﻿26 
  Becker 
  — 
  Some 
  Queries 
  on 
  Rock 
  Differentiation. 
  

  

  stated 
  area 
  is 
  proportional 
  to 
  the 
  difference 
  between 
  the 
  con- 
  

   centrations 
  of 
  two 
  areas 
  infinitely 
  near 
  one 
  another. 
  This 
  is, 
  

   mutatis 
  mutandis, 
  the 
  same 
  law 
  which 
  underlies 
  Fourier's 
  

   treatment 
  of 
  heat 
  conduction.* 
  Very 
  extended 
  researches 
  by 
  

   many 
  physicists 
  have 
  confirmed 
  Fick's 
  law, 
  excepting 
  for 
  very 
  

   strong 
  solutions, 
  and 
  therefore 
  also 
  the 
  applicability 
  of 
  Fourier's 
  

   mathematical 
  developments 
  concerning 
  conduction 
  to 
  the 
  

   elucidation 
  of 
  diffusion. 
  It 
  can 
  be 
  shown 
  that 
  Fick's 
  hypothesis 
  

   would 
  be 
  strictly 
  applicable 
  to 
  solutions 
  of 
  any 
  concentration 
  

   if 
  Pfeffer's 
  law, 
  that 
  osmotic 
  pressure 
  and 
  concentration 
  are 
  

   proportional, 
  were 
  exact. 
  But 
  this 
  law 
  corresponds 
  to 
  Boyle's 
  

   law 
  that 
  gaseous 
  pressure 
  and 
  volume 
  are 
  inversely 
  propor- 
  

   tional, 
  and 
  this, 
  as 
  every 
  one 
  knows, 
  is 
  exact 
  only 
  when 
  the 
  

   number 
  of 
  molecules 
  per 
  unit 
  volume 
  is 
  not 
  too 
  great. 
  At 
  

   least 
  two 
  influences 
  tend 
  to 
  render 
  Pfeffer's 
  law 
  and 
  Fick's 
  

   hypothesis 
  inexact 
  for 
  high 
  concentration. 
  There 
  is 
  a 
  tendency 
  

   to 
  change 
  of 
  molecular 
  weight 
  with 
  increasing 
  concentration, 
  

   a 
  species 
  of 
  polymerization, 
  and 
  this 
  would 
  be 
  attended 
  by 
  

   decreased 
  diffusibility. 
  When 
  there 
  is 
  no 
  such 
  aggregation 
  

   there 
  is 
  an 
  increase 
  of 
  diffusibility, 
  due, 
  it 
  is 
  thought, 
  to 
  the 
  

   attraction 
  between 
  the 
  solvent 
  and 
  the 
  dissolved 
  substance. 
  

  

  While 
  it 
  is 
  proper 
  to 
  point 
  out 
  the 
  deviation 
  of 
  very 
  strong 
  

   solutions 
  undergoing 
  diffusion 
  from 
  the 
  law 
  of 
  Fick, 
  this 
  devia- 
  

   tion 
  is 
  of 
  importance 
  only 
  near 
  the 
  contact 
  from 
  which 
  diffu- 
  

   sion 
  takes 
  place, 
  and 
  not 
  always 
  then. 
  For 
  if 
  a 
  solvent 
  

   dissolves 
  a 
  salt 
  only 
  to 
  a 
  limited 
  extent, 
  even 
  a 
  saturated 
  solu- 
  

   tion 
  may 
  be 
  a 
  weak 
  one, 
  and 
  dissolved 
  molecules 
  will 
  not 
  be 
  so 
  

   crowded 
  as 
  to 
  show 
  irregular 
  behavior. 
  Thus 
  in 
  the 
  case 
  of 
  

   magmas 
  undergoing 
  molecular 
  flow, 
  Fick's 
  law 
  will 
  be 
  valid 
  at 
  

   least 
  to 
  within 
  a 
  short 
  distance 
  from 
  contacts 
  and 
  may 
  hold 
  

   absolutely 
  up 
  to 
  the 
  contact. 
  In 
  the 
  differentiation 
  of 
  a 
  homo- 
  

   geneous 
  magma 
  into 
  consanguineous 
  portions 
  it 
  is 
  hardly 
  sup- 
  

   posable 
  that 
  the 
  molecules 
  undergoing 
  transfer 
  are 
  densely 
  

   crowded. 
  Consanguineous 
  rocks 
  do 
  not 
  differ 
  very 
  greatly 
  in 
  

   composition, 
  so 
  that 
  no 
  extensive 
  transfer 
  of 
  material 
  is 
  called 
  

   for. 
  Furthermore, 
  magmas 
  must 
  be 
  regarded 
  as 
  solutions 
  of 
  a 
  

   series 
  of 
  very 
  similar 
  substances, 
  and 
  it 
  is 
  known 
  that 
  in 
  such 
  

   cases 
  the 
  solubility 
  of 
  each 
  is 
  diminished 
  by 
  the 
  presence 
  of 
  

   the 
  others. 
  This 
  w 
  T 
  as 
  first 
  pointed 
  out 
  by 
  Mr. 
  Kernst 
  and 
  has 
  

   been 
  confirmed 
  on 
  experimental 
  and 
  theoretical 
  grounds 
  by 
  Dr. 
  

  

  * 
  If 
  v 
  is 
  the 
  quantity 
  of 
  substance 
  in 
  solution 
  per 
  unit 
  volume 
  in 
  Fick's 
  case 
  (or 
  

   the 
  temperature 
  in 
  Fourier's), 
  if 
  x 
  is 
  the 
  distance 
  measured 
  in 
  the 
  single 
  direstion 
  

   in 
  which 
  diffusion 
  is 
  supposed 
  to 
  take 
  place, 
  and 
  if 
  k 
  is 
  the 
  diffusivity 
  regarded 
  

   as 
  constant, 
  then 
  in 
  either 
  problem 
  

  

  dv 
  <Pv 
  

  

  dt 
  = 
  K 
  dz*' 
  

  

  