276         M.  E.  Edlund's  Researches  on  the  Electromotive 
urination  of  the  electromotive  forces,  may  be  pretty  large; 
nor  is  this  very  astonishing,  the  differences  of  temperature  to 
be  measured  being  so  very  small.  In  the  case  of  the  zinc-copper 
combination,  for  example,  the  difference  does  not  amount  to  one 
thousandth  of  a  degree ;  in  that  of  the  cadmium-copper,  hardly 
to  one  and  a  half  hundredth ;  and  for  copper- bismuth  (which, 
of  all  the  combinations,  possesses  the  greatest  electromotive 
force),  to  1*5  degree.  But  the  errors  of  observation  are,  after 
all,  in  no  case  sufficiently  great  to  furnish  the  explanation  of 
the  considerable  variations  in  the  quotients  above  given.  Xet 
us  compare,  for  example,  the  copper-gold  with  the  iron-copper 
combination,  A  series,  consisting  of  observations  made  with 
three  different  intensities  of  current,  gave,  almost  without  va- 
riation, the  number  14*5  for  the  electromotive  force  of  the 
former  combination ;  another  series,  in  which  the  observations 
followed  one  another  at  15-minute  intervals,  gave  15*02.  The 
mean,  14*76,  cannot  be  singularly  faulty.  The  electromotive 
force  of  the  iron-copper  combination  was  determined  in  the 
same  manner  by  means  of  several  series,  which  gave,  as  the 
mean,  130*99,  in  which  the  probable  error  cannot  be  very  great. 
The  same  two  combinations  had  also  been  investigated  by 
using  two  cylinders  the  external  surface  of  which  was  not 
silvered;  and  I  obtained  12*56  for  copper-gold,  115*73  for 
iron-copper.  The  ratio  between  the  two  former  numbers  does 
not  much  differ  from  that  between  the  two  latter.  It  is  the 
same  with  most  of  the  other  combinations.  The  only  ones  which 
can  betray  a  greater  uncertainty  are  the  zinc-copper  and  copper- 
silver  combinations,  in  which  the  differences  of  temperature  were 
very  insignificant.  We  can  therefore  formulate  the  following 
proposition  : — 
4.  The  thermoelectric  forces  which,  at  a  given  difference  of  tem- 
perature, arise  in  different  metallic  combinations,  are  not  propor- 
tional to  the  electromotive  forces  of  those  same  metallic  combinations. 
By  the  application  of  the  second  fundamental  principle  of  the 
mechanical  theory  of  heat,  Clausius  has  demonstrated  that  the 
augmentation  undergone  by  the  electromotive  force  when  the 
temperature  rises  at  the  point  of  contact  should  be  proportional 
both  to  the  augmentation  of  temperature  and  to  the  electromo- 
tive force  itself.  If  Carnot's  function  be  made  equal  to  A  (a  -f  t), 
in  which  A  is  the  equivalent  of  heat  for  the  unit  of  work,  t 
the  temperature  in  degrees  Celsius,  and  a  the  number  273,  it 
follows  from  this  deduction  that  H  =  e(a  +  t),  in  which  E  is  the 
electromotive  force  at  the  temperature  t,  and  e  a  constant  de- 
pendent exclusively  on  the  nature  of  the  metals  forming  the  con- 
tact. It  would  hence  follow  that  all  the  quotients  above  given 
should  be  of  equal  amount,  which  nevertheless  experiment  has 
