the  Principle  of  the  Conservation  of  Energy.  123 
r  may  increase  again  from  r=?'0  to  r  =  oo  ,  u  at  the  same  time 
increasing  from  w=0  toM=+CA /^.j 
V    r0 
or  r  may  #^  /rs/  decrease  from  r  =  r0  to  r  =  0,  u  at  the  same 
time  decreasing  from  n  =  0  to  «=  —  c,  and  then  afterwards 
r  may  increase  from  r  =  0  to  r  =  r0,  u  at  the  same  time  de- 
creasing from  u  =  +  c  to  w  =  0. 
It  is  easily  seen  that  in  the  first  case  the  motion  is  not  a  revert- 
ing one ;  for,  after  the  distance  r  has  diminished  from  any  given 
value  to  r0,  it  increases  again  without  limit ;  that  is,  it  never 
decreases  again.  In  the  latter  case,  on  the  other  hand,  the  mo- 
tion is  reverting,  for  the  distance  r  alternately  diminishes  from 
r0  to  0  and  increases  again  from  0  to  r0. 
There  seems  indeed  to  be  a  sudden  change  in  the  value  of  the 
velocity  u  from  —  c  to  +c  at  the  moment  when  r  =  0;  but  no 
sudden  change  occurs  in  reality;  for,  when  r  vanishes,  —  c  de- 
notes the  same  velocity  as  +c  does  when  r  is  increasing  again 
from  zero. 
These  two  cases  of  motion  are  moreover  distinguished  from 
each  other  by  the  fact  that  no  transition  takes  place  from  one  to 
the  other;  for,  according  to  the  above  equation,  such  a  transi- 
tion, in  the  case  of  the  interval  pr0  or  r0p  could  only  occur  by  u 
taking  imaginary  values. 
Now  upon  this  separateness  of  the  two  kinds  of  motion  a  di- 
stinction may  be  founded  between  two  states  of  aggregation  of  a 
system  of  two  similar  particles — that  is,  between  a  state  of  aggre- 
gation in  which  the  particles  can  only  move  at  a  distance  from 
each  other,  and  a  state  of  aggregation  in  which  they  can  take  part 
only  in  molecular  movements.  A  transition  from  the  one  state 
of  aggregation  to  the  other  cannot  take  place  so  long  as  both  par- 
ticles move  in  consequence  of  their  reciprocal  action  only. 
It  only  remains  to  be  noted  further,  that  it  has  been  here 
presupposed  that  the  two  particles,  considered  in  space,  possessed 
no  motion  except  in  the  direction  of  r ;  but  in  the  next  section 
the  opposite  case  will  be  considered. 
11.  Motion  of  two  Electrical  Particles  which  move  in  space  with 
different  velocities,  in  directions  at  right  angles  to  the  straight 
line  joining  them. 
Let  «  denote  the  difference  of  the  two  velocities  which  two 
electrical  particles  e  and  e',  at  a  distance  r  from  each  other,  pos- 
sess in  space  in  a  direction  perpendicular  to  the  straight  line  r 
which  joins  them  ;  then  —  denotes  the  part  of  the  relative  acce- 
leration  —  which  depends  upon  a. 
