﻿DYNAMICAL 
  THEORY 
  OF 
  HEAT. 
  277 
  

  

  consequently 
  render 
  considerable 
  alterations 
  in 
  my 
  results 
  necessary, 
  I 
  shall 
  still 
  

   continue 
  to 
  use 
  Table 
  I. 
  of 
  that 
  paper, 
  which 
  shews 
  the 
  values 
  of// 
  for 
  the 
  tem- 
  

   peratures 
  \, 
  1^, 
  2^ 
  . 
  . 
  . 
  23(% 
  or, 
  the 
  mean 
  values 
  of 
  fx 
  for 
  each 
  of 
  the 
  230 
  

   successive 
  centigrade 
  degrees 
  of 
  the 
  air-thermometer 
  above 
  the 
  freezing 
  point, 
  

   as 
  the 
  basis 
  of 
  numerical 
  applications 
  of 
  the 
  theory. 
  It 
  may 
  be 
  added, 
  that 
  any 
  

   experimental 
  researches, 
  sufficiently 
  trustworthy 
  in 
  point 
  of 
  accuracy, 
  yet 
  to 
  be 
  

   made, 
  either 
  on 
  air 
  or 
  on 
  any 
  other 
  substance, 
  which 
  may 
  lead 
  to 
  values 
  of 
  // 
  dif- 
  

   fering 
  from 
  those, 
  must 
  be 
  admitted 
  as 
  proving 
  a 
  discrepancy 
  between 
  the 
  true 
  

   densities 
  of 
  saturated 
  steam, 
  and 
  those 
  which 
  have 
  been 
  assumed.* 
  

  

  35. 
  Table 
  II. 
  of 
  my 
  former 
  paper, 
  which 
  shews 
  the 
  values 
  of 
  / 
  fJ-dt 
  

  

  for 
  t 
  = 
  1, 
  t 
  = 
  2, 
  t 
  = 
  3, 
  . 
  ■ 
  . 
  . 
  t 
  = 
  231, 
  renders 
  the 
  calculation 
  of 
  the 
  mechani- 
  

   cal 
  effect 
  derivable 
  from 
  a 
  given 
  quantity 
  of 
  heat 
  by 
  means 
  of 
  a 
  perfect 
  engine, 
  

   with 
  any 
  given 
  range 
  included 
  between 
  the 
  limits 
  and 
  231, 
  extremely 
  easy 
  ; 
  

   since 
  the 
  quantity 
  to 
  be 
  divided 
  by 
  J 
  f 
  in 
  the 
  index 
  of 
  the 
  exponential 
  in 
  expres- 
  

   sion 
  (8) 
  will 
  be 
  found 
  by 
  subtracting 
  the 
  number 
  in 
  that 
  Table 
  corresponding 
  to 
  

   the 
  value 
  of 
  T, 
  from 
  that 
  corresponding 
  to 
  the 
  value 
  of 
  S. 
  

  

  36. 
  The 
  following 
  Tables 
  shew 
  some 
  numerical 
  results 
  which 
  have 
  been 
  

   obtained 
  in 
  this 
  way, 
  with 
  a 
  few 
  (contained 
  in 
  the 
  lower 
  part 
  of 
  the 
  second 
  

  

  Table) 
  calculated 
  from 
  values 
  of 
  J 
  fx 
  dt 
  estimated 
  for 
  temperatures 
  above 
  230°, 
  

  

  roughly, 
  according 
  to 
  the 
  rate 
  of 
  variation 
  of 
  that 
  function 
  within 
  the 
  experi- 
  

   mental 
  limits. 
  

  

  37. 
  Explanation 
  of 
  the 
  Tables. 
  

   Column 
  I. 
  in 
  each 
  Table 
  shews 
  the 
  assumed 
  ranges. 
  

   Column 
  II. 
  shews 
  ranges 
  deduced 
  by 
  means 
  of 
  Table 
  II. 
  of 
  the 
  former 
  paper, 
  

  

  so 
  that 
  the 
  value 
  of 
  / 
  T 
  jx 
  dt 
  for 
  each 
  may 
  be 
  the 
  same 
  as 
  for 
  the 
  corresponding 
  

  

  range 
  shewn 
  in 
  Column 
  I. 
  

  

  Column 
  III. 
  shews 
  what 
  would 
  be 
  the 
  duty 
  of 
  a 
  unit 
  of 
  heat 
  if 
  Carnot's 
  

   theory 
  required 
  no 
  modification 
  [or 
  the 
  actual 
  duty 
  of 
  a 
  unit 
  of 
  heat 
  with 
  addi- 
  

  

  * 
  I 
  cannot 
  see 
  that 
  any 
  hypothesis, 
  such 
  as 
  that 
  adopted 
  by 
  Clausius 
  fundamentally 
  in- 
  his 
  

   investigations 
  on 
  this 
  subject, 
  and 
  leading, 
  as 
  he 
  shews, 
  to 
  determinations 
  of 
  the 
  densities 
  of 
  saturated 
  

   steam 
  at 
  different 
  temperatures, 
  which 
  indicate 
  enormous 
  deviations 
  from 
  the 
  gaseous 
  laws 
  of 
  varia- 
  

   tion 
  with 
  temperature 
  and 
  pressure, 
  is 
  more 
  probable, 
  or 
  is 
  probably 
  nearer 
  the 
  truth, 
  than 
  that 
  the 
  

   density 
  of 
  saturated 
  steam 
  does 
  follow 
  these 
  laws 
  as 
  it 
  is 
  usually 
  assumed 
  to 
  do. 
  In 
  the 
  present 
  

   state 
  of 
  science 
  it 
  would 
  perhaps 
  be 
  wrong 
  to 
  say 
  that 
  either 
  hypothesis 
  is 
  more 
  probable 
  than 
  the 
  

   other. 
  

  

  \ 
  It 
  ought 
  to 
  be 
  remarked 
  that, 
  as 
  the 
  unit 
  of 
  force 
  implied 
  in 
  the 
  determinations 
  of 
  p 
  is 
  the 
  

   weight 
  of 
  a 
  pound 
  of 
  matter 
  at 
  Paris, 
  and 
  the 
  unit 
  of 
  force 
  in 
  terms 
  of 
  which 
  J 
  is 
  expressed 
  is 
  the 
  

   weight 
  of 
  a 
  pound 
  at 
  Manchester, 
  these 
  numbers 
  ought 
  in 
  strictness 
  to 
  be 
  modified 
  so 
  as 
  to 
  

   express 
  the 
  values 
  in 
  terms 
  of 
  a 
  common 
  unit 
  of 
  force 
  ; 
  but 
  as 
  the 
  force 
  of 
  gravity 
  at 
  Paris 
  differs 
  

   by 
  less 
  than 
  ^oVo 
  °f 
  its 
  own 
  value 
  from 
  the 
  force 
  of 
  gravity 
  at 
  Manchester, 
  this 
  correction 
  will 
  be 
  

   much 
  less 
  than 
  the 
  probable 
  errors 
  from 
  other 
  sources, 
  and 
  may 
  therefore 
  be 
  neglected. 
  

  

  VOL. 
  XX. 
  PART 
  II. 
  2 
  F 
  

  

  