﻿P. 
  de 
  Saussure 
  — 
  Graphical 
  Thermodynamics. 
  31 
  

  

  4th. 
  The 
  equation 
  of 
  the 
  path 
  described 
  when 
  the 
  pressure 
  

   is 
  maintained 
  constant, 
  by 
  putting 
  dY 
  = 
  or 
  P 
  = 
  constant, 
  or 
  

   again 
  by 
  the 
  same 
  substitution 
  : 
  

  

  A<P,s) 
  =A 
  ( 
  Po> 
  s 
  J 
  

   5th. 
  The 
  equation 
  to 
  the 
  curve 
  of 
  constant 
  symbolical 
  vol- 
  

   ume; 
  since 
  s 
  = 
  na 
  2 
  , 
  the 
  amplitude 
  a 
  is 
  constant 
  when 
  s 
  is 
  con- 
  

   stant, 
  hence 
  this 
  curve 
  can 
  be 
  defined 
  as 
  the 
  path 
  described 
  by 
  

   the 
  substance 
  when 
  the 
  amplitude 
  of 
  the 
  vibratory 
  motion 
  is 
  

   maintained 
  constant 
  and 
  its 
  equation 
  is 
  found 
  by 
  putting 
  

   ds 
  = 
  0, 
  whence 
  : 
  

  

  s 
  = 
  s 
  

  

  which 
  is 
  the 
  equation 
  to 
  a 
  straight 
  line 
  parallel 
  to 
  the 
  axis 
  of 
  <p. 
  

   6th. 
  The 
  curve 
  of 
  constant 
  symbolical 
  pressure, 
  which, 
  since 
  

  

  <p 
  = 
  — 
  ? 
  can 
  be 
  defined 
  as 
  the 
  path 
  described 
  when 
  the 
  period 
  

  

  of 
  the 
  vibratory 
  motion 
  of 
  the 
  heat 
  is 
  maintained 
  constant. 
  

   The 
  equation 
  of 
  this 
  curve 
  is 
  derived 
  from 
  the 
  condition 
  : 
  

   d<p 
  = 
  0, 
  whence 
  : 
  

  

  9 
  = 
  9, 
  

   which 
  represents 
  a 
  straight 
  line 
  parallel 
  to 
  the 
  axis 
  of 
  s. 
  

  

  7th. 
  The 
  path 
  along 
  which 
  the 
  total 
  work 
  dK 
  = 
  0, 
  or 
  

   ipds 
  = 
  0, 
  or 
  : 
  

  

  s 
  = 
  s 
  

  

  which 
  is 
  the 
  same 
  as 
  the 
  equation 
  to 
  the 
  curve 
  of 
  constant 
  

   symbolical 
  volume. 
  

  

  8th. 
  The 
  path 
  along 
  which 
  the 
  external 
  work 
  dr 
  — 
  or 
  

   P£V 
  = 
  0or: 
  

  

  V 
  = 
  constant 
  

  

  We 
  see 
  here 
  again 
  that 
  the 
  symbolical 
  volume 
  is 
  in 
  the 
  same 
  

   relation 
  with 
  the 
  total 
  work 
  as 
  is 
  the 
  ordinary 
  volume 
  with 
  the 
  

   external 
  work. 
  

  

  We 
  might 
  also 
  remark 
  that 
  since 
  dH 
  = 
  along 
  the 
  curve 
  of 
  

   constant 
  symbolical 
  volume, 
  this 
  curve 
  may 
  be 
  defined 
  as 
  rep- 
  

   resenting 
  a 
  transformation 
  in 
  which 
  all 
  the 
  heat 
  furnished 
  is 
  

   used 
  in 
  raising 
  the 
  temperature 
  of 
  the 
  substance 
  (or 
  increasing 
  

   its 
  heat-energy), 
  no 
  part 
  of 
  it 
  being 
  transformed 
  into 
  work. 
  

  

  9th. 
  The 
  path 
  along 
  which 
  the 
  internal 
  work, 
  <9?I 
  = 
  0or: 
  

   dK—dT— 
  or 
  again 
  : 
  ipds—YdY 
  *= 
  O. 
  Expressing 
  P 
  and 
  V 
  

   in 
  terms 
  of 
  tp 
  and 
  s, 
  with 
  the 
  aid 
  of 
  equations 
  (8) 
  : 
  

   cpds 
  ~f(cp, 
  s)d[g(q>, 
  s)] 
  = 
  

  

  which 
  will 
  furnish 
  by 
  integration 
  the 
  equation 
  of 
  the 
  required 
  

   curve. 
  

  

  Such 
  are 
  the 
  principal 
  curves 
  passing 
  through 
  any 
  point 
  If. 
  

   When 
  M 
  describes 
  an 
  elementary 
  path 
  MM\ 
  the 
  direction 
  of 
  

  

  