96  M.  E.  Edlund's  Researches  on  the  Electromotive 
pair  of  wires  is  exchanged  for  another ;  so  that  /8  must  be  de- 
termined for  each  pair  by  observation. 
Now,  if  at  two  different  current-intensities,  s  and  sp  the  cor- 
responding values  t  and  tl  of  the  movement  of  the  index  be 
measured,  we  obtain,  from  equation  (5), 
P~  f.sfit  +  Mt-t,) W 
The  observations  given  further  on  have  been  calculated  by  means 
of  equations  (5)  and  (6). 
As  is  evident  from  what  precedes,  the  method  of  observation 
we  have  described  is  founded  on  the  circumstance  that,  once  the 
temperature  is  stationary,  the  cylinder  loses  a  quantity  of  heat 
equal  to  that  generated  in  the  wires.  In  principle  this  method 
is  correct.  Nevertheless  the  formulae  by  which  the  quantity  of 
heat  that  disappears  is  calculated  are  only  approximative ;  but 
the  experiments  demonstrate  that  the  approximation  is  sufficient. 
As  the  interval  from  one  observation  to  another  was  three  quar- 
ters of  an  hour,  the  work  took  a  considerable  time.  When  the 
whole  of  the  metallic  combinations  had  thus  been  studied  from 
both  points  of  view,  electromotive  and  thermoelectric,  wishing, 
as  a  control,  to  determine  the  electromotive  forces  again,  I  pro- 
ceeded in  the  following  manner : — The  current  was  reversed  at 
the  end  of  a  quarter  of  an  hour,  during  which  the  temperature 
of  the  cylinder  had  not  time  to  acquire  equilibrium.  If  now  all 
the  heat  generated  in  the  wire  passed  into  the  air  enclosed  in  the 
cylinder,  without  any  of  it  remaining  in  the  wire  or  disappearing 
through  the  sides  of  the  cylinder,  an  exact  measure  of  the  heat 
produced  would  be  obtained  by  determining,  from  the  displace- 
ment of  the  index,  the  increase  of  the  mean  temperature  of  the 
air.  But  this  is  not  the  case  :  a  part  of  the  heat  remains  in  the 
wire ;  and  a  part  passes  into  the  sides.  The  quantity  of  heat 
which,  remaining  in  the  wire,  occasions  the  heating  of  it,  de- 
pends on  the  calorific  capacity  of  the  wire ;  but  the  whole  amount 
of  this  is  insignificant  in  comparison  with  that  which  passes  into 
the  copper  sides.  It  is  therefore  quite  unnecessary  to  take  ac- 
count of  the  difference,  still  more  insignificant,  between  the 
quantities  of  heat  remaining  in  the  different  pairs  of  wires.  The 
part  of  the  heat  generated  which  thus  does  not*pass  into  the  air 
may  be  regarded  as  a  function  of  the  total  augmentation  of  the 
temperature  of  the  air  during  the  interval  of  time,  and  may  be 
expressed  by  the  first  two  powers  of  that  augmentation.  This 
hypothesis  must  be  verified  by  the  observations  themselves  before 
it  can  be  admitted  as  correct ;  as  will  be  afterwards  seen,  the 
observations  made  furnish  this  verification.  If  t  is  the  increase 
of  the  mean  temperature  of  the  air  at  the  end  of  a  quarter  of  an 
