﻿864 
  

  

  Mr. 
  B. 
  W. 
  Clack 
  on 
  the 
  

  

  -ement 
  of 
  the 
  liquid 
  along 
  the 
  tube, 
  

  

  Fia. 
  1. 
  

  

  pi 
  

  

  the 
  effect 
  of 
  the 
  mov 
  

  

  mentioned 
  in 
  the 
  next 
  section, 
  on 
  the 
  quantity 
  diffused. 
  

   Although 
  this 
  omission 
  would 
  produce 
  less 
  effect 
  in 
  his 
  

   method 
  than 
  in 
  that 
  about 
  to 
  be 
  described, 
  it 
  would 
  never- 
  

   theless 
  cause 
  a 
  measurable 
  difference 
  in 
  the 
  calculated 
  value 
  

   of 
  the 
  coefficient 
  of 
  diffusion. 
  

  

  2. 
  Theory. 
  

  

  In 
  the 
  diagram 
  (fig. 
  1) 
  let 
  A 
  represent 
  a 
  spherical 
  vessel, 
  

   to 
  the 
  upper 
  side 
  of 
  which 
  is 
  fitted 
  a 
  vertical 
  tube 
  D 
  of 
  unit 
  

   cross-section. 
  

  

  Suppose 
  the 
  bulb 
  A 
  and 
  the 
  tube 
  

   D 
  to 
  be 
  initially 
  filled 
  with 
  a 
  salt 
  

   solution 
  of 
  uniform 
  density, 
  and 
  to 
  

   be 
  suspended 
  in 
  a 
  vessel 
  containing 
  

   pure 
  water. 
  Further, 
  let 
  it 
  be 
  

   assumed 
  thai 
  the 
  upper 
  end 
  of 
  Dis 
  

   maintained 
  m 
  contact 
  with 
  pure 
  

   water, 
  and 
  that 
  the 
  concentration 
  

   of 
  the 
  salt 
  solution 
  at 
  the 
  lower 
  

   end 
  is 
  also 
  kepi 
  constant. 
  

  

  Under 
  these 
  conditions 
  the 
  salt 
  

   will 
  commence 
  to 
  diffuse 
  ap 
  the 
  

   tube 
  D,and 
  ultimately 
  the 
  diffusion 
  current 
  thus 
  commenced 
  

   will 
  be 
  found 
  to 
  become 
  uniform. 
  

  

  Now 
  when 
  the 
  steady 
  state 
  has 
  been 
  attained 
  the 
  quantities 
  

   of 
  water 
  and 
  of 
  sail 
  in 
  tube 
  I) 
  remain 
  constant, 
  and 
  in 
  dealing 
  

   with 
  variations 
  in 
  

   attention 
  to 
  the 
  bu 
  

   the 
  liquid 
  originally 
  in 
  it 
  will 
  decrease, 
  since 
  in 
  general 
  the 
  

   addition 
  of 
  salt 
  to 
  water 
  increases 
  the 
  resultant 
  volume. 
  

   Hence 
  some 
  of 
  the 
  water 
  outside 
  A 
  will 
  enter 
  the 
  apparatus 
  

   on 
  account 
  of 
  this 
  decrease 
  in 
  volume, 
  with 
  the 
  result 
  that 
  

   as 
  the 
  salt 
  diffuse- 
  up 
  the 
  tube 
  D 
  it 
  meets 
  a 
  current 
  of 
  liquid 
  

   which 
  continually 
  passes 
  downwards, 
  and 
  which 
  is 
  due 
  to 
  the 
  

   decrease 
  in 
  volume 
  mentioned. 
  

  

  The 
  weight 
  of 
  the 
  suspended 
  bulb 
  A 
  will 
  decrease 
  on 
  

   account 
  of 
  the 
  salt 
  which 
  leaves 
  it, 
  and 
  w 
  r 
  ill 
  increase 
  owing 
  

   to 
  the 
  water 
  which 
  enters, 
  and 
  the 
  resultant 
  loss 
  in 
  weight 
  is 
  

   equal 
  to 
  the 
  difference 
  between 
  the 
  two. 
  

  

  Let 
  d 
  = 
  densitv 
  of 
  solution 
  at 
  a 
  point 
  I 
  cms. 
  from 
  top 
  of 
  

   tube 
  D. 
  

   v= 
  velocity 
  downwards 
  at 
  the 
  same 
  point. 
  

   n 
  = 
  concentration 
  in 
  gms. 
  per 
  c.c. 
  at 
  the 
  same 
  point. 
  

   » 
  = 
  velocity 
  downwards 
  at 
  top 
  of 
  tube 
  where 
  1 
  = 
  0. 
  

   N 
  = 
  concentration 
  in 
  gms. 
  per 
  c.c. 
  at 
  the 
  end 
  of 
  tube 
  

   where 
  l 
  = 
  L. 
  

  

  volume 
  and 
  weight 
  we 
  may 
  confine 
  our 
  

   L> 
  A. 
  When 
  salt 
  leaves 
  A 
  the 
  volume 
  of 
  

  

  