﻿DYNAMICAL 
  THEOEY 
  OF 
  HEAT. 
  265 
  

  

  negative). 
  Now, 
  let 
  there 
  be 
  either 
  no 
  molecular 
  change 
  or 
  alteration 
  of 
  tempe- 
  

   rature 
  in 
  any 
  part 
  of 
  the 
  body, 
  or, 
  by 
  a 
  cycle 
  of 
  operations, 
  let 
  the 
  temperature 
  

   and 
  physical 
  condition 
  be 
  restored 
  exactly 
  to 
  what 
  they 
  were 
  at 
  the 
  beginning 
  ; 
  

   the 
  second 
  and 
  third 
  of 
  the 
  three 
  parts 
  of 
  the 
  work 
  which 
  it 
  has 
  to 
  produce 
  

   vanish 
  ; 
  and 
  we 
  conclude 
  that 
  the 
  heat 
  which 
  it 
  emits 
  or 
  absorbs 
  will 
  be 
  the 
  

   thermal 
  equivalent 
  of 
  the 
  work 
  done 
  upon 
  it 
  by 
  external 
  forces, 
  or 
  done 
  by 
  it 
  

   against 
  external 
  forces 
  ; 
  which 
  is 
  the 
  proposition 
  to 
  be 
  proved. 
  

  

  12. 
  The 
  demonstration 
  of 
  the 
  second 
  proposition 
  is 
  founded 
  on 
  the 
  following 
  

   axiom 
  : 
  — 
  

  

  It 
  is 
  impossible, 
  by 
  means 
  of 
  inanimate 
  material 
  agency, 
  to 
  derive 
  mechanical 
  

   effect 
  from 
  any 
  portion 
  of 
  matter 
  by 
  cooling 
  it 
  below 
  the 
  temperature 
  of 
  the 
  coldest 
  

   of 
  the 
  surrounding 
  objects.* 
  

  

  13. 
  To 
  demonstrate 
  the 
  second 
  proposition, 
  let 
  A 
  and 
  B 
  be 
  two 
  thermo-dynamic 
  

   engines, 
  of 
  which 
  B 
  satisfies 
  the 
  conditions 
  expressed 
  in 
  the 
  enunciation 
  ; 
  and 
  let, 
  

   if 
  possible, 
  A 
  derive 
  more 
  work 
  from 
  a 
  given 
  quantity 
  of 
  heat 
  than 
  B, 
  when 
  their 
  

   sources 
  and 
  refrigerators 
  are 
  at 
  the 
  same 
  temperatures, 
  respectively. 
  Then, 
  on 
  

   account 
  of 
  the 
  condition 
  of 
  complete 
  reversibility 
  in 
  all 
  its 
  operations 
  which 
  it 
  

   fulfils, 
  B 
  may 
  be 
  worked 
  backwards, 
  and 
  made 
  to 
  restore 
  any 
  quantity 
  of 
  heat 
  to 
  

   its 
  source, 
  by 
  the 
  expenditure 
  of 
  the 
  amount 
  of 
  work 
  which, 
  by 
  its 
  forward 
  ac- 
  

   tion, 
  it 
  would 
  derive 
  from 
  the 
  same 
  quantity 
  of 
  heat. 
  If, 
  therefore, 
  B 
  be 
  worked 
  

   backwards, 
  and 
  made 
  to 
  restore 
  to 
  the 
  source 
  of 
  A 
  (which 
  we 
  may 
  suppose 
  to 
  be 
  

   adjustable 
  to 
  the 
  engine 
  B) 
  as 
  much 
  heat 
  as 
  has 
  been 
  drawn 
  from 
  it 
  during 
  a 
  

   certain 
  period 
  of 
  the 
  working 
  of 
  A, 
  a 
  smaller 
  amount 
  of 
  work 
  will 
  be 
  spent 
  thus 
  

   than 
  was 
  gained 
  by 
  the 
  working 
  of 
  A. 
  Hence, 
  if 
  such 
  a 
  series 
  of 
  operations 
  of 
  A 
  

   forwards 
  and 
  of 
  B 
  backwards 
  be 
  continued, 
  either 
  alternately 
  or 
  simultaneously, 
  

   there 
  will 
  result 
  a 
  continued 
  production 
  of 
  work 
  without 
  any 
  continued 
  abstrac- 
  

   tion 
  of 
  heat 
  from 
  the 
  source 
  ; 
  and, 
  by 
  Prop. 
  I., 
  it 
  follows 
  that 
  there 
  must 
  be 
  more 
  

   heat 
  abstracted 
  from 
  the 
  refrigerator 
  by 
  the 
  working 
  of 
  B 
  backwards 
  than 
  is 
  de- 
  

   posited 
  in 
  it 
  by 
  A. 
  Now, 
  it 
  is 
  obvious 
  that 
  A 
  might 
  be 
  made 
  to 
  spend 
  part 
  of 
  its 
  

   work 
  in 
  working 
  B 
  backwards, 
  and 
  the 
  whole 
  might 
  be 
  made 
  self-acting. 
  Also, 
  

   there 
  being 
  no 
  heat 
  either 
  taken 
  from 
  or 
  given 
  to 
  the 
  source 
  on 
  the 
  whole, 
  all 
  the 
  

   surrounding 
  bodies 
  and 
  space, 
  except 
  the 
  refrigerator, 
  might, 
  without 
  interfering 
  

   with 
  any 
  of 
  the 
  conditions 
  which 
  have 
  been 
  assumed, 
  be 
  made 
  of 
  the 
  same 
  tem- 
  

   perature 
  as 
  the 
  source, 
  whatever 
  that 
  may 
  be. 
  We 
  should 
  thus 
  have 
  a 
  self-acting 
  

   machine, 
  capable 
  of 
  drawing 
  heat 
  constantly 
  from 
  a 
  body 
  surrounded 
  by 
  others 
  

   at 
  a 
  higher 
  temperature, 
  and 
  converting 
  it 
  into 
  mechanical 
  effect. 
  But 
  this 
  is 
  

   contrary 
  to 
  the 
  axiom, 
  and, 
  therefore, 
  we 
  conclude 
  that 
  the 
  hypothesis 
  that 
  A 
  

  

  * 
  If 
  this 
  axiom 
  be 
  denied 
  for 
  all 
  temperatures, 
  it 
  would 
  have 
  to 
  he 
  admitted 
  that 
  a 
  self-acting 
  

   machine 
  might 
  be 
  set 
  to 
  work 
  and 
  produce 
  mechanical 
  effect 
  by 
  cooling 
  the 
  sea 
  or 
  earth, 
  with 
  no 
  

   limit 
  but 
  the 
  total 
  loss 
  of 
  heat 
  from 
  the 
  earth 
  and 
  sea, 
  or, 
  in 
  reality, 
  from 
  the 
  whole 
  material 
  world. 
  

  

  VOL. 
  XX. 
  PART 
  II. 
  4 
  C 
  

  

  