﻿358 
  Dr. 
  S. 
  R. 
  Milner 
  on 
  the 
  Effect 
  of 
  

  

  positions 
  P 
  1# 
  ..P 
  m 
  , 
  the 
  mutual 
  energy 
  is 
  ^ 
  = 
  ^1 
  + 
  ^/, 
  and 
  the 
  

   number 
  of 
  views 
  in 
  which 
  it 
  is 
  found 
  is 
  

  

  v 
  = 
  Kne"^' 
  /kT 
  e-^ 
  kT 
  dv 
  1 
  ..dv 
  m 
  (9) 
  

  

  In 
  P' 
  let 
  A 
  2 
  ...A 
  OT 
  be 
  in 
  the 
  same 
  positions 
  as 
  before, 
  but 
  

   let 
  A 
  x 
  be 
  in 
  a 
  place 
  of 
  zero 
  mutual 
  energy. 
  The 
  mutual 
  

   energy 
  of 
  the 
  group 
  is 
  now 
  $/ 
  and 
  the 
  number 
  of 
  views 
  in 
  

   which 
  this 
  configuration 
  is 
  found 
  is 
  

  

  y' 
  = 
  Kne^' 
  kT 
  dv 
  l 
  ...dv 
  m 
  . 
  

  

  In 
  the 
  series 
  of 
  n 
  views 
  taken 
  one 
  after 
  the 
  other 
  at 
  

   arbitrary 
  times 
  the 
  configuration 
  of 
  the 
  system 
  is 
  changed 
  

   between 
  one 
  view 
  and 
  the 
  next 
  by 
  complex 
  thermal 
  motions. 
  

   Omitting 
  all 
  the 
  other 
  views, 
  let 
  us 
  confine 
  our 
  attention 
  to 
  

   the 
  if 
  views 
  of 
  the 
  configuration 
  P 
  and 
  the 
  V 
  views 
  of 
  P'. 
  

   These 
  are 
  observed 
  at 
  certain 
  successive 
  times 
  and 
  are 
  all 
  

   the 
  views 
  of 
  these 
  configurations 
  which 
  are 
  observed 
  in 
  the 
  

   series. 
  In 
  the 
  intervals 
  between 
  them 
  the 
  configurations 
  

   change 
  over 
  one 
  into 
  the 
  other 
  as 
  the 
  result 
  of 
  thermal 
  

   motions, 
  but 
  not 
  indiscriminately. 
  It 
  is 
  only 
  in 
  a 
  fraction 
  

   v 
  ' 
  jv 
  of 
  the 
  v 
  views 
  of 
  the 
  P 
  configuration 
  that 
  a 
  change 
  by 
  

   thermal 
  motions 
  into 
  the 
  P' 
  configuration 
  will 
  occur. 
  On 
  a 
  

   random 
  distribution 
  the 
  fraction 
  would 
  be 
  unity. 
  The 
  change 
  

   in 
  the 
  configuration 
  considered 
  consists 
  simply 
  in 
  the 
  trans- 
  

   ference 
  by 
  thermal 
  motion 
  of 
  the 
  ion 
  A 
  2 
  from 
  a 
  position 
  of 
  

   mutual 
  energy 
  </>j 
  to 
  one 
  of 
  zero 
  mutual 
  energy. 
  We 
  see 
  

   that, 
  given 
  the 
  ion 
  in 
  this 
  position, 
  the 
  probability 
  that 
  such 
  

   a 
  transference 
  will 
  take 
  place 
  is 
  not 
  the 
  same 
  as 
  it 
  would 
  be 
  

   on 
  a 
  random 
  distribution 
  (i. 
  e. 
  in 
  the 
  absence 
  of 
  interionic 
  

   forces), 
  but 
  v'\v 
  or 
  ^ 
  l/AT 
  times 
  as 
  great 
  *. 
  

  

  On 
  a 
  random 
  distribution 
  the 
  whole 
  of 
  the 
  scalar 
  property 
  

   \mv 
  2 
  associated 
  with 
  each 
  ion 
  is 
  capable 
  of 
  being 
  transferred 
  

   from 
  one 
  position 
  to 
  another. 
  This 
  gives 
  a 
  random, 
  or 
  on 
  the 
  

   large 
  scale 
  a 
  uniform, 
  distribution 
  of 
  the 
  pressure 
  throughout 
  

   the 
  volume. 
  It 
  follows 
  from 
  the 
  preceding 
  proposition 
  that, 
  

  

  * 
  The 
  proposition 
  is 
  so 
  far 
  only 
  proved 
  for 
  the 
  case 
  in 
  which 
  the 
  

   m 
  — 
  1 
  ions 
  other 
  than 
  Ai 
  remain 
  fixed 
  during 
  the 
  transference 
  of 
  A 
  x 
  . 
  

   If 
  these 
  also 
  undergo 
  displacements 
  we 
  shall 
  have 
  a 
  simultaneous 
  

   alteration 
  of 
  <£ 
  x 
  and 
  $ 
  t 
  '. 
  In 
  so 
  far 
  as 
  these 
  displacements 
  affect 
  <j> 
  x 
  only, 
  

   it 
  is 
  immaterial 
  to 
  the 
  argument 
  whether 
  A 
  x 
  reaches 
  a 
  state 
  of 
  zero 
  

   mutual 
  energy 
  by 
  its 
  own 
  displacement 
  or 
  hy 
  suitable 
  ones 
  of 
  the 
  other 
  

   ions, 
  the 
  expression 
  for 
  v'/v 
  being 
  the 
  same 
  in 
  either 
  case. 
  If, 
  on 
  the 
  

   other 
  hand, 
  they 
  alter 
  <p 
  L 
  ' 
  f 
  the 
  expression 
  (9) 
  shows 
  that 
  this 
  is 
  an 
  event 
  

   independent 
  of 
  the 
  change 
  in 
  A 
  x 
  's 
  mutual 
  energy, 
  the 
  probability 
  of 
  the 
  

   simultaneous 
  occurrence 
  of 
  the 
  two 
  events 
  being 
  the 
  product 
  of 
  the 
  two 
  

   probabilities. 
  The 
  truth 
  of 
  the 
  proposition 
  is 
  thus 
  unaffected 
  by 
  all 
  

   other 
  ionic 
  changes 
  which 
  may 
  proceed 
  simultaneously 
  with 
  the 
  trans- 
  

   ference 
  of 
  the 
  ion 
  A 
  x 
  to 
  a 
  position 
  of 
  zero 
  energy. 
  

  

  