the  Principle  of  the  Conservation  of  Energy.  135 
current,  is 
-iee'd, 
.  rW  cos  v1 
since  in  this  case  u=0.  But  the  difference  between  the  value 
given  to  r  here  and  that  assigned  to  it  previously  (namely  the 
distance  from  the  particie  +e,  in  motion  about  the  particle  — ea 
to  the  given  element  of  current),  may  be  regarded  as  a  negligible 
fraction  of  ;*,  so  that  we  get,  for  the  repelling  force  exerted  by 
the  moving  particle  -f  e  and  stationary  particle  —  e  together  upon 
the  element  of  current,  the  expression 
±eJds' 
(3  cos  0  cos  0'— 2  cos  e)  .  uu'. 
ccrr 
If  we  were  to  put  in  place  of  the  moving  electrical  particle  +  e 
a  second  element  of  current,  the  positive  electricity  of  which, 
moving  with  the  velocity  -\-\u,  was  denoted  by  -f  eds,  and  whose 
negative  electricity,  moving  with  the  velocity  —  |w,  was  denoted 
by  —  eds,  we  should  obtain  for  the  mutual  repelling  force  of  the 
two  elements  of  current  the  value 
= (3  cos  0  cos  ©'  —  2  cos  d) .  uu': 
ccrr      v  ' 
that  is  to  say,  the  same  expression  as  before,  if  the  electrical 
particle  previously  denoted  by  -\-e  (and  moving  with  the  velo- 
city u)  were  taken  as  equal  to  the  positive  electricity  contained 
in  the  second  element  of  current,  namely  +eds  (moving  with 
the  velocity  \u). 
It  follows  from  this  that  the  rotatory  motion  of  the  electrical 
particle  -\-e  about  the  stationary  particle  — e  replaces  a  circular 
double  current,  if  the  positive  electricity  contained  in  the  latter 
is  equal  to  -f  e  and  moves  in  its  circular  orbit  with  half  the 
velocity  of  the  aforesaid  electrical  particle  +  e,  and  if  also  the 
negative  electricity  contained  in  the  current  is  equal  to  —  e  and 
moves  with  the  same  velocity  as  the  positive  electricity  but  in 
the  opposite  direction. 
Hence  it  appears  that  an  electrical  particle  -\-e  moving  in  a 
circle  about  the  electrical  particle  —  e  exerts  upon  all  galvanic 
currents  the  same  effects  as  those  assumed  by  Ampere  in  the 
case  of  his  molecular  currents. 
The  molecular  currents  assumed  by  Ampere,  however,  differ 
essentially  from  all  other  galvanic  currents  in  this  respect,  that, 
according  to  Ampere's  assumption,  they  continue  without  elec- 
tromotive force ;  whereas  all  other  galvanic  currents,  in  accord- 
ance with  Ohm's  law,  are  proportional  to  the  electromotive  force, 
and  cease  when  the  electromotive  force  vanishes.     But  it  is  evi- 
