﻿B. 
  deSaussure 
  — 
  Graphical 
  Thermodynamics. 
  39 
  

  

  

  

  Id 
  short, 
  all 
  the 
  different 
  physical 
  coefficients 
  can 
  be 
  ex- 
  

   pressed 
  very 
  simply 
  in 
  terms 
  of 
  A 
  and 
  B, 
  so 
  that 
  if 
  the 
  value 
  

   of 
  A 
  and 
  B 
  can 
  be 
  obtained 
  by 
  a 
  graphical 
  method, 
  these 
  

   coefficients 
  may 
  also 
  be 
  regarded 
  as 
  known 
  graphically. 
  

  

  A 
  and 
  B 
  are 
  the 
  components 
  of 
  JV 
  parallel 
  to 
  the 
  axes 
  OV 
  

   and 
  OB, 
  i. 
  e. 
  : 
  parallel 
  to 
  the 
  axes 
  of 
  coordinates 
  used 
  in 
  

   Clapeyron's 
  graphical 
  method. 
  Hence 
  if 
  K 
  

  

  M 
  represents 
  the 
  state 
  of 
  the 
  substance 
  

   (fig. 
  5), 
  defined 
  by 
  its 
  volume 
  and 
  its 
  pres- 
  

   sure, 
  the 
  component 
  A 
  will 
  be 
  parallel 
  to 
  

   O 
  V, 
  while 
  B 
  will 
  be 
  parallel 
  to 
  OB 
  and 
  

   the 
  resultant 
  R 
  will 
  be 
  the 
  projection 
  of 
  

   i^on 
  the 
  plane 
  BOV. 
  

  

  Now, 
  if 
  B 
  be 
  known 
  both 
  in 
  length 
  

   and 
  direction, 
  the 
  components 
  A 
  and 
  B 
  

   (and 
  therefore 
  all 
  the 
  physical 
  coefficients) 
  

   can 
  be 
  obtained 
  graphically, 
  so 
  that 
  it 
  will 
  

   not 
  be 
  necessary 
  to 
  compute 
  A 
  and 
  B 
  from 
  the 
  equations 
  to 
  

   the 
  thermodynamic 
  surface. 
  The 
  projecting 
  plane 
  of 
  JV 
  is 
  

   perpendicular 
  to 
  the 
  contour 
  lines 
  of 
  the 
  thermodynamic 
  sur- 
  

   face 
  (i. 
  e., 
  supposing 
  that 
  the 
  plane 
  BO 
  V 
  is 
  horizontal). 
  

   These 
  contour 
  lines 
  are 
  precisely 
  the 
  isothermal 
  curves, 
  hence 
  

   the 
  direction 
  of 
  B 
  can 
  be 
  obtained 
  graphically 
  by 
  the 
  condi- 
  

   tion 
  that 
  it 
  be 
  perpendicular 
  to 
  the 
  isothermal 
  MT 
  passing 
  

   through 
  M. 
  

  

  On 
  the 
  other 
  hand, 
  the 
  length 
  of 
  B 
  is 
  determined 
  by 
  the 
  

   fact 
  that 
  the 
  vertical 
  component 
  C 
  is 
  equal 
  to 
  the 
  unit. 
  

  

  The 
  altitude 
  of 
  point 
  M 
  in 
  space 
  is 
  equal 
  to 
  the 
  temperature 
  

   T 
  ; 
  hence, 
  since 
  = 
  1, 
  the 
  altitude 
  of 
  the 
  other 
  extremity 
  of 
  

   JV 
  is 
  equal 
  to 
  T+l 
  ; 
  in 
  other 
  words, 
  this 
  extremity 
  is 
  the 
  

   point 
  where 
  the 
  normal 
  to 
  the 
  thermodynamic 
  surface 
  inter- 
  

   sects 
  the 
  horizontal 
  plane 
  of 
  the 
  isothermal 
  T+l, 
  so 
  that 
  it 
  can 
  

   be 
  obtained 
  graphically 
  by 
  a 
  simple 
  construction 
  of 
  descriptive 
  

   geometry, 
  as 
  follows 
  : 
  

  

  Draw 
  through 
  M 
  the 
  normal 
  to 
  

   the 
  isothermal 
  MT 
  (fig. 
  6) 
  and 
  let 
  

   JV 
  denote 
  the 
  point 
  where 
  this 
  

   normal 
  intersects 
  the 
  isothermal 
  

   T-\-l 
  ; 
  draw 
  MB 
  tangent 
  to 
  the 
  

   isothermal 
  and 
  measure 
  off 
  MB=J 
  y 
  ; 
  

   join 
  JV 
  to 
  B 
  / 
  draw 
  at 
  B 
  a 
  perpen- 
  

   dicular 
  to 
  NB 
  and 
  let 
  Q 
  denote 
  the 
  

   point 
  where 
  it 
  intersects 
  the 
  normal 
  

   MJV 
  produced 
  ; 
  then 
  MQ 
  will 
  be 
  

   equal 
  to 
  B 
  both 
  in 
  length 
  and 
  direc- 
  

   tion. 
  

  

  The 
  isothermal 
  T+l 
  can 
  be 
  re- 
  

   placed 
  by 
  the 
  isothermal 
  T+n, 
  pro- 
  

  

  