Prof.  Jeans'*  Dynamical  Theory  of  Gases.  4651 
"  whose  velocities  are  u  v  w  and  u'  vf  w' ,  which  is  evanescent 
"  except  for  small  values  of  r."  This  does  not  satisfy  Con- 
dition A.  Also  the  second  condition  is  evidently  satisfied 
because  Q  is  a  quadratic  function. 
20.  I  suggested  myself  in  'Nature/  February  1895,  in 
aid  of  the  H  Theorem,  that  no  material  system  ever  does 
remain  for  any  considerable  time  in  exactly  continuous 
motion,  free  from  external  disturbances.  Such  disturbances 
are  always  happening,  and  their  effect,  if  they  come  at  hap- 
hazard without  regard  to  the  state  of  the  system  for  the  time 
being,  is  pro  tanto  to  renew  or  to  maintain  the  independence 
of  the  molecular  motions,  i.  e.  Condition  A,  and  so  to  make  H 
dimmish.  I  think  that  is  true.  We  may  assume  that 
if  the  disturbances  are  frequent  enough  and  great  enough, 
—-.    will  be  in  general  negative  or  zero.     But  then  we  must 
remember  that,  as  regards  this  disturbed  system,  it  is  not 
true  that  were  all  the  velocities  at  any  instant  reversed  the 
system  would  retrace  its  course,  because  the  disturbances  are 
not  included  in  the  reversal.  I  think  therefore  that  the  true 
explanation  of  the  paradox  of  art.  1  above  is  as  follows : — 
The  system  either  is  or  is  not  isolated,  that  is  protected 
throughout  the  motion  from  all  external  disturbances.  If  we 
take  the  first  hypothesis,  that  it  is  isolated,  it  is  not  true  that 
the  condition  of  independence  (art.  17)  exists.     Therefore  it  is 
not  true  that  -j  is  necessarily  negative.     But  it  is  true  that 
on  reversal  of  the  velocities  the  system  would  retrace  its 
course.  There  is  a  reversed  motion,  but  there  is  no  H  Theorem. 
If  we  take  the  second  hypothesis,  that  disturbances  are  con- 
dK 
dt 
negative.  But  it  is  not  true  that  on  reversal  of  the  velocities 
the  system  would  retrace  its  course.  There  is  an  H  Theorem, 
but  there  is  no  reversed  motion.  The  reason  why  we  obtain 
for  the  same  system  first  one  and  then  the  other  of  two  incon- 
sistent results,  first  that      .     is    negative,   secondlv  that      , 
at  "  at 
is  positive,  is  because  we  apply  to  the  same  system  first  one 
and  then  the  other  of  two  inconsistent  hypotheses. 
tinually  happening,  it  may  be    true  that   —    is   generally 
