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  PROFESSOR 
  WILLIAM 
  THOMSON 
  ON 
  THE 
  

  

  8. 
  The 
  source 
  of 
  heat 
  will 
  always 
  be 
  supposed 
  to 
  be 
  a 
  hot 
  body 
  at 
  a 
  given 
  

   constant 
  temperature, 
  put 
  in 
  contact 
  with 
  some 
  part 
  of 
  the 
  engine 
  ; 
  and 
  when 
  

   any 
  part 
  of 
  the 
  engine 
  is 
  to 
  be 
  kept 
  from 
  rising 
  in 
  temperature 
  (which 
  can 
  only 
  

   be 
  done 
  by 
  drawing 
  off 
  whatever 
  heat 
  is 
  deposited 
  in 
  it), 
  this 
  will 
  be 
  supposed 
  to 
  

   be 
  done 
  by 
  putting 
  a 
  cold 
  body, 
  which 
  will 
  be 
  called 
  the 
  refrigerator, 
  at 
  a 
  given 
  

   constant 
  temperature, 
  in 
  contact 
  with 
  it. 
  

  

  9. 
  The 
  whole 
  theory 
  of 
  the 
  motive 
  power 
  of 
  heat 
  is 
  founded 
  on 
  the 
  two 
  

   following 
  propositions, 
  due 
  respectively 
  to 
  Joule, 
  and 
  to 
  Carnot 
  and 
  Clausius. 
  

  

  Prop. 
  I. 
  (Joule) 
  — 
  When 
  equal 
  quantities 
  of 
  mechanical 
  effect 
  are 
  produced 
  

   by 
  any 
  means 
  whatever, 
  from 
  purely 
  thermal 
  sources, 
  or 
  lost 
  in 
  purely 
  thermal 
  

   effects, 
  equal 
  quantities 
  of 
  heat 
  are 
  put 
  out 
  of 
  existence, 
  or 
  are 
  generated. 
  

  

  Prop. 
  II. 
  (Carnot 
  and 
  Clausius). 
  — 
  If 
  an 
  engine 
  be 
  such 
  that, 
  when 
  it 
  is 
  

   worked 
  backwards, 
  the 
  physical 
  and 
  mechanical 
  agencies 
  in 
  every 
  part 
  of 
  its 
  

   motions 
  are 
  all 
  reversed 
  ; 
  it 
  produces 
  as 
  much 
  mechanical 
  effect 
  as 
  can 
  be 
  pro- 
  

   duced 
  by 
  any 
  thermo-dynamic 
  engine, 
  with 
  the 
  same 
  temperatures 
  of 
  source 
  and 
  

   refrigerator, 
  from 
  a 
  given 
  quantity 
  of 
  heat. 
  

  

  10. 
  The 
  former 
  proposition 
  is 
  shewn 
  to 
  be 
  included 
  in 
  the 
  general 
  " 
  principle 
  

   of 
  mechanical 
  effect," 
  and 
  is 
  so 
  established 
  beyond 
  all 
  doubt 
  by 
  the 
  following 
  

   demonstration. 
  

  

  11. 
  By 
  whatever 
  direct 
  effect 
  the 
  heat 
  gained 
  or 
  lost 
  by 
  a 
  body, 
  in 
  any 
  con- 
  

   ceivable 
  circumstances, 
  is 
  tested, 
  the 
  measurement 
  of 
  its 
  quantity 
  may 
  always 
  be 
  

   founded 
  on 
  a 
  determination 
  of 
  the 
  quantity 
  of 
  some 
  standard 
  substance, 
  which 
  it 
  

   or 
  any 
  equal 
  quantity 
  of 
  heat 
  could 
  raise 
  from 
  one 
  standard 
  temperature 
  to 
  

   another 
  ; 
  the 
  test 
  of 
  equality 
  between 
  two 
  quantities 
  of 
  heat 
  being 
  their 
  capa- 
  

   bility 
  of 
  raising 
  equal 
  quantities 
  of 
  any 
  substance 
  from 
  any 
  temperature 
  to 
  the 
  

   same 
  higher 
  temperature. 
  Now, 
  according 
  to 
  the 
  dynamical 
  theory 
  of 
  heat, 
  the 
  

   temperature 
  of 
  a 
  substance 
  can 
  only 
  be 
  raised 
  by 
  working 
  upon 
  it 
  in 
  some 
  way 
  

   so 
  as 
  to 
  produce 
  increased 
  thermal 
  motions 
  within 
  it, 
  besides 
  effecting 
  any 
  modi- 
  

   fications 
  in 
  the 
  mutual 
  distances 
  or 
  arrangements 
  of 
  its 
  particles 
  which 
  may 
  

   accompany 
  a 
  change 
  of 
  temperature. 
  The 
  work 
  necessary 
  to 
  produce 
  this 
  total 
  

   mechanical 
  effect 
  is 
  of 
  course 
  proportional 
  to 
  the 
  quantity 
  of 
  the 
  substance 
  raised 
  

   from 
  one 
  standard 
  temperature 
  to 
  another 
  ; 
  and 
  therefore 
  when 
  a 
  body, 
  or 
  a 
  

   group 
  of 
  bodies, 
  or 
  a 
  machine, 
  parts 
  with 
  or 
  receives 
  heat, 
  there 
  is 
  in 
  reality 
  

   mechanical 
  effect 
  produced 
  from 
  it, 
  or 
  taken 
  into 
  it, 
  to 
  an 
  extent 
  precisely 
  pro- 
  

   portional 
  to 
  the 
  quantity 
  of 
  heat 
  which 
  it 
  emits 
  or 
  absorbs. 
  But 
  the 
  work 
  which 
  

   any 
  external 
  forces 
  do 
  upon 
  it, 
  the 
  work 
  done 
  by 
  its 
  own 
  molecular 
  forces, 
  and 
  

   the 
  amount 
  by 
  which 
  the 
  half 
  vis 
  viva 
  of 
  the 
  thermal 
  motions 
  of 
  all 
  its 
  parts 
  is 
  

   diminished, 
  must 
  together 
  be 
  equal 
  to 
  the 
  mechanical 
  effect 
  produced 
  from 
  it 
  ; 
  

   and 
  consequently, 
  to 
  the 
  mechanical 
  equivalent 
  of 
  the 
  heat 
  which 
  it 
  emits 
  (which 
  

   will 
  be 
  positive 
  or 
  negative, 
  according 
  as 
  the 
  sum 
  of 
  those 
  terms 
  is 
  positive 
  or 
  

  

  