92  M.  E.  Edlund's  Researches  on  the  Electromotive 
is  constant  during  the  time  of  the  observation,  or  its  modification 
is  proportional  to  the  time.  As  a  rule,  several  such  determina- 
tions were  made,  in  order  to  obtain  a  result  so  much  more  cer- 
tain. But  this  made  it  very  slow  work,  and  involved  a  great  loss 
of  time. 
The  sensitiveness  of  the  apparatus  it  is  very  easy  to  determine. 
It  follows,  from  the  dimensions  above  given  of  the  copper  cylin- 
ders, the  diameter  of  the  glass  tube  being  2*5  millims.,  that  the 
volume  of  a  millimetre  length  of  the  latter  is  to  that  of  each 
copper  cylinder  as  1  to  12800.  Supposing  we  had  only  one 
cylinder,  and  that  the  indicating  tube  fixed  to  it  opened  into  the 
free  air,  it  would  be  necessary,  for  a  variation  =  t  in  the  tempe- 
rature of  the  enclosed  air,  that  the  displacement  of  the  index 
should  be  such  that 
mv = 0-00366  t.Y, 
in  which  V  represents  the  volume  of  the  cylinder,  v  that  of  a 
millimetre  length  of  the  tube,  and  m  the  number  of  divisions  of 
the  scale  giving  the  displacement  of  the  index. 
v  1 
Putting   ~=/3=  -  9knn>  we  obtain  mfi  —  0*00366/.  Of  course 
this  value  is  correct  only  as  long  as  the  pressure  of  the  air  re- 
mains constant.  If  now  the  copper  cylinder  be  connected  with 
another  cylinder  of  the  same  volume,  as  was  the  case  in  the  ex- 
periments, we  shall  have,  H  designating  the  pressure  before,  and 
h  the  pressure  after  the  variation  t, 
Y(l  +  0'00366t)j-V=mv=mj3V. 
The  copper  cylinders  being  of  equal  dimensions,  and  the  tempe- 
rature of  one  diminishing,  on  the  reversal  of  the  current,  by  a 
quantity  equal  to  the  augmentation  of  temperature  in  the  other, 
we  obtain  further  (i  __O00366*) 
h=ti = 5 
1  —  m/3 
Substituting  this  value  in  the  preceding  equation,  we  obtain 
0-00366  t=m/3. 
The  deviation  obtained  with  the  combined  cylinders  will  there- 
fore be  of  the  same  amount  as  if  only  one  cylinder  were  em- 
ployed and  the  indicating  tube  were  open  to  the  external  air, 
supposing  the  pressure  of  the  latter  constant.  Making  m  =  l, 
we  obtain  £  =  0o,002134  Cels.  A  deviation  of  one  division  of 
the  scale  requires,  therefore,  a  variation  (in  round  numbers)  of 
0-002  degree  in  the  temperature  of  the  cylinder.  Now  it  is 
evident  that,  if  this  deviation  is  to  be  obtained  for  the  above- 
mentioned  increase  of  temperature,  the  index  must  not  be  ob- 
structed in  its  movement  by  friction,   adhesion, .  &c.     It  was 
