110  Prof.  Clausius  on  the  History  of 
second  theorem  of  the  mechanical  theory.  At  the  same  time  he 
amplified  the  considerations :  while,  in  the  mathematical  treat- 
ment of  the  subject,  I  confined  myself  to  the  consideration  of 
gases  and  the  process  of  evaporation,  merely  adding  that  it 
would  be  easily  seen  how  corresponding  applications  to  other 
cases  also  could  be  made,  Thomson  developed  a  series  of  more 
general  equations  independent  of  the  state  of  aggregation  of  the 
bodies,  and  then  passed  on  to  more  special  applications. 
In  one  point,  however,  this  later  memoir  also  remained  behind 
my  own.  That  is  to  say,  here  also  he  adheres  to  Mariotte  and 
Gay-Lussac's  law  in  the  case  of  saturated  steam,  while  he  hesi- 
tates about  an  hypothesis  relative  to  permanent  gases  which  I 
had  made  use  of  in  my  developments.  On  this  point  he  says*: — 
"X  cannot  see  that  any  hypothesis,  such  as  that  adopted  by 
Clausius  fundamentally  in  his  investigations  on  this  subject;  and 
leading,  as  he  shows,  to  determinations  of  the  densities  of  satu- 
rated steam  at  different  temperatures,  which  indicate  enormous 
deviations  from  the  gaseous  laws  of  variation  with  temperature 
and  pressure,  is  more  probable,  or  is  probably  nearer  the  truth, 
than  that  the  density  of  saturated  steam  does  follow  these  laws 
as  it  is  usually  assumed  to  do.  In  the  present  state  of  science 
it  would  perhaps  be  wrong  to  say  that  either  hypothesis  is  more 
probable  than  the  other." 
Several  years  later,  after  he  had  convinced  himself,  by  experi- 
ments which  he  and  Joule  made  in  common,  of  the  correctness 
of  the  hypothesis  adopted  by  me,  within  the  limits  already  indi- 
cated by  myself,  he  also,  for  the  first  time,  employed  the  same 
procedure  as  I  for  the  determination  of  the  densities  of  saturated 
steam  f. 
The  position  above  stated  has  always,  so  far  as  I  know,  been 
most  readily  acknowledged  by  Messrs.  Rankine  and  Thomson 
as  that  occupied  in  relation  to  one  another  by  our  first  writings 
on  the  mechanical  theory  of  heat.  Thomson,  in  his  memoir  of 
1851 X,  says  : — "  The  whole  theory  of  the  motive  power  of  heat 
is  founded  on  the  two  following  propositions — due  respectively 
to  Joule,  and  to  Carnot  and  Clausius."  Accordingly  he  pro- 
ceeds to  cite  the  second  theorem  of  the  mechanical  theory  of  heat 
under  the  designation  of  "Prop.  II.  (Carnot  and  Clausius)." 
Then,  after  communicating  a  demonstration  discovered  by  him- 
self of  this  proposition,  he  continues  §  : — "It  is  with  no  wish  to 
claim  priority  that  I  make  these  statements,  as  the  merit  of  first 
establishing  the  proposition  upon  correct  principles  is  entirely 
*  Edinb.  Trans,  vol.  xx.  p.  2/7;  and  Phil.  Mag.  S.  4.  vol.  iv.p.  111. 
f  Phil.  Trans.  1854. 
%  Edinb.  Trans,  vol.  xx.  p.  264  ;  and  Phil.  Mag.  S.  4.  vol.  iv.  p.  11. 
§  LI.  cc.  pp.  266  et  14. 
