﻿26 
  B. 
  de 
  Saussure 
  — 
  Graphical 
  Thermody 
  

  

  narnics. 
  

  

  By 
  the 
  aid 
  of 
  tnis 
  equation 
  and 
  of 
  the 
  preceding 
  one, 
  the 
  value 
  

   of 
  dH 
  can 
  also 
  be 
  obtained 
  in 
  terms 
  of 
  T 
  and 
  i 
  or 
  of 
  a 
  and 
  i 
  : 
  

  

  ' 
  dH 
  Tr 
  /dT 
  da 
  \ 
  

  

  dn 
  ^rrf^T 
  di\ 
  

  

  aH 
  

  

  da. 
  __/ 
  da 
  di\ 
  

  

  6. 
  The 
  two 
  variables, 
  which 
  we 
  intend 
  to 
  take 
  as 
  coordinates 
  

   in 
  this 
  graphical 
  study, 
  depend 
  directly 
  upon 
  the 
  amplitude 
  a 
  

   and 
  the 
  period 
  i 
  of 
  the 
  vibratory 
  motion 
  of 
  heat 
  ; 
  denoting 
  

   these 
  variables 
  by 
  <p 
  and 
  s, 
  we 
  shall 
  define 
  them 
  by 
  the 
  equa- 
  

  

  tions 
  

  

  '*=r- 
  ( 
  7) 
  

  

  S 
  = 
  no 
  1 
  

  

  By 
  the 
  aid 
  of 
  equation 
  (7), 
  any 
  of 
  the 
  formulae 
  given 
  above 
  

   and 
  involving 
  a 
  and 
  i, 
  can 
  be 
  transformed 
  into 
  corresponding 
  

   formulae 
  involving 
  <p 
  and 
  s. 
  

  

  For 
  instance, 
  by 
  solving 
  equations 
  (7) 
  with 
  respect 
  to 
  a 
  and 
  

   i 
  9 
  and 
  substituting 
  the 
  result 
  in 
  equations 
  (5), 
  we 
  shall 
  obtain 
  

   the 
  equation 
  to 
  the 
  thermodynamic 
  surface 
  in 
  terms 
  of 
  <p 
  and 
  

   s, 
  as 
  follows 
  : 
  

  

  I 
  V=g(cp,s) 
  (8) 
  

  

  All 
  the 
  other 
  equations 
  can 
  be 
  transformed 
  in 
  the 
  same 
  

   manner, 
  so 
  that 
  it 
  is 
  understood 
  that 
  the 
  two 
  independent 
  

   variables 
  are 
  now 
  <p 
  and 
  s, 
  and 
  that 
  these 
  two 
  quantities 
  shall 
  

   be 
  taken 
  as 
  the 
  coordinates 
  of 
  the 
  point 
  representing 
  the 
  phys- 
  

   ical 
  state 
  of 
  the 
  substance. 
  

  

  As 
  these 
  variables 
  have 
  been 
  defined 
  in 
  an 
  arbitrary 
  manner, 
  

   let 
  us 
  first 
  investigate 
  their 
  physical 
  nature. 
  To 
  reach 
  this 
  

   end, 
  we 
  must 
  consider 
  the 
  vibratory 
  motion 
  of 
  the 
  particles 
  as 
  

   the 
  projection 
  of 
  a 
  uniform 
  circular 
  motion 
  on 
  one 
  of 
  its 
  

   diameters 
  ; 
  the 
  radius 
  of 
  the 
  circle 
  is 
  then 
  equal 
  to 
  the 
  ampli- 
  

   tude 
  of 
  the 
  vibration, 
  and 
  the 
  velocity 
  of 
  the 
  uniform 
  motion 
  

   is 
  equal 
  to 
  the 
  maximum 
  velocity 
  of 
  the 
  vibratory 
  motion. 
  It 
  

   can 
  readily 
  be 
  seen, 
  that 
  the 
  centripetal 
  force 
  of 
  the 
  circular 
  

   motion 
  is 
  equal 
  to 
  the 
  mean 
  value 
  f 
  of 
  the 
  force 
  supposed 
  to 
  

   produce 
  the 
  vibratory 
  motion. 
  

  

  The 
  total 
  work 
  (external 
  and 
  internal) 
  absorbed 
  by 
  the 
  sub- 
  

   stance 
  during 
  an 
  elementary 
  transformation 
  is 
  2fda 
  as 
  seen 
  

   above. 
  We 
  can 
  write 
  identically 
  : 
  

  

  