﻿348 
  Mr. 
  W. 
  Sutlierland 
  on 
  

  

  or 
  electrized 
  sphere, 
  similar 
  to 
  a 
  uniformly 
  magnetized 
  

   sphere, 
  and 
  its 
  electric 
  axis 
  tends 
  to 
  set 
  itself 
  very 
  readily 
  

   along 
  the 
  lines 
  of 
  electric 
  force. 
  In 
  the 
  absence 
  of 
  external 
  

   electric 
  force 
  the 
  axes 
  of 
  neighbours 
  so 
  adjust 
  their 
  mutual 
  

   directions 
  as 
  to 
  produce 
  cohesion. 
  But 
  when 
  the 
  powerful 
  

   central 
  electric 
  force 
  of 
  an 
  electron 
  acts 
  upon 
  neighbour 
  

   molecules, 
  it 
  forces 
  their 
  electric 
  axes 
  all 
  to 
  pass 
  nearly 
  

   through 
  itself. 
  Those 
  molecules 
  next 
  to 
  the 
  nearest 
  neigh- 
  

   bours 
  have 
  their 
  axes 
  caused 
  to 
  converge 
  towards 
  the 
  electron, 
  

   but 
  not 
  so 
  accurately, 
  and 
  so 
  on. 
  Thus 
  the 
  cohesive 
  forces 
  

   of 
  the 
  molecules 
  are 
  deranged, 
  and 
  the 
  surrounding 
  molecules 
  

   are 
  attracted 
  towards 
  the 
  electron. 
  We 
  shall 
  consider 
  the 
  

   law 
  of 
  this 
  attraction 
  soon^ 
  but 
  just 
  now 
  we 
  must 
  recognise 
  

   that 
  near 
  the 
  electron 
  the 
  gas 
  will 
  be 
  compressed 
  by 
  this 
  

   attraction 
  to 
  a 
  greater 
  density 
  than 
  the 
  average. 
  The 
  ten- 
  

   dency 
  of 
  this 
  denser 
  gas 
  to 
  diffuse 
  outwards 
  from 
  the 
  central 
  

   electron 
  is 
  just 
  equilibrated 
  by 
  the 
  inward 
  electric 
  attraction. 
  

   Let 
  r 
  be 
  the 
  distance 
  between 
  two 
  neighbour 
  electrons, 
  then 
  

   we 
  may 
  take 
  the 
  average 
  value 
  of 
  the 
  force 
  of 
  diffusion 
  per 
  

   cm.^ 
  of 
  section 
  to 
  vary 
  as 
  Ijr. 
  Hence, 
  when 
  two 
  neighbour 
  

   electrons 
  have 
  r 
  between 
  them 
  changed 
  to 
  r-{-dr 
  by 
  electric 
  

   force, 
  the 
  unequilibrated 
  force 
  of 
  diffusion 
  called 
  into 
  action 
  

   will 
  be 
  proportional 
  to 
  dr/r^. 
  But 
  dr/r 
  is 
  the 
  strain 
  to 
  which 
  

   the 
  associated 
  stress 
  F^ 
  is 
  proportional^ 
  so 
  the 
  force 
  restoring 
  

   uniformity 
  is 
  proportional 
  to 
  F7^ 
  ; 
  but 
  in 
  Maxwell's 
  theory 
  

   of 
  transition 
  from 
  rigidity 
  to 
  viscosity 
  this 
  is 
  proportional 
  to 
  

   r7T, 
  therefore 
  in 
  a 
  gas 
  T 
  is 
  proportional 
  to 
  r. 
  It 
  must 
  also 
  

   be 
  proportional 
  to 
  the 
  resistance 
  offered 
  by 
  the 
  gas 
  to 
  the 
  

   motion 
  of 
  the 
  whole 
  ion 
  with 
  unit 
  velocity, 
  which 
  we 
  have 
  

   denoted 
  by 
  F. 
  Thus 
  we 
  have 
  T 
  cc 
  F^~^/^ 
  and 
  therefore 
  ^, 
  the 
  

   viscosity 
  NT 
  derived 
  from 
  N, 
  varies 
  as 
  Yqe^l'K. 
  For 
  a 
  gas 
  

   we 
  may 
  put 
  K 
  = 
  l. 
  

  

  We 
  have 
  now 
  to 
  obtain 
  an 
  expression 
  for 
  6. 
  The 
  electric 
  

   polarization 
  consists 
  in 
  the 
  directing 
  of 
  the 
  axes 
  of 
  electriza- 
  

   tion 
  of 
  the 
  molecules 
  towards 
  the 
  nearest 
  ion. 
  Let 
  H 
  be 
  the 
  

   distance 
  from 
  an 
  ion 
  to 
  the 
  six 
  nearest 
  molecules. 
  Though 
  

   this 
  is 
  less 
  than 
  the 
  average 
  distance 
  between 
  two 
  molecules 
  

   because 
  of 
  condensation 
  due 
  to 
  attractive 
  forces 
  round 
  the 
  

   ion, 
  it 
  is 
  proportional 
  to 
  that 
  distance. 
  The 
  mutual 
  potential 
  

   energy 
  of 
  an 
  ion 
  and 
  a 
  neighbour 
  molecule 
  is 
  (^(R) 
  ^-^/^(il). 
  

   The 
  rigidity 
  N 
  of 
  the 
  system 
  ion 
  and 
  molecules 
  is 
  equal 
  to 
  

   the 
  potential 
  energv 
  per 
  unit 
  volume 
  and 
  is 
  therefore 
  pro- 
  

   portional 
  to 
  {(/>(R)+'^(Il)}/R^ 
  

  

  We 
  have 
  now 
  to 
  find 
  the 
  time 
  of 
  relaxation 
  T. 
  The 
  force 
  

   between 
  ion 
  and 
  molecule 
  is 
  

  

  ^{</)(R) 
  + 
  t(R)}/^R. 
  

  

  