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  XVI. 
  — 
  On 
  a 
  Method 
  of 
  Discovering 
  experimentally 
  the 
  Relation 
  between 
  the 
  Mecha- 
  

   nical 
  Work 
  spent, 
  and 
  the 
  Heat 
  produced 
  by 
  the 
  Compression 
  of 
  a 
  Gaseous 
  

   Fluid. 
  By 
  William 
  Thomson, 
  M.A., 
  Fellow 
  of 
  St 
  Peter's 
  College, 
  Cambridge, 
  

   and 
  Professor 
  of 
  Natural 
  Philosophy 
  in 
  the 
  University 
  of 
  Glasgow. 
  

  

  (Read 
  21st 
  April 
  1851.) 
  

  

  1 
  . 
  The 
  important 
  researches 
  of 
  Joule 
  on 
  the 
  thermal 
  circumstances 
  connected 
  

   with 
  the 
  expansion 
  and 
  compression 
  of 
  air, 
  and 
  the 
  admirable 
  reasoning 
  upon 
  

   them, 
  expressed 
  in 
  his 
  paper* 
  " 
  On 
  the 
  Changes 
  of 
  Temperature 
  produced 
  by 
  the 
  

   Rarefaction 
  and 
  Condensation 
  of 
  Air," 
  especially 
  the 
  way 
  in 
  which 
  he 
  takes 
  into 
  

   account 
  any 
  mechanical 
  effect 
  that 
  may 
  be 
  externally 
  produced, 
  or 
  internally 
  lost, 
  

   in 
  fluid 
  friction, 
  have 
  introduced 
  an 
  entirely 
  new 
  method 
  of 
  treating 
  questions 
  

   regarding 
  the 
  physical 
  properties 
  of 
  fluids. 
  The 
  object 
  of 
  the 
  present 
  paper 
  is 
  to 
  

   show 
  how, 
  by 
  the 
  use 
  of 
  this 
  new 
  method, 
  in 
  connection 
  with 
  the 
  principles 
  ex- 
  

   plained 
  in 
  my 
  preceding 
  paper, 
  a 
  complete 
  theoretical 
  view 
  may 
  be 
  obtained 
  of 
  

   the 
  phenomena 
  experimented 
  on 
  by 
  Joule 
  ; 
  and 
  to 
  point 
  out 
  some 
  of 
  the 
  objects 
  

   to 
  be 
  attained 
  by 
  a 
  continuation 
  and 
  extension 
  of 
  his 
  experimental 
  researches. 
  

  

  2. 
  The 
  Appendix 
  to 
  my 
  Account 
  of 
  Carnot's 
  Theoryf 
  contains 
  a 
  theoretical 
  

   investigation 
  of 
  the 
  heat 
  developed 
  by 
  the 
  compression 
  of 
  any 
  fluid 
  fulfilling 
  the 
  

   laws 
  X 
  of 
  Boyle 
  and 
  Mariotte 
  and 
  of 
  Dalton 
  and 
  Gay 
  Lussac. 
  It 
  has 
  since 
  been 
  

   shown 
  that 
  that 
  investigation 
  requires 
  no 
  modification 
  when 
  the 
  Dynamical 
  Theory 
  

   is 
  adopted, 
  and 
  therefore 
  the 
  formula 
  obtained 
  as 
  the 
  result 
  may 
  be 
  regarded 
  as 
  

   being 
  established 
  for 
  a 
  fluid 
  of 
  the 
  kind 
  assumed, 
  independently 
  of 
  any 
  hypothesis 
  

   whatever. 
  We 
  may 
  obtain 
  a 
  corresponding 
  formula 
  applicable 
  to 
  a 
  fluid 
  not 
  ful- 
  

   filling 
  the 
  gaseous 
  laws 
  of 
  density, 
  or 
  to 
  a 
  solid 
  pressed 
  uniformly 
  on 
  all 
  sides, 
  in 
  

   the 
  following 
  manner. 
  

  

  3. 
  Let 
  M 
  d 
  v 
  be 
  the 
  quantity 
  of 
  heat 
  absorbed 
  by 
  a 
  body 
  kept 
  at 
  a 
  constant 
  

   temperature 
  t, 
  when 
  its 
  volume 
  is 
  increased 
  from 
  v 
  to 
  v 
  + 
  d 
  v 
  ; 
  let 
  p 
  be 
  the 
  uniform 
  

   pressure 
  which 
  it 
  experiences 
  from 
  without, 
  when 
  its 
  volume 
  is 
  v 
  and 
  its 
  tempe- 
  

   rature 
  t 
  ; 
  and 
  let 
  p 
  + 
  -— 
  d 
  t 
  denote 
  the 
  value 
  p 
  would 
  acquire 
  if 
  the 
  temperature 
  

   were 
  raised 
  to 
  t 
  + 
  dt, 
  the 
  volume 
  remaining 
  unchanged. 
  Then, 
  by 
  equation 
  (3) 
  of 
  

  

  * 
  Philosophical 
  Magazine, 
  May 
  1845, 
  vol. 
  xxvi., 
  p. 
  369. 
  

   | 
  Transactions, 
  vol. 
  xvi., 
  part 
  V. 
  

  

  J 
  To 
  avoid 
  circumlocution 
  these 
  laws 
  will, 
  in 
  what 
  follows, 
  be 
  called 
  simply, 
  the 
  gaseous 
  laws, 
  

   or 
  the 
  gaseous 
  laws 
  of 
  density. 
  

  

  VOL. 
  XX. 
  PART 
  II. 
  4 
  I 
  

  

  