132  Prof.  W.  Weber  on  Electricity  in  relation  to 
has  then  a  positive  value  for  r=2n— x,  but  diminishes  and  be- 
nx 
comes  equal  to  nothing  between  r=2n— x  and  r  =  2n-\ ; 
n  ~~"  x 
so  that,  for  r  =  2n-\ ,  -r-  has  a  negative  value.     It  is  evi- 
'  n—x    at 
dent  from  this  that  repulsion  of  the  two  particles  takes  place 
du 
from  r  =  2n— x  as  far  as  the  value  of  r  for  which  -=-  =0,  and 
at 
nx 
attraction  from  this  point  as  far  as  r=2n-\ ,  and  conse- 
n  —  x 
quently  that  the  two  particles  must  always  remain  in  oscillatory 
motion  relatively  to  each  other  within  the  indicated  limits. 
17.   On  Ampere's  Molecular  Currents. 
The  molecular  state  of  aggregation  of  two  dissimilar  electrical 
particles  that  has  just  been  described,  namely  that  in  which  the 
distance  of  the  two  particles  alternately  increases  and  diminishes 
between  exactly  defined  limits  and  the  path  in  which  one  particle 
moves  about  the  other  becomes  a  circular  orbit  at  the  two  limits, 
is  deserving  of  closer  consideration,  especially  in  those  cases  in 
which  it  is  admissible  to  regard  one  of  the  particles  as  being  at 
rest  and  the  other  particle  as  moving  in  a  circle  about  the  first. 
The  relation  between  the  particles  in  respect  of  their  partici- 
pation in  the  motion  depends  upon  the  ratio  of  their  masses  e 
and  e';  and,  according  to  section  15,  the  values  of  e  and  e'  must 
include  the  masses  of  the  ponderable  atoms  adhering  to  the 
electrical  atoms.  Let  e  be  the  positive  electrical  particle,  and 
let  the  negative  particle  be  equal  and  opposite  to  it,  and  let  it 
therefore  be  denoted  by  —  e  (instead  of  by  e1).  Now  let  a  pon- 
derable atom  adhere  to  the  latter  only,  whereby  its  mass  is  so 
much  increased  that  the  mass  of  the  positive  particle  becomes 
negligible  in  comparison.  The  particle  — e  may  then  be  re- 
garded as  being  at  rest,  and  the  particle  -\-e  alone  as  being  in 
motion  around  the  particle  —e. 
The  two  dissimilar  particles,  when  in  the  molecular  state  of 
aggregation  that  has  been  described,  consequently  represent  an 
Amperian  molecular  current ;  for  it  can  be  shown  that  they  cor- 
respond completely  to  the  assumptions  which  Ampere  made  in 
relation  to  the  molecular  currents. 
In  order  to  show  this,  let  us  develope  the  expression  for  the 
force  which  the  moving  particle  e  exerts  upon  any  given  element 
of  a  current.  Let  ds1  denote  the  length  of  the  given  element  of 
current,  -\-e'ds'  the  positive,  and  —e'ds'  the  negative  electricity 
which  it  contains ;  and,  lastly,  let  u1  denote  the  velocity  of  the 
positive  particle  -\-e*ds,  and  —  u'  the  velocity  of  the  negative 
