﻿Coefficient 
  of 
  Diffusion. 
  865 
  

  

  With 
  the 
  decree 
  of 
  accuracy 
  obtained 
  in 
  the 
  present 
  work, 
  

   it 
  is 
  found 
  sufficiently 
  correct 
  to 
  assume 
  d~l 
  + 
  an 
  where 
  a 
  

   is 
  some 
  constant. 
  

  

  Since 
  the 
  same 
  mass 
  of 
  water 
  crosses 
  each 
  section 
  of 
  the 
  

   tube 
  

  

  v(d—n) 
  =v 
  0) 
  

  

  i.e. 
  v 
  (1— 
  bn) 
  = 
  v 
  , 
  where 
  b 
  = 
  l-—a. 
  . 
  . 
  . 
  (i.) 
  

  

  Now 
  when 
  the 
  steady 
  state 
  is 
  reached, 
  the 
  weight 
  of 
  salt 
  

   which 
  flows 
  through 
  each 
  cross-section 
  of 
  the 
  tube 
  per 
  second 
  

   is 
  constant=c, 
  say 
  

  

  i. 
  e. 
  —vn 
  + 
  kyr 
  = 
  c, 
  a 
  constant, 
  where 
  & 
  = 
  coeff. 
  of 
  diffusion; 
  

  

  or 
  ^y^ 
  7 
  dn 
  

  

  l 
  — 
  oii 
  ell 
  

  

  The 
  solution 
  of 
  this 
  equation 
  is 
  

  

  v 
  -bc 
  + 
  (v 
  -bcy 
  *" 
  c 
  k> 
  m 
  W 
  

  

  which, 
  as 
  (r 
  — 
  5c)N 
  is 
  small 
  compared 
  with 
  c, 
  reduces 
  to 
  

  

  i 
  (1 
  _^ 
  +s 
  &^...).j. 
  . 
  . 
  (iii 
  , 
  

  

  As 
  already 
  stated, 
  there 
  will 
  be 
  a 
  contraction 
  in 
  volume 
  

   produced 
  in 
  the 
  vessel 
  A 
  when 
  salt 
  leaves 
  it, 
  and 
  a 
  corre- 
  

   sponding 
  movement 
  downwards 
  will 
  take 
  place 
  in 
  the 
  liquid 
  

   in 
  the 
  tube 
  D. 
  The 
  amount 
  of 
  water 
  which 
  enters 
  the 
  bulb 
  

   owing 
  to 
  this 
  movement 
  may 
  be 
  calculated 
  as 
  follows 
  : 
  — 
  

  

  Mass 
  of 
  water 
  in 
  1 
  c.c. 
  of 
  solution 
  at 
  bottom 
  of 
  tube 
  D 
  

   = 
  density 
  of 
  solution 
  at 
  bottom 
  minus 
  concentration 
  

  

  of 
  solution 
  at 
  bottom. 
  

   = 
  l 
  + 
  aN-N, 
  

   = 
  l-(l-a)N, 
  

   = 
  1— 
  6N. 
  

  

  Let 
  h= 
  the 
  ratio 
  of 
  the 
  increment 
  in 
  volume 
  produced 
  to 
  

   the 
  increment 
  in 
  the 
  mass 
  of 
  salt 
  dissolved, 
  for 
  a 
  solution 
  of 
  

   the 
  strength 
  employed 
  in 
  the 
  bulb 
  A; 
  i. 
  e. 
  the 
  increase 
  in 
  

   volume 
  produced 
  when 
  1 
  gram 
  of 
  salt 
  is 
  dissolved 
  in 
  a 
  

   solution 
  of 
  the 
  given 
  concentration, 
  the 
  amount 
  of 
  the 
  solution 
  

   being 
  so 
  great 
  that 
  the 
  addition 
  of 
  the 
  salt 
  makes 
  no 
  appre- 
  

   ciable 
  change 
  in 
  the 
  concentration. 
  The 
  mass 
  of 
  water 
  which 
  

  

  Phil 
  Mag. 
  S. 
  6. 
  Vol. 
  16. 
  No. 
  96. 
  Dec. 
  1908. 
  3 
  L 
  

  

  