the  Principle  of  the  Conservation  of  Energy.  121 
When  —  is  positive  because  both  numerator  and  denominator 
are  positive,  all  the  movements  are  confined  to  the  distances  out- 
side the  interval  prQ,  and  are  divisible  into  movements  at  a  dis- 
tance and  molecular  movements  which  are  separated  from  each 
other  by  the  interval  pr0. 
But  if  —  is  positive  because  numerator  and  denominator  are 
r°. 
both  negative,  the  movements  extend  to  all  possible  distances, 
since  the  interval  pr0  then  lies  outside  all  possible  distances. 
When  —  is  negative,  in  which  case  the  interval  pr0  lies  partly 
ro 
outside  and  partly  within  the  possible  distances,  all  the  move- 
ments are  confined  to  the  part  of  the  interval  prQ  lying  within 
possible  distances ;  and  if  p  is  positive  and  r0  negative,  they  are 
molecular  movements. 
From  this  it  follows,  when  p  and  r0  are  positive,  that,  in  the 
first  place,  no  transition  from  movements  at  a  distance  to  molecular 
movements  takes  place ;  secondly,  that  uu  always  remains  less 
than  cc}  if  it  was  smaller  at  first ;  and  thirdly,  that  when  uu  is 
less  than  cc,  r  and  r0  are  (both  at  once)  either  greater  or  less 
than  p. 
If  we  keep  merely  to  experience,  some  of  these  relative  move- 
ments of  the  two  particles  may  be  left  entirely  out  of  account, 
for  it  is  evident  that  infinitely  great  relative  velocities  are  never 
1     dr2 
met  with  in  reality ;  on  the  contrary,  —  -^  is  almost  always  to 
cc    ai 
be  considered  a  very  small  fraction. 
This  limitation,  derived  from  the  nature  of  things,  is  also  tacitly 
assumed  when  V=—  (  —  '  j^—  1)   is  taken  as  the  potential, 
since  this  must  be  =0  for  an  infinitely  great  value  of  r.     For 
dr2  .  ee'  / 1    dr2        \ 
if  -T£  were  infinitely  great,  the  expression  —  (—  •  -^  — 1 )  mignt 
have  a  value  differing  from  nothing  even  for  infinitely  great 
values  of  r. 
dr2 
But  if  the  value  of  -^  is  never  infinitely  great,  there  must  be 
dr2 
a  finite  value  which  -^  never  exceeds.     We  may  assume  cc  as 
such  a  value. 
Presupposing  this  limitation  of  the  relative  velocities,  r0  is 
always  positive;  and  for  every  value  of  r0  there  exists  only  a 
single,  always  continuous  series  of  corresponding  values  of  r  and 
