444      Prof.  11.  Clausius  on  the  Mechanical  Theory  of  Heat. 
overcoming  of  friction  or  other  passive  resistances,  it  is  again 
transformed  into  heat,  and  under  suitable  conditions  can  gene- 
rate a  temperature  far  higher  than  that  of  the  boiler.  Just  so 
in  the  electrical  battery,  the  work  which  must  have  been  ac- 
complished in  order  to  put  the  electricity  in  motion  can  be  again 
transformed  into  heat  in  overcoming  the  resistances  to  conduc- 
tion, and  here  also,  under  suitable  conditions,  can  generate 
a  much  higher  temperature  than  that  of  the  heated  junctions. 
For  example,  as  Mr.  Tait  says,  if  the  heated  junctions  have  only 
the  temperature  of  boiling  water,  a  wire  can  be  heated  to  incan- 
descence. 
Let  the  temperature  which  the  wire  acquires,  and  which  can 
be  maintained  constant  as  long  as  we  please,  be  denoted  by  tQ, 
then  we  can  say  that  a  part  of  that  quantity  of  heat,  q,  which 
in  the  battery  is  expended  for  work  appears  again  as  heat  in 
another  body  at  the  temperate  t2.  As,  then,  the  heat  expended 
for  work  is  derived  from  a  heat-reservoir  of  the  temperature  tlt 
we  obtain  as  a  result  of  the  process  the  passage  of  a  certain  quan- 
tity of  heat  from  a  body  at  the  temperature  tx  into  a  body  at  the 
higher  temperature  t2. 
Now  the  question  to  be  decided  is,  whether  this  passage  of 
heat  from  a  lower  to  a  higher  temperature  has  taken  place  by 
itself. 
By  this  concise  designation,  by  itself  I  mean,  as  I  have  re- 
peatedly explained,  without  the  simultaneous  occurrence  of  another 
change  serving  for  compensation.  So  far  as  we  have  to  do  with 
cyclical  processes,  there  are  two  sorts  of  changes  which  may 
serve  for  compensation,  namely  : — first,  the  passage  of  heat  from 
a  hotter  into  a  colder  body ;  and,  secondly,  the  consumption  of 
work,  or,  to  express  it  more  definitely,  the  transformation  of 
work  into  heat. 
If  now  from  this  point  of  view  we  contemplate  our  thermo- 
electric battery  with  the  thin  conducting  wire  which  is  brought 
to  incandescence,  we  see  that  certainly  part  of  the  quantity  of 
heat  q  passes  over  from  the  temperature  tl  to  the  higher  tempe- 
rature tz,  but  that  simultaneously  the  other  quantity  Q  passes 
from  the  temperature  tl  to  the  lower  temperature  t0.  This  latter 
passage  of  heat  forms  the  compensation  of  the  former;  and  hence 
we  cannot  say  that  the  former  has  taken  place  by  itself. 
The  case  here  discussed  is  so  simple  and  clear  that  it  might 
be  chosen  as  a  perfectly  suitable  example  for  the  elucidation  and 
confirmation  of  my  axiom ;  and  yet  this  is  the  case  which  Mr. 
Tait  has  selected  as  a  demonstration  of  its  fallacy. 
Mr.  Tait  adduces  as  another  case  in  contradiction  to  my  axiom 
a  thermoelectric  circuit  in  which  the  hot  junction  is  at  a  tempe- 
rature higher  than  the  neutral  point.     Consequently  the  circuit 
