the  Mechanical  Theory  of  Heat.  109 
a  whirling  motion  of  the  molecules,  and  very  skilfully  deduces 
from  it  a  series  of  theorems  on  the  behaviour  of  heat.  It  must 
particularly  be  mentioned  that  he  also  found  the  specific  heat  of 
saturated  steam  to  be  a  negative  quantity.  He  was  unable,  how- 
ever, to  effect  so  accurate  a  quantitative  determination  of  this 
quantity  as  I,  because  at  that  time  he  still  assumed  for  saturated 
steam  the  validity  of  Mariotte  and  Gay-Lussac's  law. 
The  second  theorem  of  the  mechanical  theory  of  heat  was  not 
treated  by  Rankine  in  this  memoir,  but  first  in  another,  which 
was  brought  before  the  Edinburgh  Royal  Society  a  year  later 
(April  1851)*.  He  there  says  himself,  speaking  of  my  hand- 
ling of  the  theorem  f,  u  and  I  had  at  first  doubts  as  to  the  sound- 
ness of  the  reasoning  by  which  he  maintained  it.  Having  stated 
those  doubts  to  Professor  Thomson,  I  am  indebted  to  him  for 
having  induced  me  to  investigate  the  subject  thoroughly."  He 
then  added  that  he  had  now  come  to  the  conclusion  that  this 
theorem  was  not  to  be  regarded  as  an  independent  principle  in 
the  theory  of  heat,  but  that  it  could  be  derived  as  a  consequence 
from  the  equations  which  had  been  given  in  his  earlier  memoir. 
He  then  communicates  the  new  proof  of  the  theorem.  But 
(as  I  afterwards  showed %,  without  any  contradiction  from  Mr. 
Rankine)  this  proof  agrees  with  his  own  views  on  specific  heat 
only  where  the  body  in  question  retains  its  state  of  aggregation. 
On  the  contrary,  where  alterations  in  the  state  of  aggregation 
occur  (and  these  are  the  most  important  cases),  the  proof  con- 
tradicts the  views  which  he  had  formerly  expressed  and  which 
he  subsequently  maintained  §. 
Rankine  added  the  memoir  of  1851  as  a  fifth  section  to  his 
previous  memoir,  on  account  of  the  affinity  of  the  contents. 
Thence  arose  the  error  in  some  authors — who  have  written  as  if 
this  new  memoir  had  from  the  first  formed  part  of  the  earlier 
memoir,  and  therefore  Rankine  and  I  had  simultaneously  given 
a  demonstration  of  the  second  theorem  of  the  mechanical  theoiy 
of  heat.  But  it  is  evident  from  the  foregoing,  that  his  demon- 
stration (leaving  out  of  consideration  how  far  it  is  satisfactory) 
was  first  given  a  year  after  mine. 
Likewise  in  1851  (in  March)  a  second  memoir  by  W.  Thom- 
son on  the  theory  of  heat  was  laid  before  the  Edinburgh  Royal 
Society  || .  In  this  memoir  he  abandons  his  former  position  in 
relation  to  Carnot's  theory,  and  adopts  my  conception  of  the 
*  Edinb.  Trans,  vol.  xx.  p.  205.     Phil.  Mag.  S.  4.  vol.  vii.  p.  249. 
t  Phil.  Mag.  S.  4.  vol.  vii.  p.  251. 
X  Pogrj.  Ann.  vol.  cxx.  p.  434;  and  c  Mechanical  Theory  of  TIeat,'  by 
R.  Clausiu?,  edited  by  T.  Archer  Hirst,  p.  273. 
§  Phil.  Mag.  S.  4.  vol.  xxx.  p.  410. 
||  Edinb.  Trans,  vol.  xx.  p.  261  j  reprinted  in  Phil.  Mag.  S.  4.  vol.  iv. 
pp.8,  105,  &  168. 
