﻿36 
  B. 
  de 
  Saussure 
  — 
  Graphical 
  Thermodynamics. 
  

  

  Graphical 
  representation 
  of 
  the 
  various 
  physical 
  coefficients. 
  

  

  13. 
  When 
  a 
  surface 
  is 
  defined 
  by 
  three 
  equations 
  giving 
  the 
  

   value 
  of 
  the 
  coordinates 
  P, 
  V, 
  T 
  of 
  any 
  one 
  of 
  its 
  points, 
  in 
  

   terms 
  of 
  two 
  auxiliary 
  variables 
  <p 
  and 
  s, 
  it 
  can 
  be 
  divided 
  into 
  

   an 
  infinite 
  number 
  of 
  infinitely 
  small 
  parallelograms 
  by 
  two 
  

   systems 
  of 
  curves, 
  obtained 
  respectively 
  by 
  putting 
  <p 
  = 
  con- 
  

   stant 
  and 
  s 
  = 
  constant 
  in 
  the 
  three 
  equations 
  to 
  the 
  surface. 
  

   The 
  area 
  do) 
  of 
  any 
  one 
  of 
  these 
  elementary 
  parallelograms 
  is 
  

   given 
  by 
  the 
  formula 
  : 
  

  

  doo 
  = 
  (A 
  « 
  +B 
  2 
  +C 
  2 
  )Ws 
  

   in 
  which 
  A, 
  B, 
  6 
  y 
  have 
  the 
  following 
  values 
  : 
  

  

  cZV 
  dT_ 
  dTdV 
  

  

  dcp 
  ds 
  dcp 
  ds 
  

  

  dT 
  dP 
  dP 
  dT 
  

  

  dcp 
  ds 
  dcp 
  ds 
  

  

  c 
  __dP_dY_ 
  dV 
  dP 
  

  

  dcp 
  ds 
  dcp 
  ds 
  

  

  The 
  projection 
  of 
  the 
  element 
  do) 
  on 
  the 
  plane 
  PO 
  V 
  is 
  

   equal 
  to 
  : 
  ±Cd<pds 
  / 
  and 
  the 
  area 
  of 
  this 
  projection 
  is 
  equal, 
  

   according 
  to 
  the 
  fundamental 
  property 
  of 
  Clapeyron's 
  graph- 
  

   ical 
  representation, 
  to 
  the 
  external 
  work 
  done 
  by 
  the 
  substance 
  

   when 
  describing 
  a 
  path 
  corresponding 
  to 
  the 
  outline 
  of 
  the 
  

   parallelogram 
  da). 
  On 
  the 
  other 
  hand, 
  when 
  <p 
  and 
  s 
  are 
  taken 
  

   as 
  coordinates, 
  the 
  element 
  do 
  is 
  represented 
  by 
  a 
  small 
  rec- 
  

   tangle, 
  whose 
  sides 
  are 
  respectively 
  dip 
  and 
  ds, 
  since 
  this 
  ele- 
  

   ment 
  is 
  cut 
  off 
  by 
  the 
  curves 
  : 
  <p 
  — 
  constant 
  and 
  s 
  = 
  constant 
  ; 
  

   the 
  area 
  of 
  this 
  rectangle 
  is 
  : 
  dip. 
  ds 
  and 
  is 
  equal, 
  according 
  to 
  

   the 
  last 
  remark 
  (§ 
  12), 
  to 
  the 
  external 
  work 
  done 
  by 
  the 
  sub- 
  

   stance 
  when 
  describing 
  the 
  outline 
  of 
  the 
  same 
  element 
  do), 
  

  

  hence 
  : 
  

  

  ± 
  Cdcpds 
  = 
  dcpds 
  

  

  Or: 
  C=±l 
  

  

  Keplacing 
  C 
  by 
  its 
  value, 
  we 
  find 
  a 
  new 
  condition 
  to 
  which 
  the 
  

  

  functions/ 
  and 
  g 
  (equations 
  8) 
  are 
  submitted, 
  i. 
  e. 
  : 
  

  

  dfa\_didf__ 
  

  

  dcp 
  ds 
  dcp 
  ds 
  

  

  This 
  condition 
  will 
  be 
  utilized 
  in 
  the 
  determination 
  of 
  the 
  

   functions/ 
  and 
  g, 
  as 
  it 
  is 
  a 
  more 
  convenient 
  form 
  of 
  the 
  con- 
  

   dition 
  found 
  above 
  :Jcpds=z^Pdv, 
  for 
  any 
  closed 
  cycle. 
  

  

  cps 
  

   By 
  the 
  aid 
  of 
  equation 
  T 
  = 
  = 
  , 
  we 
  have 
  : 
  

  

  