the  Principle  of  the  Conservation  of  Energy.  143 
force.  Ado!  since  all  the  other  forces  which  act  upon  such  such 
a  particle  in  a  conductor  must  together  balance  each  other,  this 
work  will  make  its  appearance  as  an  equivalent  increase  of  the 
vis  viva  of  the  particle  ;  whence  it  follows  that  the  vis  viva  of  all 
the  Amperian  molecular  currents  contained  in  the  conductor 
must,  while  the  current  traverses  the  conductor,  increase  j  that 
is  to  say,  the  square  of  the  velocity  with  which  the  particles  in 
the  Amperian  molecular  current  revolve  about  one  another 
must  increase  proportionally  to  the  force  of  segregation  {electro- 
motive force),  and  proportionally  to  the  distance  through  which 
this  force  acts  in  its  own  direction  (or  tothe  strength  of  the  current). 
If  the  ratio  of  the  electromotive  force  to  the  strength  of  the  cur- 
rent be  called  resistance,  we  may  say  instead  of  the  above  that  the 
vis  viva  of  all  the  molecular  currents  contained  in  the  conductor 
increases,  during  the  passage  of  the  current,  proportionally  to 
the  resistance,  and  proportionally  to  the  square  of  the  strength  of 
the  current. 
This  increase  of  kinetic  energy  of  the  electrical  particles  con- 
tained in  a  conductor  while  a  current  traverses  it,  follows  there- 
fore as  a  necessary  consequence  of  the  action  of  the  electromotive 
force  upon  the  particles,  while  these  particles,  as  the  result  of  the 
current,  move  onward  in  the  direction  of  this  force. 
This  theoretical  conclusion  receives,  not  indeed  a  direct, 
but  an  indirect  confirmation  from  experiment,  inasmuch  as  an 
increase  of  thermal  energy  is  observed  in  the  conductor  while  a 
current  traverses  it.  And  this  observed  increase  of  the  thermal 
energy  in  the  conductor  is  equal  to  the  calculated  increase  of  the 
kinetic  energy  of  the  electrical  particles  in  the  Amperian  molecu- 
lar currents  of  the  conductor. 
Now  the  thermal  energy  of  a  body  is  a  kinetic  energy  re- 
sulting from  movements  in  the  interior  of  the  body,  which  are 
therefore  inaccessible  to  direct  observation.  In  like  manner,  the 
kinetic  energy  belonging  to  the  electrical  particles  in  the  Am- 
perian molecular  currents  in  a  conductor  is  a  kinetic  energy 
which  results  from  movements  taking  place  in  the  interior  of  the 
conductor,  and  therefore  inaccessible  to  direct  observation. 
But  notwithstanding  this  agreement,  the  thermal  energy  of  a 
body  and  this  kinetic  energy  of  the  electrical  particles  in  the 
Amperian  currents  contained  in  the  same  body  might  possibly 
be  altogether  different  as  to  their  essential  nature.  For  it  is 
possible  that  the  thermal  energy  might  be  energy  resulting  from 
the  motion  of  quite  other  particles  than  those  of  electricity,  and 
the  motion  of  these  other  particles  might  be  of  quite  a  different 
kind  from  those  of  the  particles  in  Amperian  currents. 
In  order  to  explain  the  identity  of  the  increase  of  the  energy 
of  the  Amperian  molecular  currents,  as  determined  above,  with 
