﻿166 
  Mr. 
  W. 
  Sutherland 
  on 
  Io 
  nization, 
  

  

  that 
  it 
  exhibits 
  great 
  viscosity 
  and 
  quasi- 
  solidity 
  as 
  regards 
  

   bulk 
  movements, 
  while 
  to 
  ions 
  moving 
  through 
  its 
  meshes 
  

   quite 
  freely 
  the 
  confined 
  water 
  exhibits 
  almost 
  only 
  the 
  viscosity 
  

   of 
  ordinary 
  water. 
  Many 
  experiments 
  could 
  be 
  mentioned 
  to 
  

   illustrate 
  how 
  the 
  resistance 
  of 
  electrolytes 
  is 
  proportional 
  

   to 
  viscosity, 
  other 
  things 
  being 
  equal, 
  but 
  a 
  reference 
  to 
  those 
  

   of 
  Manoulier 
  (Compt. 
  Rend. 
  cxxx. 
  p. 
  773) 
  with 
  mixtures 
  of 
  

   glycerine 
  and 
  water 
  and 
  CuS0 
  4 
  will 
  suffice, 
  as 
  the 
  importance 
  

   of 
  viscosity 
  appears 
  at 
  once 
  in 
  the 
  following 
  elementary 
  

   theoretical 
  treatment. 
  

  

  Let 
  us 
  regard 
  an 
  ion 
  as 
  a 
  sphere 
  of 
  radius 
  % 
  moving 
  

   with 
  ionic 
  velocity 
  V 
  through 
  a 
  solution 
  of 
  viscosity 
  77, 
  then 
  

   for 
  the 
  frictional 
  resistance 
  B, 
  experienced 
  by 
  the 
  sphere, 
  if 
  

   there 
  is 
  no 
  slipping 
  at 
  its 
  surface, 
  w 
  r 
  e 
  have 
  by 
  Stokes's 
  

   formula 
  

  

  n=67rY 
  V 
  a 
  1 
  (5) 
  

  

  Now 
  if 
  the 
  fall 
  of 
  electric 
  potential 
  is 
  at 
  the 
  rate 
  dl&jdx 
  

   in 
  the 
  direction 
  of 
  motion 
  of 
  the 
  % 
  ion 
  when 
  a 
  current 
  is 
  

   traversing 
  the 
  solution, 
  then 
  the 
  force 
  on 
  each 
  such 
  ion 
  is 
  

   edJZ/dx 
  where 
  e 
  is 
  its 
  charge. 
  For 
  steady 
  ionic 
  velocity 
  V 
  

   the 
  condition 
  is 
  

  

  e^~ 
  = 
  67rYr)a 
  1 
  (6) 
  

  

  For 
  the 
  t> 
  ions 
  with 
  velocity 
  U 
  we 
  have 
  likewise 
  

  

  dE 
  z 
  tt 
  

   — 
  e-r- 
  =07rU??a 
  2 
  . 
  

  

  ax 
  

  

  In 
  a 
  c. 
  c. 
  of 
  solution 
  10~ 
  3 
  ?m 
  molecules 
  are 
  split 
  up 
  into 
  as 
  

   many 
  ions 
  of 
  each 
  sort, 
  and 
  the 
  current 
  C 
  per 
  cm. 
  2 
  is 
  

  

  C 
  = 
  10- 
  3 
  mzV(V-U) 
  

  

  1 
  /l 
  1 
  WE 
  

   67rrj 
  \a 
  L 
  a 
  2 
  Jdx 
  ' 
  

  

  (?) 
  

  

  therefore 
  by 
  Ohm's 
  law 
  and 
  the 
  definition 
  of 
  specific 
  con- 
  

   ductivity 
  the 
  latter 
  is 
  

  

  l0-3 
  m 
  ie*. 
  — 
  .(- 
  + 
  -), 
  

  

  b7rrj 
  \«i 
  a 
  2 
  / 
  

  

  and 
  \ 
  the 
  specific 
  molecular 
  conductivity 
  is 
  given 
  by 
  

  

  * 
  67r?7 
  '\a,i 
  a 
  2 
  /' 
  

  

  If 
  7] 
  is 
  taken 
  to 
  be 
  constant, 
  as 
  is 
  usually 
  done 
  with 
  dilute 
  

   solutions, 
  V 
  and 
  U 
  are 
  both 
  constant 
  for 
  all 
  dilutions, 
  if 
  

  

  