[     443     ] 
LVI.   On  the  Objections  raised  by  Mr.  Tait  against  my  Treat- 
ment of  the  Mechanical  Theory  of  Heat.     By  R.  Clausius*. 
IN  reply  to  my  "  Contribution  to  the  History  of  the  Mecha- 
nical Theory  of  Heat "  f,  Mr.  Tait  J  has  given  the  matter 
a  turn  which  to  me  is  agreeable.  For  he  therein  contests  not 
the  priority  of  my  investigations,  but  their  correctness;  so  that 
it  is  now  no  longer  a  question  of  historic  and  personal  explana- 
tions, but  of  scientific  elucidations,  which,  on  account  of  the 
importance  of  the  subject  to  which  they  relate,  may  perhaps  not 
be  without  a  more  general  interest.  I  will  therefore  take  no 
notice  of  the  somewhat  irritated  tone  of  the  reply,  and  only  take 
into  consideration  the  matter  it  contains. 
As  already  mentioned  in  my  previous  article,  the  axiom  em- 
ployed by  me  for  the  demonstration  of  Carnot's  theorem  modified, 
viz.  that  heat  cannot  pass  by  itself  from  a  colder  into  a  hotter  body, 
was  immediately  acknowledged  as  correct  by  Sir  W.  Thomson, 
and  since  then  has  likewise  been  made  use  of  by  many  other 
authors  for  the  same  demonstration.  Mr.  Tait,  on  the  contrary, 
now  declares  it  to  be  fallacious. 
Of  the  two  phenomena  adduced  by  him  for  the  refutation  of 
the  proposition,  I  will  first  discuss  that  of  which  he  says  that  it 
gives  an  "excellent  instance  of  the  fallacy  of  the  so-called 
axiom" — namely,  the  phenomenon  that  a  thermoelectric  battery 
worked  with  ice  and  boiling  water  is  capable  of  raising  a  fine  wire 
to  incandescence. 
In  one  of  my  memoirs  §,  I  have  myself  applied  the  mecha- 
nical theory  of  heat  to  thermoelectrical  phenomena.  I  therein 
showed  that  a  thermoelectric  element  (and  so,  of  course,  a 
thermoelectrical  battery)  may  be  compared  to  a  steam-engine, 
the  heated  junction  corresponding  to  the  boiler,  and  the  cold 
junction  to  the  condenser.  At  the  hot  junction  heat  is  with- 
drawn from  a  heat-reservoir,  the  temperature  of  which  we  will 
name  t} ;  and  at  the  cold  junction  heat  is  given  up  to  another 
heat-reservoir,  the  temperature  of  which  may  be  called  t0.  But 
the  quantity  of  heat  given  up  is  something  less  than  the  heat 
received;  and  hence  the  quantity  of  heat  given  up  in  the  unit 
of  time  we  will  denote  by  Q,  and  the  heat  received  by  Q  +  q. 
The  portion  q  of  the  latter  quantity  is  expended  in  the  work  ne- 
cessary for  the  production  of  the  electric  current ;  and  the  other 
portion,  Q,  passes  from  a  body  of  the  temperature  tl  into  a  body 
of  the  temperature  t0. 
When  the  work  performed  by  a  steam-engine  is  applied  to  the 
*  Translated  from  the  MS.  communicated  by  the  Author, 
t  Phil.  Mag.  February,  1872.  J  Ibid.  May  18/2. 
§  Pogg.  Ann.  vol.  xc.  p.  513. 
