﻿278 
  

  

  PROFESSOR 
  WILLIAM 
  THOMSON 
  ON 
  THE 
  

  

  tions 
  through 
  the 
  range, 
  to 
  compensate 
  for 
  the 
  quantities 
  converted 
  into 
  mechani- 
  

   cal 
  effect]. 
  

  

  Column 
  IV. 
  shews 
  the 
  true 
  duty 
  of 
  a 
  unit 
  of 
  heat, 
  and 
  a 
  comparison 
  of 
  the 
  

   numbers 
  in 
  it 
  with 
  the 
  corresponding 
  numbers 
  in 
  Column 
  III. 
  shews 
  how 
  much 
  

   the 
  true 
  duty 
  falls 
  short 
  of 
  Carnot's 
  theoretical 
  duty 
  in 
  each 
  case. 
  

  

  Column 
  VI. 
  is 
  calculated 
  by 
  the 
  formula 
  

  

  i 
  f 
  S 
  

  

  R 
  = 
  e 
  -1390 
  7 
  T 
  \ 
  ldt 
  

  

  where 
  e 
  = 
  271828, 
  and 
  for 
  / 
  adt 
  the 
  successive 
  values 
  shewn 
  in 
  Column 
  III. 
  

  

  are 
  used. 
  

  

  Column 
  IV. 
  is 
  calculated 
  by 
  the 
  formula 
  

  

  W 
  = 
  1390 
  (1-R 
  

  

  from 
  the 
  values 
  of 
  1 
  — 
  R 
  shewn 
  in 
  Column 
  V.. 
  

  

  38. 
  Table 
  of 
  the 
  Motive 
  Power 
  of 
  Heat. 
  

  

  

  Range 
  o: 
  

  

  ' 
  Temperatures. 
  

  

  

  III. 
  

  

  Duty 
  of 
  a 
  Unit 
  

   of 
  Heat 
  through 
  

   the 
  whole 
  range. 
  

  

  IV. 
  

  

  Duty 
  of 
  a 
  Unit 
  

   of 
  Heat 
  sup- 
  

   plied 
  from 
  the 
  

   source. 
  

  

  V. 
  

  

  Quantity 
  of 
  

   Heat 
  con- 
  

   verted 
  into 
  

   mechanical 
  

   effect. 
  

  

  VI. 
  

  

  Quantity 
  of 
  

   Heat 
  wasted. 
  

  

  I. 
  

  

  II. 
  

  

  s 
  

  

  T 
  

  

  S 
  

  

  T 
  

  

  / 
  /j. 
  d 
  t 
  

  

  W 
  

  

  1 
  -R 
  

  

  R 
  

  

  o 
  

  

  1 
  

  

  O 
  

  

  

  

  31-08 
  

  

  o 
  

  

  30 
  

  

  Ft.-lbs. 
  

   4-960 
  

  

  Ft.-lbs. 
  

   4-948 
  

  

  •00356 
  

  

  •99644 
  

  

  10 
  

  

  

  

  40-86 
  

  

  30 
  

  

  48-987 
  

  

  48-1 
  

  

  •0346 
  

  

  •9654 
  

  

  20 
  

  

  

  

  51-7 
  

  

  30 
  

  

  96-656 
  

  

  93-4 
  

  

  •067 
  

  

  •933 
  

  

  30 
  

  

  

  

  62-6 
  

  

  30 
  

  

  143-06 
  

  

  136- 
  

  

  •098 
  

  

  •902 
  

  

  40 
  

  

  

  

  73-6 
  

  

  30 
  

  

  188-22 
  

  

  176- 
  

  

  •127 
  

  

  •873 
  

  

  50 
  

  

  

  

  84-5 
  

  

  30 
  

  

  232-18 
  

  

  214- 
  

  

  •154 
  

  

  •846 
  

  

  60 
  

  

  

  

  95-4 
  

  

  30 
  

  

  274-97 
  

  

  249- 
  

  

  •179 
  

  

  •821 
  

  

  70 
  

  

  

  

  106-3 
  

  

  30 
  

  

  316-64 
  

  

  283- 
  

  

  •204 
  

  

  •796 
  

  

  80 
  

  

  

  

  117-2 
  

  

  30 
  

  

  357-27 
  

  

  315- 
  

  

  •227 
  

  

  •773 
  

  

  90 
  

  

  

  

  128-0 
  

  

  30 
  

  

  396-93 
  

  

  345- 
  

  

  •248 
  

  

  •752 
  

  

  100 
  

  

  

  

  138-8 
  

  

  30 
  

  

  435-69 
  

  

  374- 
  

  

  •269 
  

  

  •731 
  

  

  110 
  

  

  

  

  149-1 
  

  

  30 
  

  

  473-62 
  

  

  401- 
  

  

  •289 
  

  

  •711 
  

  

  120 
  

  

  

  

  160-3 
  

  

  30 
  

  

  510-77 
  

  

  427- 
  

  

  •308 
  

  

  •692 
  

  

  130 
  

  

  

  

  171-0 
  

  

  30 
  

  

  547-21 
  

  

  452- 
  

  

  •325 
  

  

  •675 
  

  

  140 
  

  

  

  

  181-7 
  

  

  30 
  

  

  582-98 
  

  

  476- 
  

  

  •343 
  

  

  •657 
  

  

  150 
  

  

  

  

  192-3 
  

  

  30 
  

  

  61814 
  

  

  499- 
  

  

  •359 
  

  

  •641 
  

  

  160 
  

  

  

  

  203-0 
  

  

  30 
  

  

  652-74 
  

  

  521- 
  

  

  •375 
  

  

  •625 
  

  

  170 
  

  

  

  

  213-6 
  

  

  30 
  

  

  686-80 
  

  

  542- 
  

  

  •390 
  

  

  •610 
  

  

  180 
  

  

  

  

  224-2 
  

  

  30 
  

  

  720-39 
  

  

  562- 
  

  

  •404 
  

  

  •596 
  

  

  190 
  

  

  

  

  190- 
  

  

  

  

  753-50 
  

  

  582- 
  

  

  •418 
  

  

  •582 
  

  

  200 
  

  

  

  

  200- 
  

  

  

  

  786-17 
  

  

  600- 
  

  

  •432 
  

  

  •568 
  

  

  210 
  

  

  

  

  210- 
  

  

  

  

  818-45 
  

  

  619- 
  

  

  •445 
  

  

  •555 
  

  

  220 
  

  

  

  

  220- 
  

  

  

  

  850-34 
  

  

  636- 
  

  

  •457 
  

  

  •542 
  

  

  230 
  

  

  

  

  230- 
  

  

  

  

  881-87 
  

  

  653- 
  

  

  •470 
  

  

  •530 
  

  

  