458  Mr.  S.  H.  Burbury  on  the  H  Theorem  and 
velocities  is  (98).  It  is  therefore  assumed  (b)  that  the 
chance  of  a  molecule  having  velocities  within  assigned  limits 
is,  subject  to  (98),  independent  of  the  velocities  of  all  the 
other  molecules  for  the  time  being.  Assumptions  (a)  and  (h) 
together  amount  to  Condition  A,  or  wi  molecular  chaos." 
Jeans  has  therefore  by  implication  assumed  Condition  A. 
Maxwell's  law  distinctly  asserts  Condition  A.  If  therefore 
you  could  prove  Maxwell's  law  without  expressly  or  by  im- 
plication assuming  Condition  A,  you  would  prove  Condition  A 
to  be  a  physical  fact,  self-existent  I  suppose.  But  Jeans  has 
proved  Maxwell's  law  only  on  the  implied  assumption  of 
Condition  A.  He  has  proved  it,  that  is,  on  precisely  the 
same  assumption  as  all  former  writers  have  done.  He  has 
in  no  way  altered  the  logical  position  of  the  Kinetic  Theory 
of  Gases. 
7.  With  regard  to  the  proof  contained  in  arts.  39-54, 
Jeans  proves,  as  I  said,  that  0  is  maximum  when  a1=a2  •  •  =#»• 
And  this  he  shows  is  equivalent  to  making  v  constant  on 
average.  And  further  that,  the  a's  being  very  great,  0 
becomes  infinitely  less  than  its  maximum  when  v  differs  con- 
siderably from  its  constant  or  mean  value,  so  that  v  may  be 
regarded  as  everywhere  constant.  I  think  that  with  infinitely 
small  molecules  and  no  forces  acting,  this  follows  from  the 
definition  of  v.  Also,  is  not  the  result  that  all  the  «'s  are 
equal  when  6  is  maximum  evident  from  the  mere  inspection 
of  6  ?  And  then  may  we  not  write  as  =  cosv.„  And,  there- 
fore.  V-y  =  1>2  .   .    =  Vn  ? 
8.  The  question  occurred  to  me  whether  the  number  of  pos- 
sible arrangements  of  the  molecules,  which  Jeans  calculates, 
has  any  effect  on  the  state  of  any  physical  system.  Consider, 
for  instance,  a  vertical  column  of  gas  under  the  earth's 
attraction.  The  number  of  ways  in  which  the  molecules  can  be 
assigned  to  equal  elements  of  the  column  is  immensely  greater, 
according  to  Jeans's  calculation  of  0,  when  they  are  distributed 
with  uniform  density  than  when  they  are  distributed  according 
to  any  other  law.  Has  this  fact  any  influence  on  the  actual 
distribution  ?  I  think  none  whatever,  if  the  molecules  are,  as 
Jeans  assumes  (p.  39),  infinitely  small.  I  do  not  think  Jeans 
would  say  that  it  has  any.     In  Jeans's  distribution  the  chance 
of  a  given  molecule  being  in  the  cell  o>,  is  ^ ,  and  is  inde- 
pendent of  the  position  of  the  cell.  We  might  say  that  equal 
cells  have  equal  value  for  the  purposes  of  the  distribution. 
In  the  vertical  column  the  chance  of  a  given  molecule  being 
in  the  elementary  cell  co  is  ^  e~2]i3-\  s  being  the  height  of  the 
