﻿JR. 
  de 
  Saussure 
  — 
  Graphical 
  Thermodynamics. 
  25 
  

  

  the 
  functions 
  X 
  and 
  [i 
  being 
  still 
  submitted 
  to 
  the 
  condition 
  

   that 
  the 
  result 
  of 
  eliminating 
  a 
  and 
  i 
  between 
  equations 
  (5) 
  be 
  : 
  

   F(P, 
  Y, 
  T)= 
  0. 
  

  

  When 
  the 
  functions 
  X 
  and 
  fi 
  have 
  been 
  determined 
  for 
  a 
  

   particular 
  substance, 
  equations 
  (5) 
  do 
  not 
  only 
  represent 
  the 
  

   thermodynamic 
  surface, 
  but 
  also 
  the 
  value 
  of 
  the 
  two 
  elements 
  

   (a 
  and 
  i) 
  of 
  the 
  vibratory 
  motion, 
  corresponding 
  to 
  any 
  state 
  

   of 
  the 
  substance 
  defined 
  by 
  experimental 
  data 
  (J^, 
  V, 
  T). 
  

  

  The 
  last 
  of 
  equations 
  (5) 
  is 
  the 
  same 
  for 
  all 
  substances, 
  

   except 
  that 
  the 
  value 
  of 
  the 
  constant 
  K 
  changes 
  from 
  one 
  

   substance 
  to 
  another. 
  The 
  determination 
  of 
  the 
  functions 
  X 
  

   and 
  jut 
  will 
  be 
  investigated 
  after 
  we 
  shall 
  have 
  studied 
  the 
  

   properties 
  of 
  the 
  graphical 
  representation, 
  which 
  properties 
  

   can 
  be 
  found 
  by 
  assuming 
  that 
  these 
  functions 
  are 
  known. 
  

  

  5. 
  When 
  a 
  substance 
  undergoes 
  an 
  elementary 
  and 
  reversible 
  

   transformation,* 
  the 
  amount 
  of 
  heat 
  dJET, 
  absorbed 
  by 
  the 
  unit 
  

   of 
  mass, 
  is 
  composed 
  of 
  two 
  parts 
  : 
  the 
  variation 
  of 
  the 
  actual 
  

   energy 
  of 
  the 
  heat 
  contained 
  in 
  the 
  substance, 
  and 
  the 
  amount 
  

   of 
  heat 
  absorbed 
  by 
  the 
  total 
  work 
  (external 
  and 
  internal). 
  

  

  The 
  first 
  part 
  is 
  the 
  elementary 
  variation 
  of 
  the 
  expression 
  

  

  ^ 
  2imu 
  2 
  , 
  as 
  found 
  above 
  ; 
  the 
  second 
  is 
  the 
  heat 
  absorbed 
  by 
  

   hi 
  

  

  the 
  work 
  done 
  by 
  the 
  force 
  /"for 
  a 
  variation 
  da 
  of 
  the 
  ampli- 
  

   tude. 
  Hence 
  : 
  

  

  EdK 
  = 
  d2£mu* 
  + 
  2fda 
  

  

  But, 
  by 
  differentiating 
  equation 
  (2) 
  : 
  

  

  d^,\mtf- 
  KEdT 
  

  

  This 
  relation 
  shows 
  that 
  the 
  constant 
  JK 
  is 
  the 
  quotient 
  of 
  the 
  

   variation 
  of 
  the 
  actual 
  amount 
  of 
  heat 
  contained 
  in 
  the 
  sub- 
  

   stance, 
  by 
  the 
  corresponding 
  variation 
  of 
  temperature, 
  so 
  that 
  

   iT 
  is 
  by 
  definition 
  the 
  absolute 
  specific 
  heat 
  of 
  the 
  substance. 
  

   We 
  have 
  also, 
  from 
  preceding 
  formulae 
  : 
  

  

  Whence 
  finally 
  

  

  2fda 
  = 
  ^mif— 
  = 
  2KTE 
  — 
  

   a 
  a 
  

  

  dR 
  = 
  KdT-f 
  2KT 
  — 
  

  

  a 
  

  

  Such 
  is 
  the 
  expression 
  of 
  dH 
  in 
  terms 
  of 
  7 
  7 
  and 
  a 
  ; 
  equation 
  

   (4) 
  gives 
  by 
  differentiation 
  : 
  

  

  da 
  di 
  , 
  dT 
  

  

  * 
  The 
  formulae 
  contained 
  in 
  this 
  paragraph 
  have 
  been 
  already 
  established 
  in 
  

   "La 
  Thermodynamique 
  et 
  ses 
  principales 
  applications," 
  by 
  J. 
  Moutier, 
  Paris, 
  

   1885; 
  we 
  recall 
  them 
  here, 
  as 
  we 
  will 
  have 
  to 
  use 
  them 
  in 
  some 
  of 
  the 
  demon- 
  

   strations. 
  

  

  