464  Mr.  S.  H.  Burbury  on  the  II  Theorem  and 
nothing  else  whatever.  Now  that  the  velocities  of  a  set  of 
molecules,  being  functions  of  the  same  set  of  initial  variables 
and  of  the  same  time,  should  be  always  independent  of  each 
other,  is,  if  it  is  to  be  taken  as  an  exact  statement,  a  mathe- 
matical impossibility.  There  must  arise  correlation  between 
the  velocities,  at  least  of  neighbouring  molecules,  as  Jeans 
suggests  in  his  art.  15. 
18.  In  my  unorthodox  opinion  therefore,  neither  Maxwell's 
law  nor  the  H  Theorem  are  true  accurately,  if  the  motion  is 
continuous.  As  regards  Maxwell's  law,  it  may  be  for  some 
important  purposes  accurate  enough.  If,  for  instance,  we 
wish  to  calculate  the  theoretical  value  of  the  coefficient  of 
diffusion  between  rare  gases  for  comparison  with  experiment, 
approximate  numerical  results  are  all  we  require,  and  all  we 
can  have..  And  it  may  well  be  that  Maxwell's  law  gives  a 
sufficiently  near  approximation.  This  I  have  never  denied 
But  in  considering  the  question  of  reversibility,  the  method 
of  approximation  is  ineffectual.  For  suppose  two  states  of  a 
gas,  state  A  and  state  B.  In  state  A  the  position  and  velocities 
of  the  molecules  are  denoted  respectively  by  #,  y,  z  and 
u,  v,  io.  In  state  B  they  have  nearly  the  same  values  as  in 
A,  and  the  differences  are  for  some  purposes  negligible. 
Nevertheless  these  differences,  however  small,  may  in  time- 
cause  the  two  systems  to  diverge  widely  from  each  other. 
One  may  be  asymptotic,  H  continually  approaching  its 
minimum,  the  other  may  be  cyclic.  The  asymptotic  character 
cannot  be  established  by  any  approximate  reasoning. 
19.  If  I  am  right  in  saying  that  Maxwell's  law^,  founded  as 
it  is  on  the  assumption  of  Condition  A,  and  asserting  as 
it  does  the  truth  of  Condition  A,  cannot  in  continuous 
motion  be  accurately  true,  nevertheless  the  system  started 
as  I  have  supposed  in  art.  16  above  and  left  to  itself  to  move 
in  continuous  motion,  must  ultimately  settle  down  into 
stationary  motion  of  some  kind,  and  must  then  have  a 
normal  state  of  some  kind.  If  it  be  not  Maxwell's  law,  what 
is  it  ?  I  should  answer  the  question  thus — Firstly,  in  that 
normal  state  Condition  A  must  not  completely  prevail. 
Secondly,  the  state  in  which  the  velocities  of  the  N  molecules 
are  typically  u,  v,  w,  and  the  state  in  which  they  are  typically 
—u,  —v,  —w,  must  in  the  stationary  motion  be  equally 
probable.  Both  conditions  are  satisfied  if  ci  The  chance  of 
"  the  N  molecules  having  velocities  within  assigned  limits  is 
"  Ae-^dui  .  .  .  dwx,      and 
"  Q  =  2w(«2  +  u2  +  w3)+22&(««'  +  w'  +  icw'), 
"  where  h  is  a  function  of  r.  the  distance  between  the  molecules 
