
  

   during 
  the 
  passage 
  of 
  a 
  volume 
  u 
  through 
  the 
  first 
  spiral, 
  or 
  u 
  through 
  any 
  por- 
  

   tion 
  of 
  the 
  second 
  spiral 
  where 
  the 
  temperature 
  is 
  sensibly 
  t. 
  

  

  15. 
  To 
  apply 
  this 
  result 
  to 
  the 
  case 
  of 
  a 
  gas 
  fulfilling 
  the 
  gaseous 
  laws, 
  we 
  

  

  may 
  put 
  

  

  p 
  u—p 
  u'. 
  

  

  Hence 
  (e) 
  becomes 
  

  

  W= 
  / 
  Z5 
  d 
  v 
  =p 
  u 
  log 
  - 
  = 
  p' 
  u' 
  log 
  -, 
  (5), 
  

  

  and, 
  by 
  (3), 
  we 
  have 
  

  

  dW 
  E»m 
  . 
  v! 
  EW 
  

   log 
  

  

  dt 
  1 
  + 
  E* 
  ° 
  u 
  1+E/' 
  

   Hence 
  the 
  expression 
  (/) 
  for 
  the 
  heat 
  emitted 
  becomes 
  

  

  = 
  {j-;^ifE7)} 
  w 
  < 
  6) 
  - 
  

  

  iU(l+E0 
  

  

  16. 
  Lastly, 
  if 
  Mayer's 
  hypothesis 
  be 
  fulfilled 
  for 
  the 
  gas 
  used 
  in 
  the 
  experi- 
  

   ment, 
  the 
  coefficient 
  of 
  W 
  vanishes, 
  by 
  (I.), 
  and 
  therefore 
  

  

  H=0 
  (III.) 
  

  

  17. 
  From 
  equation 
  (III.) 
  it 
  follows 
  that, 
  if 
  Mayer's 
  hypothesis 
  be 
  true, 
  there 
  

   is 
  neither 
  emission 
  nor 
  absorption 
  of 
  heat, 
  on 
  the 
  whole, 
  required 
  to 
  reduce 
  the 
  

   temperature 
  of 
  the 
  air 
  after 
  passing 
  through 
  the 
  orifice, 
  to 
  its 
  primitive 
  value, 
  t. 
  

   Hence, 
  although 
  no 
  doubt 
  those 
  portions 
  of 
  the 
  air 
  in 
  the 
  intermediate 
  neighbour- 
  

   hood 
  of 
  the 
  orifice, 
  which 
  are 
  communicating, 
  by 
  their 
  expansion, 
  vis 
  viva 
  to 
  those 
  

   contiguous 
  to 
  them, 
  will 
  be 
  becoming 
  colder, 
  and 
  those 
  which 
  are 
  the 
  means 
  of 
  

   occasioning 
  the 
  portions 
  contiguous 
  to 
  them 
  to 
  lose 
  vis 
  viva, 
  through 
  fluid 
  fric- 
  

   tion, 
  will 
  be 
  becoming 
  warmer 
  at 
  each 
  instant 
  ; 
  yet 
  very 
  near 
  the 
  orifice 
  on 
  each 
  

   side, 
  where 
  the 
  motion 
  of 
  the 
  air 
  is 
  uniform, 
  the 
  temperature 
  would 
  be 
  con- 
  

   stantly 
  equal 
  to 
  t. 
  Hence 
  the 
  simplest 
  conceivable 
  test 
  of 
  the 
  truth 
  of 
  Mayer's 
  

   hypothesis 
  would 
  be 
  to 
  try 
  whether 
  the 
  temperature 
  of 
  the 
  air 
  is 
  exactly 
  the 
  same 
  

   on 
  the 
  two 
  sides 
  of 
  the 
  orifice. 
  This 
  might 
  be 
  done 
  by 
  very 
  delicate 
  thermo- 
  

   meters 
  adjusted 
  in 
  the 
  tube 
  at 
  sufficient 
  distances 
  on 
  each 
  side 
  of 
  the 
  orifice 
  to 
  be 
  

   quite 
  out 
  of 
  the 
  rush 
  which 
  there 
  is 
  of 
  air 
  in 
  the 
  immediate 
  neighbourhood 
  of 
  the 
  

   orifice 
  ; 
  but 
  it 
  might 
  be 
  done 
  in 
  a 
  still 
  more 
  refined 
  manner 
  by 
  means 
  of 
  a 
  deli- 
  

  

  