﻿282 
  

  

  G. 
  F. 
  Becker 
  — 
  Computing 
  Diffusion. 
  

  

  any 
  two 
  may 
  be 
  assumed 
  and 
  the 
  corresponding 
  value 
  of 
  the 
  

   third 
  found. 
  The 
  practical 
  awkwardness 
  of 
  the 
  results 
  is 
  a 
  

   consequence 
  of 
  the 
  fact 
  that 
  the 
  tabulations 
  are 
  made 
  with 
  a 
  

   for 
  an 
  argument. 
  Hence, 
  the 
  least 
  laborious 
  method 
  is 
  to 
  

   assume 
  q 
  at 
  some 
  tabulated 
  even 
  value, 
  find 
  x 
  or 
  t 
  from 
  the 
  

  

  o 
  v/c 
  1 
  

  

  Diffusion 
  Curve. 
  

  

  first 
  of 
  the 
  above 
  equations 
  and 
  v 
  from 
  the 
  second. 
  Thus 
  

   assuming 
  t 
  — 
  86400 
  seconds 
  (one 
  day) 
  and 
  k 
  = 
  -00001, 
  which 
  

   is 
  about 
  the 
  value 
  for 
  common 
  salt, 
  and 
  taking 
  q 
  — 
  *4, 
  one 
  finds 
  

   x 
  = 
  0*7436 
  and 
  by 
  the 
  help 
  of 
  the 
  tables 
  of 
  the 
  integral, 
  v 
  = 
  

   0*5716 
  c. 
  A 
  series 
  of 
  corresponding 
  values 
  thus 
  obtained 
  for 
  

   v 
  and 
  x 
  is 
  not 
  easily 
  grasped 
  numerically. 
  On 
  the 
  other 
  hand, 
  

   these 
  values 
  are 
  readily 
  plotted. 
  It 
  is 
  apparently 
  for 
  this 
  reason 
  

   that 
  Lord 
  Kelvin 
  has 
  on 
  various 
  occasions 
  represented 
  diffusion 
  

   by 
  diagrams. 
  Messrs. 
  King 
  and 
  Barus 
  used 
  the 
  same 
  device, 
  

   and 
  the 
  system 
  of 
  curves 
  by 
  the 
  aid 
  of 
  which 
  Lord 
  Kelvin 
  

   proposed 
  the 
  computation 
  of 
  diffusions* 
  is 
  mainly 
  useful 
  for 
  

   the 
  same 
  reason. 
  

  

  The 
  abscissa 
  of 
  the 
  probability 
  curve 
  is 
  not 
  the 
  natural 
  inde- 
  

   pendent 
  variable 
  for 
  calculating 
  diffusions. 
  Greatly 
  preferable 
  

   is 
  the 
  quality, 
  v/c. 
  It 
  is 
  entirely 
  possible 
  to 
  employ 
  it 
  in 
  this 
  

   way 
  even 
  with 
  the 
  tables 
  hitherto 
  published. 
  The 
  tables 
  of 
  

   the 
  integral 
  can 
  be 
  entered 
  with 
  rounded 
  values 
  of 
  v, 
  and 
  corre- 
  

   sponding 
  values 
  of 
  q, 
  containing 
  as 
  many 
  significant 
  places 
  as 
  

   desirable, 
  can 
  then 
  be 
  interpolated. 
  From 
  such 
  values 
  of 
  q 
  one 
  

   can 
  obtain 
  x 
  and 
  the 
  result 
  is 
  a 
  table 
  showing 
  the 
  distances 
  for 
  

   rational 
  values 
  of 
  the 
  quality. 
  This, 
  however, 
  is 
  a 
  tedious 
  

   process, 
  since, 
  for 
  a 
  satisfactory 
  degree 
  of 
  accuracy, 
  the 
  interpo- 
  

   lation 
  must 
  be 
  made 
  by 
  second 
  differences. 
  

  

  What 
  is 
  needed 
  to 
  facilitate 
  computation 
  of 
  diffusions 
  in 
  a 
  

   neat 
  form, 
  such 
  as 
  will 
  not 
  require 
  diagrams 
  to 
  render 
  the 
  

   relations 
  clear, 
  is 
  a 
  table 
  in 
  which 
  q, 
  or 
  better 
  2^, 
  is 
  expressed 
  

  

  * 
  Rep. 
  Brit. 
  Assoc, 
  1888, 
  p. 
  571. 
  

  

  