﻿40 
  B. 
  deSaussure 
  — 
  Graphical 
  Thermodynamics. 
  

  

  vided 
  that 
  the 
  result 
  be 
  divided 
  by 
  n, 
  and 
  also 
  that 
  the 
  

   portion 
  MN 
  of 
  the 
  normal 
  be 
  short 
  enough 
  to 
  be 
  practically 
  

   straight, 
  notwithstanding 
  the 
  curvature 
  of 
  the 
  surface. 
  B 
  

   being 
  obtained 
  graphically, 
  the 
  components 
  A 
  and 
  B 
  are 
  

   readily 
  obtained 
  by 
  drawing 
  parallels 
  to 
  the 
  axes 
  of 
  coordinates 
  

   through 
  the 
  points 
  M 
  and 
  Q. 
  

  

  This 
  graphical 
  determination 
  of 
  B, 
  does 
  not 
  apply 
  when 
  <p 
  

   and 
  s 
  are 
  chosen 
  as 
  coordinates 
  : 
  in 
  this 
  case 
  A 
  and 
  B 
  have 
  to 
  

   be 
  computed 
  by 
  the 
  aid 
  of 
  equations 
  (11) 
  ; 
  but, 
  when 
  this 
  has 
  

   been 
  done, 
  A 
  and 
  B 
  can 
  still 
  be 
  considered 
  as 
  two 
  magnitudes 
  

   parallel 
  to 
  the 
  axes 
  o<p 
  and 
  os 
  and 
  they 
  can 
  be 
  combined 
  into 
  a 
  

   single 
  one 
  B 
  having 
  a 
  definite 
  direction, 
  so 
  that 
  in 
  any 
  case, 
  all 
  

   the 
  physical 
  coefficients 
  referring 
  to 
  a 
  particular 
  state 
  of 
  the 
  

   substance 
  can 
  be 
  represented 
  graphically 
  by 
  a 
  single 
  magnitude 
  

   of 
  a 
  certain 
  length, 
  drawn 
  in 
  a 
  proper 
  direction. 
  

  

  Research 
  of 
  the 
  thermodynamic 
  function. 
  

  

  14. 
  The 
  thermodynamic 
  function 
  of 
  a 
  given 
  substance 
  may 
  

   be 
  known 
  under 
  the 
  usual 
  form 
  : 
  F(P, 
  V, 
  T) 
  = 
  0, 
  or 
  it 
  may 
  

   not 
  be 
  known 
  at 
  all, 
  as 
  is 
  the 
  case 
  for 
  most 
  substances. 
  

  

  In 
  the 
  first 
  case, 
  the 
  thermodynamic 
  function 
  can 
  be 
  ex- 
  

   pressed 
  in 
  terms 
  of 
  <p 
  and 
  s 
  by 
  the 
  aid 
  of 
  the 
  equations 
  : 
  

  

  dR=cdT 
  + 
  ldV 
  

   dH=zCdT 
  + 
  hdP 
  

  

  d-T 
  dcp 
  ds 
  

  

  By 
  combining 
  these 
  equations, 
  they 
  can 
  be 
  written 
  : 
  

  

  j^V 
  +(c 
  - 
  2 
  K)f=-K^ 
  (12) 
  

  

  f^P 
  + 
  (C-K)f 
  = 
  l4 
  

   j^<flP 
  + 
  (C-2K)f 
  = 
  - 
  K 
  f 
  

  

  Let 
  us 
  take 
  for 
  instance 
  the 
  case 
  of 
  the 
  perfect 
  gases, 
  whose 
  

   thermodynamic 
  function 
  is 
  PV 
  = 
  RT, 
  R 
  being 
  a 
  constant. 
  

  

  If 
  in 
  the 
  third 
  of 
  the 
  equations 
  to 
  the 
  thermodynamic 
  sur- 
  

   face, 
  which 
  is 
  <ps 
  = 
  KTE 
  for 
  any 
  substance, 
  <p 
  and 
  s 
  be 
  replaced 
  

   by 
  their 
  value 
  in 
  terms 
  of 
  P 
  and 
  V, 
  obtained 
  from 
  the 
  first 
  

  

  