4  Prof.  W.  Weber  on  Electricity  in  relation  to 
ddr1 
where  the  first  part,  —n?,  is  the  relative  acceleration  due  to  the  mu- 
ddr" 
tual  action  of  thejwo  particles,  and  the  second  part,  -jj-,  is  the  ac- 
celeration due  to  other  causes  (namely  to  the  acquired  velocity  of 
the  particles  perpendicular  to  r,  and  to  the  mutual  action  between 
them  and  other  bodies).  The  first  part,  however,  or  that  due  to 
the  mutual  action  of  the  two  particles,  is  proportional  to  the 
force  arising  from  this  mutual  action,  and  is  represented  by  the 
quotient  of  this  force  by  the  mass  upon  which  it  acts. 
Hence  there  easily  follows,  as  was  shown  in  the  memoir 
already  quoted  (page  168),  another  expression  for  the  force  which 
the  particles  e  and  e1  mutually  exert  upon  each  other,  containing 
only  terms  which  are  independent  of  the  force  to  be  determined, 
namely  the  expression 
ee'  f         1  dr*      2rf\ 
2r ,        ,,   \        cc  dl*       cc  / 
rr—  —  ( 
ddrn 
(in  which  /is  put  for  — ~)i  or,  if  the  electrical  particles  e  and  e1 
are  distinguished  from  their  masses  e  and  e'  in  accordance  with 
the  previous  section  (a  distinction  which  was  not  made  in  the 
memoir  quoted  above),  the  expression 
rr- 
(i-ig-f2-^ 
\        cc  at1       cc  / 
From  this  it  results  that  the  law  of  electrical  force  is  by  no 
means  so  simple  as  we  expect  a  fundamental  law  to  be ;  on  the 
contrary,  it  appears  in  two  respects  to  be  particularly  complex. 
In  the  first  place,  it  is  a  consequence  of  this  expression  for  the 
force,  that,  as  was  pointed  out  in  the  memoir  referred  to,  the 
force  which  two  electrical  particles  exert  upon  each  other  does 
not  depend  exclusively  upon  these  particles  themselves,  but  also 
upon  the  portion  of  their  relative  acceleration  denoted  by  f, 
which  is  in  part  due  to  the  action  of  other  bodies.  It  was  also 
pointed  out  that,  inasmuch  as  the  forces  exerted  by  two  bodies 
upon  each  other  have  been  called  by  Berzelius  catalytic  forces 
when  they  depend  upon  the  presence  of  a  third  body,  electrical 
forces  considered  generally  are,  in  this  sense,  catalytic  forces. 
In  the  second  place,  another  noteworthy  result  follows  from 
this  expression  for  the  force — namely,  that  when  the  particles  e 
and  e'  are  of  the  same  kind,  they  do  not  by  any  means  always 
