﻿Absorption 
  of 
  Light 
  in 
  Heterogeneous 
  Media. 
  425 
  

  

  The 
  ratio 
  of 
  the 
  mass 
  of 
  reduced 
  silver 
  per 
  unit 
  area 
  to 
  the 
  

   density 
  (4) 
  is 
  an 
  important 
  quantity, 
  the 
  so-called 
  photographic 
  

   constant. 
  

  

  Now 
  the 
  film 
  is 
  m 
  layers 
  deep, 
  hence 
  ?n?i 
  = 
  N 
  is 
  the 
  whole 
  

   number 
  of 
  grains 
  per 
  unit 
  area. 
  Mass 
  of 
  silver 
  (M) 
  per 
  

   unit 
  area 
  is 
  then 
  proportional 
  to 
  N 
  and 
  to 
  the 
  average 
  

   volume 
  of 
  the 
  grains, 
  

  

  M 
  = 
  cNa 
  3 
  / 
  2 
  , 
  (7) 
  

  

  the 
  constant 
  c 
  involving 
  the 
  specific 
  gravity 
  of 
  the 
  silver 
  

   and 
  certain 
  numerical 
  factors. 
  

  

  The 
  photographic 
  constant 
  (P), 
  defined 
  as 
  mass 
  of 
  silver 
  

   per 
  unit 
  area 
  per 
  unit 
  density, 
  is 
  then 
  

  

  M 
  cNa*/ 
  2 
  /- 
  

  

  r= 
  ^ 
  == 
  — 
  — 
  =c\/ 
  a 
  

  

  I) 
  

  

  Na 
  

  

  if 
  the 
  overlapping 
  of 
  grains 
  is 
  negligible, 
  or 
  is 
  

  

  cNa 
  3 
  / 
  2 
  

  

  X 
  log 
  (1— 
  na) 
  

  

  (8> 
  

  

  (9) 
  

  

  without 
  assumptions 
  as 
  to 
  overlapping 
  or 
  uniformity 
  of 
  

   grain 
  through 
  the 
  film. 
  

  

  From 
  these 
  equations 
  it 
  appears 
  that 
  P, 
  to 
  a 
  first 
  

   approximation, 
  is 
  independent 
  of 
  N 
  and 
  hence 
  of 
  exposure 
  

   and 
  development, 
  but 
  that 
  it 
  will 
  vary 
  among 
  different 
  

   brands 
  of 
  plates 
  in 
  proportion 
  to 
  the 
  mean 
  diameter 
  of 
  

   grain. 
  The 
  first 
  of 
  these 
  conclusions 
  is 
  a 
  well-known 
  

   experimental 
  fact. 
  P 
  is 
  of 
  the 
  order 
  10 
  mg. 
  of 
  silver 
  per 
  

   square 
  decimetre 
  of 
  film, 
  per 
  unit 
  density. 
  The 
  relation 
  

   between 
  P 
  and 
  size 
  of 
  grain 
  has 
  not 
  yet 
  received 
  experi- 
  

   mental 
  confirmation. 
  

  

  In 
  the 
  following 
  table 
  are 
  numerical 
  values 
  calculated 
  for 
  

   different 
  photographic 
  densities. 
  

  

  D. 
  

  

  T. 
  

  

  1-A. 
  

  

  A. 
  

  

  10 
  A. 
  

  

  5 
  

  

  o-ooooi 
  

  

  0-316 
  

  

  0-684 
  

  

  6-8 
  

  

  3 
  

  

  0001 
  

  

  0-501 
  

  

  0-499 
  

  

  5-0 
  

  

  2 
  

  

  o-oio 
  

  

  0631 
  

  

  0-369 
  

  

  3-7 
  

  

  1 
  

  

  o-ioo 
  

  

  0-794 
  

  

  0-206 
  

  

  21 
  

  

  0-7 
  

  

  0-200 
  

  

  0-851 
  

  

  0-149 
  

  

  1-5 
  

  

  0-5 
  

  

  0-316 
  

  

  891 
  

  

  0-109 
  

  

  11 
  

  

  0-2 
  

  

  0-631 
  

  

  0-955 
  

  

  0045 
  

  

  0-45 
  

  

  o-i 
  

  

  0-794 
  

  

  0-977 
  

  

  0023 
  

  

  023 
  

  

  