﻿Rhythmic 
  Precipitation. 
  21 
  

  

  centrations 
  a, 
  and 
  c, 
  and 
  the 
  distances 
  between 
  successive 
  

   bands 
  is 
  of 
  the 
  form 
  

  

  d(D 
  — 
  d) 
  = 
  K.ac 
  where 
  K 
  is 
  a 
  constant. 
  (3) 
  

  

  It 
  seems 
  legitimate 
  to 
  assume 
  that 
  D 
  varies 
  very 
  slowly 
  over 
  

   the 
  region 
  occupied 
  by 
  a 
  few 
  consecutive 
  bands. 
  In 
  these 
  cir- 
  

   cumstances 
  the 
  variation 
  of 
  d 
  with 
  the 
  product 
  ac 
  is 
  exhibited 
  

   graphically 
  in 
  fig. 
  6, 
  the 
  curve 
  being 
  a 
  parabola 
  having 
  a 
  

  

  maximum 
  ordinate 
  at 
  d 
  = 
  D/2, 
  when 
  ac 
  = 
  - 
  ' 
  " 
  . 
  

  

  It 
  will 
  be 
  seen 
  from 
  this 
  curve 
  that 
  as 
  the 
  concentration 
  pro- 
  

   duct 
  a.c 
  decreases, 
  the 
  distance 
  between 
  successive 
  bands 
  will 
  

   diminish 
  or 
  increase 
  according 
  as 
  cl 
  < 
  or 
  1/2D. 
  If 
  the 
  con- 
  

   centration 
  product 
  happens 
  to 
  take 
  the 
  value 
  —-^ 
  — 
  the 
  bands 
  

  

  will 
  be 
  equally 
  spaced 
  ; 
  otherwise 
  they 
  will 
  be 
  spaced 
  at 
  

   diminishing 
  or 
  increasing 
  distances 
  according 
  as 
  the 
  rate 
  of 
  

   variation 
  of 
  a.c 
  with 
  d 
  is 
  positive 
  or 
  negative. 
  

  

  For 
  most 
  cases 
  of 
  outward 
  diffusion 
  of 
  a 
  strong 
  solution 
  

  

  CD 
  

  

  against 
  a 
  weak 
  solution 
  d>l/2D 
  so 
  that 
  the 
  usual 
  result 
  is 
  that 
  

   the 
  bands 
  are 
  formed 
  at 
  successively 
  increasing 
  distances 
  apart. 
  

   An 
  illustration 
  of 
  this 
  is 
  seen 
  in 
  the 
  inner 
  part 
  of 
  fig. 
  1. 
  The 
  

   outer 
  part 
  of 
  the 
  same 
  figure 
  illustrates 
  equal 
  spacing 
  of 
  the 
  

   bands, 
  which 
  is 
  only 
  rarely 
  obtained. 
  An 
  example 
  of 
  the 
  third 
  

   case, 
  where 
  the 
  bands 
  become 
  successively 
  closer, 
  is 
  discussed 
  

   below. 
  (See 
  page 
  24.) 
  

  

  In 
  some 
  of 
  the 
  experiments 
  described 
  above 
  measurements 
  

   of 
  distances 
  of 
  diffusion 
  were 
  made 
  over 
  an 
  extended 
  period, 
  

   the 
  results 
  being 
  plotted 
  in 
  the 
  form 
  of 
  curves, 
  with 
  times 
  as 
  

   abscissae 
  and 
  distances 
  as 
  ordinates. 
  These 
  curves 
  bring 
  out 
  

   clearly 
  the 
  way 
  in 
  which 
  diffusion 
  is 
  prevented 
  by 
  approach 
  of 
  

   the 
  molecular 
  concentrations 
  of 
  the 
  two 
  reacting 
  solutions 
  

   toward 
  the 
  same 
  point. 
  They 
  also 
  show 
  that 
  in 
  those 
  cases 
  

   where 
  the 
  diffusion 
  proceeds 
  rapidly 
  at 
  first 
  there 
  is 
  a 
  remark- 
  

   ably 
  sudden 
  drop 
  in 
  the 
  rate 
  of 
  diffusion, 
  and 
  that 
  this 
  drop 
  

   coincides 
  with 
  an 
  almost 
  uniform 
  distance 
  of 
  diffusion. 
  Some 
  

   of 
  these 
  curves 
  are 
  reproduced 
  in 
  figs. 
  7 
  and 
  12. 
  A 
  compari- 
  

   son 
  with 
  figure 
  12 
  appears 
  to 
  indicate 
  that 
  the 
  flat 
  portions 
  of 
  

   the 
  upper 
  curves 
  in 
  figure 
  7 
  are 
  due 
  to 
  a 
  change 
  in 
  the 
  vis- 
  

   cosity 
  of 
  the 
  gelatine. 
  

  

  A 
  comparison 
  of 
  the 
  curves 
  for 
  silver 
  and 
  lead 
  solutions 
  

   against 
  the 
  same 
  concentrations 
  of 
  chromate 
  solution 
  shows 
  

   that 
  the 
  lead 
  diffuses 
  the 
  more 
  slowly. 
  This 
  is 
  in 
  agreement 
  

   with 
  the 
  higher 
  rate 
  of 
  diffusion 
  of 
  the 
  silver 
  solution 
  in 
  pure 
  

   gelatine. 
  

  

  From 
  this 
  a 
  consideration 
  of 
  the 
  possibility 
  that 
  the 
  speed 
  of 
  

  

  