﻿MECHANICAL 
  ACTION 
  OF 
  HEAT. 
  587 
  

  

  already 
  found 
  is 
  sufficiently 
  near 
  the 
  truth, 
  viz., 
  2°-l 
  centigrade 
  ; 
  so 
  that, 
  in 
  the 
  

   present 
  instance 
  t— 
  k=272 
  0, 
  5 
  centigrade. 
  

  

  Then 
  we 
  find 
  the 
  following 
  results 
  when 
  t=t 
  , 
  and 
  D=D 
  ; 
  

  

  Metres. 
  Feet. 
  

  

  P 
  V 
  K 
  

  

  (t 
  — 
  k) 
  —2 
  — 
  - 
  • 
  — 
  = 
  per 
  centigrade 
  degree, 
  0*145 
  0-48 
  

  

  T 
  o 
  T 
  

  

  (r- 
  K)f^ 
  2 
  dV 
  = 
  „ 
  ..... 
  0150 
  0-49 
  

  

  Sum 
  = 
  K 
  v 
  — 
  ft 
  = 
  excess 
  of 
  apparent 
  specific 
  heat 
  at 
  constant 
  volume 
  

  

  above 
  real 
  specific 
  heat, 
  ..... 
  0'295 
  0-97 
  

  

  (fY 
  

  

  (t 
  — 
  k) 
  ^— 
  = 
  difference 
  between 
  apparent 
  specific 
  heats 
  at 
  con- 
  

  

  - 
  jtr 
  stant 
  volume 
  and 
  at 
  constant 
  pressure, 
  . 
  19-565 
  64-19 
  

  

  K 
  P 
  — 
  It 
  = 
  excess 
  of 
  apparent 
  specific 
  heat 
  at 
  constant 
  pres- 
  

  

  sure 
  above 
  real 
  specific 
  heat, 
  . 
  . 
  . 
  19-860 
  65-16 
  

  

  § 
  of 
  the 
  above 
  quantities 
  are 
  of 
  course 
  the 
  corresponding 
  quantities 
  for 
  Fahren- 
  

   heit's 
  scale. 
  

  

  Secondly, 
  If 
  the 
  velocity 
  of 
  sound 
  in 
  the 
  gas 
  is 
  given, 
  let 
  this 
  = 
  u. 
  Then 
  we 
  

   know 
  that 
  

  

  dP 
  K 
  P 
  

   dD 
  ' 
  K, 
  

   in 
  which 
  

  

  d_P 
  ^ 
  Tr 
  f 
  t 
  d. 
  

   dB' 
  

  

  u2 
  = 
  9-m-rr 
  (U2-) 
  

  

  '_P 
  v 
  !I- 
  + 
  IiA<J>_.1*jAiJ>\ 
  ni2A^ 
  

  

  » 
  ° 
  °Uo 
  dV 
  r 
  dV 
  ) 
  • 
  (11^ 
  a.) 
  

  

  So 
  that 
  from 
  the 
  velocity 
  of 
  sound 
  we 
  can 
  calculate 
  the 
  ratio 
  of 
  the 
  specific 
  heats 
  

  

  at 
  constant 
  pressure 
  and 
  at 
  constant 
  volume. 
  Let 
  this 
  ratio 
  be 
  denoted 
  by 
  7, 
  

  

  and 
  let 
  

  

  K 
  v 
  - 
  = 
  ft 
  + 
  c 
  ; 
  K 
  P 
  = 
  Jt 
  + 
  c' 
  ; 
  then 
  

  

  ft 
  + 
  c' 
  , 
  .. 
  c' 
  — 
  7 
  c 
  ,,.„„, 
  

  

  7 
  = 
  j; 
  ; 
  and 
  ft 
  = 
  V 
  .... 
  (112 
  B.) 
  

  

  ' 
  ft 
  + 
  c 
  7 
  — 
  1 
  K 
  ' 
  

  

  in 
  which 
  c' 
  and 
  c 
  are 
  to 
  be 
  calculated 
  as 
  above.* 
  

  

  (63.) 
  In 
  using 
  the 
  formula 
  (110) 
  for 
  a 
  gas 
  whose 
  pressure 
  is 
  represented 
  by 
  

   the 
  formula, 
  

  

  the 
  integrals 
  may 
  be 
  transformed 
  so 
  as 
  to 
  be 
  taken, 
  with 
  respect 
  to 
  the 
  density, 
  as 
  

   in 
  the 
  preceding 
  article. 
  Thus 
  we 
  obtain 
  

  

  See 
  Appendix, 
  Note 
  B. 
  

  

  