108  Prof.  Clausius  on  the  History  of 
independent  of  the  mode  of  the  alterations,  while  the  latter  is 
dependent  thereon. 
The  heat  expended  for  internal  work  I  united  with  the  heat 
actually  present  in  the  body  into  one  quantity,  which  has.  the 
character  previously  assumed  to  be  that  of  the  total  heat,  viz. 
that  it  may  be  represented  by  a  function  of  the  volume  and  tem- 
perature. To  this  function,  which  I  denoted  by  U,  Thomson 
subsequently  gave  the  very  suitable  name  of  energy  of  the  body. 
In  the  second  part  of  the  memoir,  which  related  to  Carnot's 
theorem,  I  showed  that,  in  the  form  in  which  Carnot  expressed 
it,  this  theorem  cannot  be  correct — and,  further,  that  Carnot's 
proof  of  it  (resting  on  the  axiom  that  it  is  impossible  to  create 
moving  force  out  of  nothing)  is,  after  the  acceptation  of  the  above- 
mentioned  first  theorem,  no  longer  tenable.  On  the  other  hand, 
I  showed,  further,  that,  by  a  certain  modification  of  Carnot's 
theorem,  its  agreement  with  the  first  theorem  can  be  restored ; 
and  I  demonstrated  the  theorem,  thus  modified,  by  admitting  a 
new  axiom.  This  axiom,  in  its  briefest  form,  is : — Heat  cannot 
of  itself  pass  from  a  cooler  into  a  hotter  body. 
After  the  establishment  of  the  general  notions,  I  applied  the 
two  theorems  to  permanent  gases  and  to  the  process  of  evapo- 
ration. 
Among  other  results,  the  application  to  gases  gave  the  first 
reliable  determination  of  Carnot's  temperature-function ;  for  an 
earlier  determination,  made  by  Holtzmann,  rested  on  calculations 
demonstrably  inaccurate,  and  hence  incapable  of  affording  any 
guarantee  for  the  correctness  of  the  result. 
The  application  to  the  process  of  evaporation  led  to  two  im- 
portant consequences  : — (1)  that  steam,  when  it  expands  without 
the  introduction  of  heat,  and  overcoming  a  resistance  correspond- 
ing to  its  full  force,  must  therein  be  partially  precipitated,  and, 
hence,  that  the  specific  heat  of  saturated  steam  is  a  negative 
quantity ;  and  (2)  that  saturated  steam  does  not  follow  Mariotte 
and  Gay-Lussac's  law,  as  in  all  previous  calculations  had  been 
presupposed,  but  deviates  greatly  from  it.  The  new  equations 
which  I  already  in  that  first  memoir  constructed  for  the  nearer 
determination  of  the  behaviour  of  vapours,  are  at  the  present 
time  still  recognized  as  perfectly  correct,  and  are  universally  em- 
ployed. 
In  the  same  month  (February  1850)  in  which  my  memoir 
was  brought  before  the  Berlin  Academy,  a  very  valuable  memoir, 
by  Rankine,  was  brought  before  the  Royal  Society  of  Edinburgh, 
and  was  published  in  the  Transactions  of  that  Society*. 
Therein  Rankine  advances  the  hypothesis  that  heat  consists  in 
*  Vol.  xx.  p.  147.  In  1854  it  was  reprinted,  with  some  alterations,  in 
the  Phil.  Mag.  S.  4.  vol.  vii.  pp.  1,  111,  &  1/2. 
