﻿G. 
  F. 
  Becker 
  — 
  Computing 
  Diffusion. 
  283 
  

  

  in 
  terms 
  of 
  v/c. 
  Such 
  a 
  table 
  is 
  given 
  below, 
  but 
  only 
  in 
  

   skeleton 
  for 
  intervals 
  of 
  v/c 
  of 
  '05. 
  It 
  will, 
  I 
  think, 
  suffice 
  

   for 
  the 
  needs 
  of 
  geologists, 
  and 
  it 
  is 
  hardly 
  worth 
  while 
  to 
  

   extend 
  it 
  to 
  single 
  hundredths 
  unless 
  some 
  desire 
  for 
  such 
  an 
  

   extension 
  should 
  be 
  manifested.* 
  Knowing 
  2^ 
  for 
  a 
  stated 
  

   value 
  of 
  v/c 
  the 
  value 
  of 
  x 
  in 
  centimeters 
  follows 
  easily 
  from 
  

   the 
  equation, 
  

  

  x 
  — 
  2qVxt 
  . 
  

  

  To 
  find 
  the 
  distance 
  at 
  which 
  any 
  chosen 
  quality 
  exists 
  in 
  

   linear 
  diffusion 
  after 
  the 
  lapse 
  of 
  t 
  seconds, 
  it 
  is 
  now 
  only 
  nec- 
  

   essary 
  to 
  add 
  half 
  the 
  logarithm 
  of 
  /ct 
  to 
  log. 
  %q 
  and 
  take 
  the 
  

   number 
  corresponding 
  to 
  the 
  sum 
  from 
  a 
  table 
  of 
  common 
  

   logarithms. 
  This 
  is 
  a 
  labor 
  from 
  which 
  no 
  geologist 
  interested 
  

   in 
  diffusion 
  can 
  shrink. 
  

  

  The 
  values 
  of 
  %q 
  are 
  given 
  in 
  part 
  because 
  they 
  are 
  the 
  dis- 
  

   tances 
  in 
  centimeters 
  after 
  the 
  lapse 
  of 
  one 
  particular 
  time, 
  

   that, 
  namely, 
  which 
  is 
  the 
  reciprocal 
  of 
  the 
  diffusivity. 
  Thus 
  

   in 
  the 
  case 
  of 
  salt 
  with 
  a 
  diffusivity 
  of 
  *00001, 
  after 
  a 
  lapse 
  of 
  

   100,000 
  seconds, 
  or 
  some 
  28 
  hours, 
  /ct 
  — 
  1 
  and 
  2q 
  represents 
  

   the 
  distances 
  answering 
  to 
  v/c. 
  

  

  If 
  one 
  is 
  not 
  anxious 
  to 
  preserve 
  the 
  severe 
  simplicity 
  of 
  the 
  

   C. 
  G. 
  S. 
  system, 
  the 
  day 
  or 
  the 
  year 
  is 
  a 
  more 
  convenient 
  time 
  

   unit 
  than 
  the 
  second 
  for 
  computing 
  diffusions 
  of 
  liquids 
  as 
  well 
  

   as 
  of 
  heat 
  in 
  large 
  masses 
  of 
  matter 
  such 
  as 
  the 
  earth. 
  I 
  have 
  

   therefore 
  tabulated 
  $ 
  as 
  defined 
  by 
  the 
  expression 
  

  

  x 
  = 
  2^^/86400 
  • 
  a/kA 
  = 
  Sa/kA 
  , 
  

  

  where 
  A 
  is 
  the 
  time 
  expressed 
  in 
  days 
  ; 
  and 
  also 
  7 
  in 
  

  

  £C 
  = 
  8\/365-2-l22 
  V*r 
  = 
  y 
  V 
  kT 
  

  

  where 
  T 
  is 
  the 
  time 
  expressed 
  in 
  years. 
  To 
  make 
  the 
  logar- 
  

   ithms 
  of 
  2q 
  useful 
  in 
  this 
  connection 
  it 
  may 
  be 
  noted 
  that 
  

   log 
  S 
  = 
  log 
  2^ 
  + 
  2-46826 
  ; 
  log 
  y 
  = 
  log 
  2q 
  + 
  3*74955. 
  

  

  In 
  German 
  papers 
  it 
  is 
  usual 
  to 
  state 
  the 
  diffusivities 
  of 
  liquids 
  

   in 
  terms 
  of 
  days, 
  so 
  that 
  if 
  \ 
  is 
  the 
  diffusivity 
  thus 
  stated 
  

   X 
  = 
  86400 
  k 
  and 
  

  

  x 
  = 
  2q 
  VAA 
  , 
  

   Of 
  course 
  the 
  tabulated 
  values 
  of 
  S 
  answer 
  to 
  a 
  period 
  for 
  

  

  *The 
  values 
  of 
  q 
  were 
  computed 
  from 
  the 
  seven 
  -place 
  table 
  of 
  the 
  integral 
  

   given 
  by 
  Lord 
  Kelvin, 
  Phys 
  and 
  Math. 
  Papers, 
  vol. 
  iii, 
  1»90, 
  p. 
  434. 
  The 
  inter- 
  

   polations 
  were 
  made 
  by 
  a 
  known 
  formula 
  of 
  the 
  same 
  order 
  of 
  accuracy 
  as 
  the 
  

   formula 
  for 
  second 
  differences, 
  and 
  the 
  results 
  were 
  tested 
  by 
  substitution 
  in 
  the 
  

   formula 
  for 
  second 
  differences. 
  Seven-place 
  logarithms 
  were 
  used. 
  The 
  abbrevia- 
  

   tion 
  to 
  five 
  places 
  introduces 
  an 
  apparent 
  inaccuracy, 
  inasmuch 
  as 
  the 
  log 
  2q, 
  as 
  tabu- 
  

   lated, 
  sometimes 
  varies 
  in 
  the 
  last 
  place 
  from 
  the 
  five-place 
  log. 
  of 
  the 
  tabulated 
  

   value 
  of 
  2q. 
  The 
  tabulated 
  logarithms 
  are, 
  however, 
  the 
  nearest 
  in 
  five 
  places 
  to 
  

   the 
  values 
  of 
  1q 
  expressed 
  in 
  seven 
  places. 
  

  

  