Force  in  the  Contact  of  Metals.  277 
shown  not  to  be  the  case.  Another  result  of  the  theory  is,  that 
the  thermoelectric  currents  should  be,  whatever  the  temperature, 
proportional  to  the  difference  of  temperature  between  the  points 
of  contact — which,  as  we  kuow,  agrees  no  more  than  the  former 
with  the  practical  results.  Now  the  cause  of  this  may  indeed 
be,  as  Clausius  assumes,  that  at  high  temperatures  metals  undergo 
a  molecular  modification,  the  thermoelectric  effect  of  which  can- 
not be  taken  into  account  in  the  calculation.  It  is,  however, 
infinitely  more  difficult  to  explain  why  the  quotients  above  men- 
tioned are  not  identical,  as  the  theory  requires ;  here  we  have 
neither  high  temperatures  nor  sensible  molecular  modifications 
in  the  metals.  I  cannot  omit  to  call  attention  to  a  result  I  ob- 
tained some  years  since,  during  researches  on  the  calorific  phe- 
nomena arising  from  change  of  volume  in  solid  bodies*.  If  a 
wire  be  stretched,  it  cools ;  and  if  it  then  be  permitted  to  con- 
tract slowly  without  the  particles  beginning  to  oscillate,  it  be- 
comes warmer  by  a  quantity  equal  to  the  cooling  effected  by  the 
tension.  Thomson  has  calculated  these  changes  of  temperature 
by  means  of  the  second  axiom  of  the  mechanical  theory  of  heat. 
Now,  on  comparing  the  results  of  experiment  with  the  theore- 
tical calculation,  they  are  found  not  to  agree.  As  is  known, 
the  mechanical  equivalent  of  heat  enters  into  Thomson's  for- 
mula ;  and  it  is  necessary  to  give  that  equivalent  the  value  of  683 
kilogrammetres  in  order  to  make  the  result  of  the  experiments 
agree  with  the  theory.  The  concordance  between  the  series  of  ex- 
periments shows  that  this  number  cannot  be  more  than  a  few  per 
cent,  wrong ;  and  this  is  also  confirmed  by  the  circumstance  that, 
if  the  stretched  wire  be  suffered  to  contract  suddenly  and  without 
accomplishing  any  external  mechanical  work,  the  resulting  quan- 
tity of  heat,  calculated  with  the  aid  of  the  number  683  already 
found,  gives  the  correct  value  of  its  mechanical  equivalent,  viz. 
434  kilogrammetres.  It  has  been  attempted  to  explain  the 
want  of  agreement  between  the  theory  and  my  experiments  by 
the  formula  presupposing  that  the  body  undergoes,  under  the 
influence  of  heat,  an  equal  dilatation  in  all  directions,  which, 
perhaps,  is  not  the  case  with  stretched  wires  like  those  employed 
in  my  experimentst-  But  in  a  recent  paper  J,  M.  Dahlander 
has  demonstrated  the  invalidity  of  the  explanation.  As  we  have 
no  right  to  reject  a  fact  because  it  is  opposed  to  those  which  we 
already  know,  I  conclude  by  formulating  the  following  proposi- 
tion as  a  further  result  of  my  experiments : — 
*  Ofversigt  of  K.  Vet.-Akad.  Fbrhandl.for  1865,  p.  95.  Pogg.  Ann. 
vol.  cxxvi.  p.  589.     Ann.  de  Chim.  et  de  Phys.  ser.  4.  vol.  viii.  p.  257. 
t  Paul  de  Saint-Robert,  Atti  della  Reale  Accad.  delle  Scienze  di  Torino, 
Jan.  1868;  Ann.  de  Chim.  et  de  Phys.  ser.  4.  vol.  xiv. 
\  Ofversigt  af  K.  Vet.-Akad.  lorhandl.  for  1871. 
