﻿HEAT 
  PRODUCED 
  BY 
  THE 
  COMPRESSION 
  OF 
  A 
  GAS. 
  291 
  

  

  is 
  not 
  constant 
  for 
  all 
  temperatures, 
  unless 
  Carnot's 
  function 
  for 
  different 
  tem- 
  

   peratures 
  vary 
  inversely 
  as 
  1 
  + 
  E 
  t, 
  and 
  that 
  it 
  is 
  not 
  the 
  simple 
  mechanical 
  equi- 
  

   valent 
  of 
  the 
  heat, 
  as 
  it 
  was 
  unwarrantably* 
  assumed 
  by 
  Mayer 
  to 
  be, 
  unless 
  

   this 
  function 
  have 
  precisely 
  the 
  expression 
  

  

  ^ 
  = 
  J 
  TTE> 
  P) 
  

  

  This 
  formula 
  was 
  suggested 
  to 
  me 
  by 
  Mr 
  Joule, 
  in 
  a 
  letter 
  dated 
  December 
  9th, 
  

   1848, 
  as 
  probably 
  a 
  true 
  expression 
  for 
  lk, 
  being 
  required 
  to 
  reconcile 
  the 
  expres- 
  

   sion 
  derived 
  from 
  Carnot's 
  theory 
  (which 
  I 
  had 
  communicated 
  to 
  him), 
  for 
  the 
  

   heat 
  evolved 
  in 
  terms 
  of 
  the 
  work 
  spent 
  in 
  the 
  compression 
  of 
  a 
  gas, 
  with 
  the 
  

   hypothesis 
  that 
  the 
  latter 
  of 
  these 
  is 
  exactly 
  the 
  mechanical 
  equivalent 
  of 
  the 
  

   former, 
  which 
  he 
  had 
  adopted 
  in 
  consequence 
  of 
  its 
  being, 
  at 
  least 
  approximately, 
  

   verified 
  by 
  his 
  own 
  experiments. 
  This, 
  which 
  will 
  be 
  called 
  Mayer's 
  hypothesis, 
  

   from 
  its 
  having 
  been 
  first 
  assumed 
  by 
  Mayer, 
  is 
  also 
  assumed 
  by 
  Clausius 
  

   without 
  any 
  reason 
  from 
  experiment 
  ; 
  and 
  an 
  expression 
  for 
  fi 
  the 
  same 
  as 
  the 
  

   preceding, 
  is 
  consequently 
  adopted 
  by 
  him 
  as 
  the 
  foundation 
  of 
  his 
  mathematical 
  

   deductions 
  from 
  elementary 
  reasoning 
  regarding 
  the 
  motive 
  power 
  of 
  heat. 
  The 
  

   preceding 
  formulse 
  show 
  that 
  if 
  it 
  be 
  true 
  at 
  a 
  particular 
  temperature 
  for 
  any 
  one 
  

   fluid 
  fulfilling 
  the 
  gaseous 
  laws, 
  it 
  must 
  be 
  true 
  for 
  every 
  such 
  fluid 
  at 
  the 
  same 
  

   temperature. 
  

  

  6. 
  Of 
  the 
  various 
  experimental 
  researches 
  which 
  might 
  be 
  suggested 
  as 
  suit- 
  

   able 
  for 
  testing 
  Mayer's 
  hypothesis, 
  it 
  appears, 
  from 
  the 
  preceding 
  formula, 
  that 
  

   any 
  which 
  would 
  give 
  data 
  for 
  the 
  determination 
  of 
  the 
  values 
  of 
  fx 
  through 
  a 
  

   wide 
  range 
  of 
  temperatures, 
  would, 
  with 
  a 
  single 
  accurate 
  determination 
  of 
  J, 
  

   afford 
  a 
  complete 
  test. 
  Thus 
  an 
  experimental 
  determination 
  of 
  the 
  density 
  of 
  

   saturated 
  steam 
  for 
  temperatures 
  from 
  0° 
  to 
  230° 
  cent., 
  would 
  complete 
  the 
  data, 
  

   of 
  which 
  a 
  part 
  have 
  been 
  so 
  accurately 
  determined 
  by 
  Regnault, 
  for 
  the 
  calcu- 
  

   lation 
  of 
  the 
  values 
  of 
  /j. 
  between 
  those 
  wide 
  limits, 
  and 
  would 
  contribute 
  more, 
  

   perhaps, 
  than 
  any 
  set 
  of 
  experimental 
  researches 
  that 
  could 
  at 
  present 
  be 
  pro- 
  

   posed, 
  to 
  advance 
  the 
  mechanical 
  theory 
  of 
  heat. 
  

  

  7. 
  The 
  values 
  of 
  fx, 
  given 
  in 
  Table 
  I. 
  of 
  my 
  Account 
  of 
  Carnot's 
  Theory, 
  

   which 
  were 
  calculated 
  from 
  Regnault's 
  observations 
  on 
  steam, 
  with 
  the 
  assump- 
  

   tion 
  of 
  169^5' 
  (the 
  maximum 
  density 
  of 
  water 
  being 
  unity) 
  for 
  the 
  density 
  of 
  satu- 
  

   rated 
  steam 
  at 
  100° 
  cent., 
  and 
  of 
  the 
  gaseous 
  laws 
  for 
  calculating 
  it 
  by 
  means 
  

   of 
  Regnault's 
  observed 
  pressures, 
  at 
  other 
  temperatures, 
  are 
  far 
  from 
  verify- 
  

   ing 
  equation 
  (I.), 
  as 
  appears 
  from 
  the 
  Table 
  of 
  the 
  values 
  of 
  *—^p 
  — 
  -, 
  given 
  in 
  

   the 
  preceding 
  paper, 
  § 
  51 
  ; 
  or 
  as 
  the 
  following 
  comparative 
  Table 
  shows 
  : 
  — 
  

  

  * 
  In 
  violation 
  of 
  Carnot's 
  important 
  principle, 
  that 
  thermal 
  agency 
  and 
  mechanical 
  effect, 
  or 
  

   mechanical 
  agency 
  and 
  thermal 
  effect, 
  cannot 
  be 
  regarded 
  in 
  the 
  simple 
  relation 
  of 
  cause 
  and 
  effect, 
  

   when 
  any 
  other 
  effect, 
  such 
  as 
  the 
  alteration 
  of 
  the 
  density 
  of 
  a 
  body, 
  is 
  finally 
  concerned. 
  

  

  