122  Prof.  W.  Weber  on  Electricity  in  relation  to 
—  •  and 
dt2  y  when  p  is  positive  and  r0  is  >p, 
dr2 
the  corresponding  values  of?*  and  -js  extend  from  r=*r0  to  r=oo 
dr  dr         o 
and  from  -^  =  0  to  -=-g  =  — .    The  movements  are  in  this  case 
movements  at  a  distance. 
If  p  is  positive  and  r0<p,  or  if  p  is  negative, 
the  corresponding  values  extend  from  r=r0  to  r=0,  and  from 
-—  =0  to  -tz  =cc.     In  the  first  case,  when  p  is  positive  and 
r0<p,  and  likewise  in  the  second  case,  when  />  is  negative  and 
r0<p,  the  movements  are  molecular  movements;  but  ifj  in  the 
second  case,  r0  is  >  /o,  the  movements  are  partly  movements  at  a 
distance  and  partly  molecular  movements. 
Hence,  with  the  above  limitation  of  the  movements,  we  obtain 
for  two  particles  e,  e\  moving  solely  in  consequence  of  their  re- 
ciprocal action,  if  there  is  no  motion  of  rotation  of  the  particles 
about  each  other  in  space,  the  following  equation  of  motion, 
namely, 
uu  _  r— rQ     p 
cc        r  —p     r0 
dr 
in  which  u  is  put  =  -j.  and  where  p  has  a  value  that  is  given  by 
the  particles  e,  e\  their  masses  e,  e',  and  the  constant  C,  and  r0 
denotes  a  constant  to  be  determined,  according  to  this  very 
equation,  by  the  initial  value  of  r  (which  must  be  positive  and 
not  equal  to  p,  but  otherwise  may  be  any  thing  whatever)  and 
the  initial  value  of  uu  (which  must  be  positive  and  less  than  cc, 
but  otherwise  may  be  any  thing  whatever). 
10.   Two  states  of  aggregation  of  a  system  of  two  particles  of  the 
same  kind. 
For  two  like  particles  the  value  of  p  is  positive.  And  since, 
moreover,  for  every  value  of  r  the  relative  velocity  u  may  have 
two  equal  but  opposite  values,  the  value  of  r  may,  in  accordance 
with  the  above  equation  —  = •  —j 
cc       r—p     r0 
either  at  first  decrease  from  r=oo  to  r=r0,  u  at  the  same  time 
increasing  from  u—  —c\/  -  to  w  =  0,  and  afterwards 
