the  Principle  of  the  Conservation  of  Energy.  3 
in  proportion  to  the  reciprocals  of  the  accelerations  produced  in 
them  by  the  same  force)  by  e,  e7,  of  which  the  values  are  always 
positive,  we  get  for  positive  values  of  e,  e1, 
e  ~~  e'  ~"    ' 
and  for  negative  values  of  e}  e\ 
e  —  e'  —  7i 
where  a  has  a  definite  positive  and  b  a  definite  negative  value. 
Whether  or  not  we  have  here  aa  =  bb}  or  what  ratio  aa  bears  to 
bb,  has  not  as  yet  been  made  out,  any  more  than  the  numerical 
value  of  a  or  b.  In  many  cases  the  electrical  mass  e  is  connected 
with  a  ponderable  mass  m,  so  that  it  is  impossible  for  it  to  be 
moved  independently  of  it ;  in  such  cases,  only  the  combined 
mass  m  +  e  comes  into  account,  and  in  general  e  may  be  regarded 
as  vanishingly  small  in  comparison  with  m.  Consequently  it  is 
only  seldom  that  the  masses  e,  e'  have  to  be  considered. 
The  distinction  here  indicated  between  the  particles  e,  e'  and 
their  masses  e,  e7  is  not  always  made ;  on  the  contrary,  the  sym- 
bols of  the  particles  e,  d  are  also  used  to  denote  the  correspond- 
ing masses.  It  is,  however,  to  be  observed  that,  when  this  is 
done,  no  regard  can  be  had  to  the  signs  of  e,  e'.  The  omission 
of  the  unknown  factors  a  and  b  is  always  allowable  when  we  are 
dealing  only  with  the  relative  values  of  masses  of  positive  or  of 
negative  electricity. 
2.  The  Law  of  Electrical  Force. 
The  Law  of  Electrical  Force  is  thus  stated  in  '  Electrodynamic 
Measurements'  (Leipzig,  1846,  p.  119: — 
If  e  and  e'  denote  two  electrical  particles,  the  repulsive 
force  exerted  by  the  two  particles  on  each  other  at  the 
distance  r  is  represented  by 
ee' 
7         l_dj*      2rddr\ 
\         cc  dt*  +  cc  dt2  )' 
where  c  is  the  constant  denoted  at  the  place  quoted  by  -. 
But  this  expression  for  the  force  which  the  particles  e  and  e' 
mutually  exert  upon  each  other,  it  is  easy  to  see,  is  dependent 
on  a  magnitude  which  contains  as  a  factor  the  very  force  that  is 
to  be  determined.  This  is  readily  seen  when  the  relative  accelera- 
tion of  the  two  particles,  namely  -^-,  is  broken  np  into  two  parts, 
thus, 
ddr_ddr[      ddr^_ 
dt*  ~  dfi  +   df"' 
B2 
