﻿i?. 
  de 
  Sau8sure 
  — 
  Graphical 
  Thermodynamics. 
  33 
  

  

  Whence, 
  by 
  substitution 
  : 
  

  

  y 
  mA+mQ 
  AQ 
  

   K 
  ~mA 
  + 
  mP 
  ~AP 
  

   Thus 
  we 
  see 
  that 
  the 
  specific 
  heat 
  corresponding 
  to 
  any 
  direc- 
  

   tion 
  MA 
  is 
  to 
  the 
  absolute 
  specific 
  heat 
  of 
  the 
  substance 
  as 
  the 
  

   distances 
  from 
  point 
  A 
  (determined 
  by 
  the 
  direction 
  MA 
  itself) 
  

   to 
  the 
  stationary 
  points 
  P 
  and 
  Q. 
  

  

  The 
  specific 
  heats 
  c 
  and 
  C 
  can 
  then 
  be 
  easily 
  obtained 
  

   graphically 
  by 
  tracing 
  the 
  tangents 
  at 
  point 
  M 
  to 
  the 
  curve 
  of 
  

   constant 
  volume 
  and 
  to 
  the 
  curve 
  of 
  constant 
  pressure 
  ; 
  or, 
  if 
  

   desired, 
  we 
  can 
  also 
  make 
  use 
  of 
  the 
  specific 
  heats 
  to 
  find 
  these 
  

   tangents. 
  Let 
  us 
  study 
  now 
  the 
  variation 
  of 
  the 
  specific 
  heat 
  

   y, 
  when 
  the 
  direction 
  of 
  the 
  element 
  MM' 
  changes, 
  by 
  revolv- 
  

   ing 
  around 
  point 
  M. 
  

  

  1st. 
  Suppose 
  that 
  MM' 
  or 
  MA 
  be 
  at 
  first 
  parallel 
  to 
  the 
  

   axis 
  of 
  <p 
  • 
  point 
  A 
  is 
  then 
  removed 
  to 
  an 
  infinite 
  distance 
  

   in 
  the 
  negative 
  direction 
  of 
  the 
  axis 
  of 
  <p 
  and 
  we 
  have 
  : 
  

  

  £■ 
  = 
  = 
  1 
  or 
  r 
  = 
  K. 
  In 
  other 
  words, 
  the 
  specific 
  heat 
  at 
  con- 
  

  

  K 
  AP 
  

  

  stant 
  symbolical 
  volume 
  is 
  equal 
  to 
  the 
  absolute 
  specific 
  heat 
  of 
  

  

  the 
  substance, 
  and 
  therefore 
  does 
  not 
  depend 
  on 
  its 
  physical 
  

  

  state. 
  

  

  2d. 
  When 
  MA, 
  by 
  revolving 
  ninety 
  degrees 
  around 
  M, 
  coin- 
  

  

  . 
  , 
  , 
  y 
  AQ 
  raQ 
  ^ 
  Tr 
  . 
  

  

  cides 
  witn 
  M 
  m 
  we 
  have 
  : 
  £ 
  = 
  = 
  = 
  ==_ 
  = 
  2, 
  or 
  y 
  = 
  2K, 
  i. 
  e. 
  : 
  

  

  J^ 
  AP 
  mY 
  

  

  the 
  specific 
  heat 
  at 
  constant 
  symbolical 
  pressure 
  is 
  equal 
  to 
  twice 
  

   the 
  absolute 
  specific 
  heat 
  of 
  the 
  substance 
  and 
  remains 
  there- 
  

   fore 
  also 
  constant, 
  when 
  the 
  state 
  of 
  the 
  substance 
  changes. 
  

   3d. 
  When 
  MA 
  has 
  reached 
  the 
  position 
  Mn 
  (n 
  being 
  the 
  

  

  center 
  of 
  mP), 
  £ 
  = 
  ^ 
  = 
  ^ 
  = 
  3, 
  or 
  y 
  = 
  3K. 
  

   K 
  AP 
  nP 
  

  

  This 
  value 
  is 
  of 
  some 
  interest, 
  since 
  the 
  specific 
  heat 
  at 
  con- 
  

   stant 
  volume 
  of 
  certain 
  solid 
  substances 
  has 
  been 
  found 
  to 
  be 
  

   equal 
  to 
  three 
  times 
  their 
  absolute 
  specific 
  heat 
  ; 
  hence, 
  for 
  

   those 
  substances, 
  M?i 
  is 
  the 
  tangent 
  at 
  M 
  to 
  the 
  curve 
  of 
  con- 
  

   stant 
  volume. 
  

  

  4th. 
  When 
  MA 
  coincides 
  with 
  MP 
  : 
  

   y_ 
  _AQ__PQ_ 
  

   K~AP~~ 
  =" 
  

  

  Whence 
  : 
  y 
  = 
  — 
  1 
  ™= 
  °o 
  or 
  dT 
  — 
  or 
  again 
  T 
  = 
  constant. 
  This 
  

   a 
  jl 
  

  

  Am. 
  Jour. 
  Sci.— 
  Third 
  Series, 
  Vol. 
  XLIX, 
  No. 
  289.—Jan., 
  1895. 
  

   3 
  

  

  