﻿584 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  

  

  Professor 
  Thomson 
  and 
  Mr 
  Joule 
  have 
  expressed 
  the 
  opinion, 
  which 
  is 
  un- 
  

   doubtedly 
  correct, 
  that 
  those 
  experiments 
  in 
  which 
  the 
  largest 
  quantities 
  of 
  air 
  

   were 
  used 
  were 
  the 
  least 
  liable 
  to 
  error 
  from 
  disturbing 
  causes, 
  such 
  as 
  the 
  con- 
  

   duction 
  of 
  heat. 
  

  

  Now 
  it 
  may 
  be 
  observed 
  in 
  the 
  preceding 
  table, 
  that 
  the 
  calculated 
  values 
  of 
  

   k 
  are 
  generally 
  greatest, 
  and 
  the 
  discrepancies 
  amongst 
  them 
  least, 
  for 
  the 
  experi- 
  

   ments 
  in 
  which 
  most 
  air 
  was 
  used. 
  To 
  illustrate 
  this, 
  the 
  results 
  of 
  the 
  last 
  eight 
  

   series 
  are 
  arranged 
  below 
  in 
  the 
  order 
  of 
  the 
  quantities 
  of 
  air 
  employed. 
  

  

  Cubic 
  inches 
  per 
  second, 
  1-4 
  2-8 
  5-6 
  56 
  6-4 
  8-4 
  11-2 
  112 
  

  

  Values 
  of 
  K, 
  .... 
  1-683 
  1-762 
  2-09 
  2-228 
  1-51 
  2-087 
  2-345 
  2-14 
  

  

  It 
  is 
  further 
  to 
  be 
  remarked, 
  that 
  the 
  discrepancy 
  between 
  the 
  highest 
  and 
  

   the 
  lowest 
  of 
  the 
  values 
  of 
  k 
  is 
  

  

  2°-345 
  - 
  l°-08 
  = 
  l°-265 
  centigrade: 
  

  

  a 
  quantity 
  which 
  corresponds 
  to 
  a 
  difference 
  of 
  less 
  than 
  one 
  three-hundredth 
  part 
  

   in 
  computing 
  the 
  proportion 
  of 
  heat 
  converted 
  into 
  mechanical 
  power 
  by 
  any 
  or- 
  

   dinary 
  expansive 
  engine, 
  according 
  to 
  the 
  formula 
  (98), 
  which 
  has 
  been 
  deduced 
  

   from 
  the 
  hypothesis 
  of 
  Molecular 
  Vortices. 
  

  

  The 
  experiments, 
  therefore, 
  may 
  be 
  considered 
  as 
  tending 
  to 
  prove, 
  that 
  the 
  

   formulae 
  deduced 
  from 
  this 
  hypothesis 
  are 
  sufficiently 
  correct 
  for 
  practical 
  pur- 
  

   poses 
  ; 
  and 
  also 
  as 
  affording 
  a 
  strong 
  probability 
  that 
  the 
  principles 
  to 
  which 
  it 
  

   leads 
  are 
  theoretically 
  exact, 
  and 
  that 
  the 
  temperature 
  of 
  absolute 
  privation 
  of 
  

   heat 
  is 
  a 
  real 
  fixed 
  point 
  on 
  the 
  scale, 
  somewhat 
  more 
  than 
  two 
  centigrade 
  de- 
  

   grees 
  above 
  the 
  absolute 
  zero 
  of 
  a 
  perfect 
  gas-thermometer 
  (which 
  is, 
  of 
  course, 
  an 
  

   imaginary 
  point) 
  ; 
  that 
  is 
  to 
  say, 
  about 
  272| 
  centigrade 
  degrees, 
  or 
  490^ 
  degrees 
  

   of 
  Fahrenheit, 
  below 
  the 
  temperature 
  of 
  melting 
  ice. 
  

  

  If 
  these 
  conclusions 
  be 
  correct, 
  it 
  follows, 
  that 
  when 
  the 
  temperatures 
  T 
  L 
  and 
  

   T 
  2 
  , 
  between 
  which 
  an 
  expansive 
  engine 
  works, 
  are 
  measured 
  from 
  the 
  ordinary 
  

   zero 
  points 
  of 
  the 
  centigrade 
  and 
  of 
  Fahrenheit's 
  scales 
  respectively, 
  the 
  follow- 
  

   ing 
  are 
  the 
  utmost 
  proportions 
  of 
  the 
  total 
  heat 
  expended 
  which 
  it 
  can 
  be 
  made 
  

   to 
  convert 
  into 
  mechanical 
  power 
  : 
  — 
  

  

  T 
  — 
  T 
  

   For 
  the 
  centigrade 
  scale, 
  „ 
  l 
  n 
  * 
  

  

  T 
  — 
  T 
  

  

  For 
  Fahrenheit's 
  scale, 
  -^ 
  — 
  -r^ 
  

  

  (109.) 
  

  

  T 
  x 
  + 
  458i 
  ; 
  

  

  In 
  the 
  fifth 
  section 
  of 
  this 
  paper, 
  where 
  a 
  comparison 
  is 
  made 
  between 
  the 
  

   actual 
  duty 
  of 
  theCornish 
  engine 
  at 
  Old 
  Ford, 
  as 
  determined 
  by 
  Mr 
  Wicksteed, 
  

   and 
  the 
  greatest 
  possible 
  duty 
  which 
  could 
  be 
  obtained 
  from 
  a 
  given 
  quantity 
  of 
  

   heat 
  by 
  a 
  theoretically 
  perfect 
  engine 
  working 
  between 
  the 
  same 
  temperatures, 
  

   the 
  constant 
  k 
  is 
  treated 
  as 
  being 
  so 
  small 
  that 
  it 
  may 
  be 
  neglected 
  in 
  practice. 
  

  

  