﻿22 
  R. 
  de 
  Saussure 
  — 
  Graphical 
  Thermodynamics. 
  

  

  duration 
  of 
  its 
  period, 
  the 
  physical 
  state 
  of 
  the 
  substance 
  can 
  

   be 
  completely 
  defined 
  by 
  means 
  of 
  these 
  two 
  data, 
  provided 
  

   that 
  the 
  weight 
  of 
  the 
  substance 
  remains 
  the 
  same. 
  

  

  It 
  is 
  by 
  so 
  defining 
  the 
  state 
  of 
  a 
  body, 
  that 
  Clausius 
  suc- 
  

   ceeded 
  in 
  demonstrating 
  the 
  fundamental 
  theorems 
  of 
  thermo- 
  

   dynamics, 
  with 
  the 
  help 
  only 
  of 
  the 
  laws 
  of 
  mechanics, 
  without 
  

   making 
  any 
  hypothesis 
  as 
  to 
  the 
  form 
  of 
  the 
  trajectories 
  

   described 
  by 
  the 
  particles 
  of 
  the 
  body. 
  

  

  But 
  if 
  it 
  is 
  desired 
  to 
  establish 
  the 
  theory 
  of 
  the 
  transforma- 
  

   tions 
  which 
  take 
  place 
  in 
  a 
  substance 
  under 
  the 
  influence 
  of 
  

   heat, 
  it 
  is 
  necessary 
  to 
  define 
  the 
  nature 
  of 
  the 
  periodical 
  

   motions, 
  as 
  well 
  as 
  in 
  the 
  theory 
  of 
  light. 
  We 
  can 
  assume 
  for 
  

   instance, 
  that 
  this 
  motion 
  is 
  a 
  straight 
  vibratory 
  motion 
  on 
  

   either 
  side 
  of 
  a 
  fixed 
  center. 
  

  

  By 
  this 
  hypothesis, 
  we 
  still 
  need 
  two 
  data 
  to 
  define 
  com- 
  

   pletely 
  the 
  motion 
  of 
  the 
  particles, 
  i. 
  e., 
  the 
  amplitude 
  a 
  and 
  

   the 
  duration 
  i 
  of 
  one 
  period 
  of 
  the 
  vibratory 
  motion. 
  And 
  

   since 
  the 
  state 
  of 
  the 
  substance 
  (whose 
  mass 
  is 
  taken 
  as 
  the 
  

   unit) 
  is 
  a 
  result 
  of 
  the 
  state 
  of 
  motion 
  of 
  the 
  particles, 
  the 
  

   state 
  of 
  said 
  substance 
  can 
  be 
  considered 
  as 
  a 
  function 
  of 
  the 
  

   two 
  variables 
  a 
  and 
  i. 
  

  

  2. 
  On 
  the 
  other 
  hand, 
  to 
  define 
  the 
  physical 
  state 
  of 
  a 
  sub- 
  

   stance 
  by 
  means 
  of 
  experimental 
  data, 
  the 
  variables 
  used 
  are 
  : 
  

   the 
  volume 
  F, 
  the 
  absolute 
  temperature 
  T 
  and 
  the 
  outside 
  

   pressure 
  P 
  (the 
  mass 
  being 
  still 
  taken 
  as 
  the 
  unit).* 
  

  

  Hence, 
  the 
  state 
  of 
  a 
  body 
  can 
  also 
  be 
  regarded 
  as 
  a 
  func- 
  

   tion 
  of 
  the 
  three 
  variables 
  : 
  P, 
  V 
  and 
  T. 
  But 
  these 
  variables 
  

   are 
  not 
  independent, 
  that 
  is 
  to 
  say 
  : 
  the 
  same 
  weight 
  of 
  the 
  

   same 
  body 
  cannot 
  occupy 
  the 
  same 
  volume 
  at 
  the 
  same 
  pres- 
  

   sure 
  and 
  at 
  different 
  temperatures, 
  since 
  two 
  variables 
  are 
  suffi- 
  

   cient 
  to 
  define 
  the 
  state 
  of 
  the 
  substance. 
  For 
  each 
  body, 
  

   there 
  is 
  a 
  relation 
  F(P, 
  Y, 
  T) 
  = 
  known 
  as 
  the 
  equation 
  of 
  

   said 
  body, 
  so 
  that 
  the 
  value 
  of 
  either 
  of 
  the 
  three 
  variables 
  

   P, 
  For 
  Tis 
  a 
  direct 
  result 
  of 
  the 
  values 
  attributed 
  to 
  the 
  two 
  

   others. 
  

  

  Considering 
  P, 
  Fand 
  T 
  as 
  three 
  coordinates, 
  the 
  equation 
  

   F(P, 
  Y, 
  T) 
  = 
  represents 
  a 
  surface, 
  any 
  point 
  of 
  which 
  corre- 
  

   sponds 
  to 
  a 
  certain 
  state 
  of 
  the 
  body. 
  This 
  surface 
  is 
  there- 
  

   fore 
  a 
  "representative 
  locus" 
  of 
  the 
  different 
  states 
  under 
  

   which 
  the 
  body 
  can 
  exist, 
  and 
  is 
  known 
  as 
  the 
  " 
  thermodynamic 
  

   surfaced 
  

  

  3. 
  When 
  the 
  physical 
  state 
  of 
  a 
  substance 
  is 
  defined 
  by 
  the 
  

   first 
  method, 
  i. 
  e., 
  by 
  means 
  of 
  the 
  amplitude 
  a 
  and 
  of 
  the 
  

   period 
  i 
  of 
  the 
  vibratory 
  motion 
  which 
  constitutes 
  the 
  heat, 
  

   the 
  variables 
  a 
  and 
  i 
  can 
  also 
  be 
  treated 
  as 
  two 
  coordinates, 
  

  

  * 
  In 
  the 
  following 
  study, 
  we 
  assume 
  that 
  all 
  the 
  particles 
  of 
  the 
  body 
  are 
  at 
  

   the 
  same 
  temperature, 
  i. 
  e., 
  that 
  they 
  all 
  have 
  an 
  identical 
  vibratory 
  motion. 
  

  

  