Force  in  the  Contact  of  Metals.  97 
hour,  and  at  a  constant,  the  quantity  of  heat  which  has  remained 
in  the  air  is  expressed  by  atr;  and  the  quantity  which,  at  the 
expiration  of  the  same  space  of  time,  has  remained  in  the  wire 
or  has  passed  into  the  sides  of  the  cylinder,  by  a^  +  br2,  in 
which  au  and  b  are  constants.  If,  then,  we  call  the  entire  quan- 
tity of  heat  produced  Ay,  we  have  A^ar  +  br2.  On  reversing 
the  current,  we  obtain,  in  the  same  manner,  A/y  =  art  +  brf.  The 
difference  W  between  these  two  values  is  the  quantity  sought, 
which  will  be 
W=fl(T-T/).+  &(T-T|)(T  +  Ti). 
Now  t  —  t{  is  indicated  by  the  space  moved  through  by  the  index 
during  the  time  in  question;  and  t  +  t;  is  evidently  the  increase 
of  temperature  resulting  from  the  quantity  of  heat  produced  in 
the  wire  in  consequence  of  the  galvanic  resistance.  Designating, 
as  before,  the  first  by  t}  and  the  second  by  T,  we  obtain 
Vf  =  at  +  b?t, 
which  is  identical  with  equation  (3)  above  given.  Thus,  even 
when  the  observations  follow  at  intervals  of  15  minutes,  the  for- 
mulae above  given  can  be  used  for  the  calculation,  although, 
perhaps,  with  modified  values  of  the  constants. 
One  observation  following  another,  as  has  been  said,  every  15 
minutes,  it  was  found  that,  chiefly  for  the  copper-tin  combina- 
tion, the  successive  deviations  of  the  index  varied  considerably 
in  amount — a  circumstance  which  I  could  not  at  first  account 
for.  On  closer  reflection,  however,  its  cause  was  easily  disco- 
vered. As  was  said  above,  a  quarter  of  an  "hour  is  not  sufficient 
to  render  the  temperature  stationary.  Let  us  suppose  that  with 
the  same  direction  and  the  same  intensity  the  current  has  taken 
a  longer  time  to  traverse  the  cylinders — three  quarters,  for  ex- 
ample, or  even  more — and  that  then  it  is  reversed,  and  its  direc- 
tion afterwards  changed  every  quarter  of  an  hour.  In  that 
cylinder  in  which  heat  was  developed  at  the  point  of  contact 
during  the  45  minutes  above  supposed,  the  temperature  of  the 
copper  wall  is  relatively  high,  and  thence  the  cooling  greater 
than  in  the  other.  As  soon  as  the  current  is  reversed,  the  air 
which  surrounds  the  point  of  contact  in  the  first  cylinder  cools; 
while  the  wall  continues  to  lose  a  great  quantity  of  heat,  in  con- 
sequence of  its  still  comparatively  elevated  temperature ;  and  in 
the  second  cylinder  the  source  of  heat  is  augmented,  while  the 
cooling  is  relatively  very  little.  The  index,  therefore,  has  neces- 
sarily a  considerable  deviation  in  the  direction  of  the  first 
cylinder.  After  a  quarter  of  an  hour  the  current  is  again  re- 
versed before  the  sides  of  the  first  cylinder  have  had  time  to  cool 
and  those  of  the  second  to  be  heated  to  the  degree  corresponding 
Phil.  Mar/.  S.  4.  Vol.  43.  No.  284.  Feb.  1872.  H 
