the  Principle  of  the  Conservation  of  Energy.  145 
tions  between  the  strength  and  character  of  the  Amperian 
currents  in  the  two  conductors,,  but  that,  along  with  the  relation 
needed  for  this  equality  of  temperature,  the  following  difference 
may  exist  between  the  currents  of  the  two  conductors,  namely : — ■ 
that  greater  masses  of  electricity  may  move  with  smaller  velo- 
city in  the  Amperian  currents  of  the  one  conductor,  and  smaller 
masses  of  electricity  with  greater  velocity  in  those  of  the  other 
conductor. 
Let  now  a  ring  be  conceived,  formed  of  two  such  dissimilar 
conductors,  through  which  a  constant  current  passes,  so  that  in 
the  same  time  an  equal  quantity  of  electricity  passes  through 
every  section  of  the  ring;  then  it  is  evident  that  equal  quantities 
of  electricity  must  also  traverse  the  two  sections  which  bound 
the  first  layer  of  the  second  conductor.  But  the  electricity  which 
traverses  the  first  section  comes  from  the  first  conductor,  in  the 
molecular  currents  of  which  large  masses  of  electricity  move 
with  small  velocity.  Hence,  in  consequence  of  this  smaller 
velocity,  this  electricity  which  penetrates  into  the  first  layer  of 
the  second  conductor  possesses  less  vis  viva.  The  electricity  which 
passes  through  the  second  section  comes  from  the  above-men- 
tioned first  layer  of  the  second  conductor  itself,  where  a  smaller 
mass  of  electricity  moves  in  the  Amperian  currents  with  a 
greater  velocity,  and  therefore  it  possesses,  in  consequence  of 
this  greater  velocity,  a  greater  vis  viva.  It  follows  from  this, 
that,  as  a  consequence  of  the  current,  this  first  layer  of  the 
second  conductor  gives  up  more  vis  viva  to  the  following  layer 
of  the  second  conductor  than  it  receives  from  the  last  layer  of 
the  first  conductor.  Consequently  a  diminution  takes  place  in 
the  kinetic  energy  of  the  Amperian  currents  of  this  layer,  or,  in 
other  words,  a  diminution  of  the  thermal  energy  or  temperature. 
The  opposite  condition  is  found  on  considering  the  two 
sections  which  bound  the  first  layer  of  the  first  conductor.  The 
electricity  which  passes  through  the  first  section  into  this  layer 
comes  out  of  the  end  of  the  second  conductor  with  a  greater 
velocity ;  and  that  which  passes  out  of  this  layer  through  the 
second  section,  leaves  this  section  with  a  smaller  velocity  ;  whence 
it  follows  that,  as  a  consequence  of  the  current,  the  first  layer  of 
the  first  conductor  gives  up  less  vis  viva  to  the  following  layer  of 
the  same  conductor  than  it  receives  from  the  last  layer  of  the 
second  conductor ;  and  thus  an  increase  takes  place  in  the  kinetic 
energy  of  the  Amperian  currents  of  this  layer,  or,  in  other 
words,  an  increase  of  the  thermal  energy  or  temperature. 
It  will  be  seen  that  a  foundation  is  here  presented  for  the 
doctrine  of  thermomagnetism,  and  in  particular  for  Peltier's  fun- 
damental experiment,  although  it  would  lead  us  too  far  to  pursue 
it  further  here. 
Phil.  Mag.  S.  4.  Vol.  43.  No.  284.  Feb.  1872.  L 
