[     119    3 
XV.  Electro  dynamic  Measurements.  By  Professor  Wilhelm 
Weber. — Sixth  Memoir,  relating  specially  to  the  Principle  of 
the  Conservation  of  Energy. 
[Concluded  from  p.  20.] 
8.  On  the  Movement  of  two  Electrical  Particles  in  consequence  of 
their  action  on  each  other. 
THE  fundamental  electrical  law  determines  the  action  exerted 
by  any  given  particle  upon  another  under  any  circum- 
stances. The  simplest  and  most  obvious  application  that  can 
be  made  of  this  law,  would  seem  to  be  to  develope  the  laws  of 
the  motion  of  two  particles  which  act  mutually  upon  each  other. 
Greater  practical  interest,  however,  attached  to  the  determina- 
tion, in  the  first  place,  of  the  laws  of  the  distribution  of  electri- 
city at  rest  upon  conductors,  and  of  the  laws  of  the  forces  exerted 
by  a  current  of  electricity  in  a  closed  conductor,  by  reason  of  the 
current  existing  in  another  conductor,  upon  this  latter  conductor 
itself — as  well  as  to  the  development  of  the  laws  of  the  (electro- 
motive) forces  exerted  by  closed  currents  (or  by  magnets)  on  the 
electricity  in  closed  conductors — inasmuch  as  the  results  of  these 
developments  admitted  of  being  directly  tested  and  confirmed 
by  experiment.  But  although  this  important  practical  interest 
is  wanting  to  the  development  of  the  laws  of  motion  of  two  par- 
ticles subject  only  to  their  mutual  action,  many  of  its  results 
cannot  fail  to  merit  attention  in  other  respects. 
The  interest  which  belongs  to  these  results  relates  indeed 
specially  to  the  molecular  movements  of  two  particles,  movements 
which  are  shut  out  from  all  direct  experimental  investigation,  so 
that  there  is  no  authority  for  the  application  to  them  of  the  law 
that  has  been  established,  so  far  as  it  is  regarded  as  an  experi- 
mental law.  Consequently  the  development  of  the  laws  of  the 
molecular  movements  of  two  particles  in  accordance  with  the  law 
that  has  been  established  must  be  considered  only  as  an  attempt 
to  find  a  clue  to  the  theory  (which  as  yet  we  are  entirely  without) 
of  these  movements — a  clue  which  by  itself  is  certainly  not 
sufficient,  but  is  still  in  need  of  being  supplemented  in  essential 
respects.  For  so  long  as  the  molecular  forces  acting  only  at  mo- 
lecular distances,  which  doubtless  cooperate  in  the  molecular 
movements,  are  not  known  and  taken  exact  account  of,  the  results 
that  may  be  acquired  cannot  have  any  exact  quantitative  appli- 
cation, but  only  a  qualitative  value  within  certain  limits,  and 
can  be  of  consequence  only  for  a  first  reconnaissance  of  the 
territory. 
9.  Motion  of  two  Electrical  Particles  in  the  direction  of  the  straight 
line  which  joins  them. 
For  two  particles,  e,  e\  moving  simply  in  consequence  of  their 
