﻿128 
  Mr. 
  C. 
  A. 
  Sadler 
  on 
  the 
  

  

  an 
  examination 
  of 
  the 
  graphs 
  in 
  fig. 
  4 
  leads 
  to 
  the 
  following 
  

   conclusions 
  : 
  — 
  

  

  (1) 
  If 
  Xi 
  is 
  equal 
  to 
  or 
  greater 
  than 
  X2J 
  the 
  intensity 
  of 
  

   the 
  homogeneous 
  radiation 
  emitted 
  by 
  A 
  is 
  inappreciable. 
  

  

  (2) 
  If 
  Ai 
  is 
  slightly 
  less 
  than 
  X2 
  the 
  intensity 
  is 
  measurable 
  

   but 
  still 
  small. 
  

  

  (3) 
  For 
  a 
  further 
  slight 
  decrease 
  in 
  Xi 
  a 
  very 
  rapid 
  increase 
  

   in 
  the 
  intensity 
  of 
  the 
  radiation 
  from 
  A 
  takes 
  place, 
  and 
  for 
  

   a 
  value 
  of 
  Xi 
  not 
  greatly 
  less 
  than 
  X2 
  the 
  intensity 
  reaches 
  a 
  

   maximum 
  value. 
  

  

  (4) 
  Beyond 
  this 
  point, 
  over 
  a 
  considerable 
  range, 
  as 
  Xi 
  

   decreases 
  the 
  intensity 
  decreases 
  as 
  a 
  linear 
  function 
  of 
  Xi. 
  

   For 
  this 
  range 
  the 
  relationship 
  may 
  be 
  represented 
  by 
  

   /: 
  = 
  a(Xi 
  — 
  5), 
  where 
  a 
  and 
  h 
  are 
  constants. 
  For 
  the 
  group 
  of 
  

   tertiary 
  radiators 
  employed, 
  h 
  has 
  the 
  same 
  value 
  for 
  each 
  

   member 
  of 
  the 
  group, 
  while 
  a 
  increases 
  with 
  the 
  increase 
  of 
  

   the 
  atomic 
  weight 
  of 
  the 
  tertiary 
  radiator. 
  

  

  But 
  the 
  absorption 
  by 
  Al 
  of 
  the 
  radiation 
  from 
  the 
  group 
  

   of 
  metals 
  Cr-Ag 
  is 
  proportional 
  to 
  the 
  absorption 
  by 
  air 
  of 
  

   these 
  radiations, 
  as 
  previously 
  mentioned; 
  and 
  it 
  has 
  been 
  

   shown 
  that 
  the 
  intensity 
  of 
  the 
  homogeneous 
  radiation 
  excited 
  

   in 
  a 
  thin 
  sheet 
  of 
  copper 
  by 
  a 
  primary 
  beam 
  is 
  proportional 
  

   to 
  the 
  ionization 
  produced 
  in 
  air 
  by 
  the 
  same 
  beam*; 
  we 
  

   may, 
  therefore, 
  over 
  this 
  range, 
  write 
  k 
  = 
  a(ci 
  — 
  b)j 
  where 
  i 
  is 
  

   a 
  measure 
  of 
  the 
  ionization 
  produced 
  in 
  1 
  c. 
  c. 
  of 
  air 
  by 
  

   the 
  exciting 
  beam, 
  and 
  c 
  the 
  ratio 
  of 
  the 
  absorption 
  by 
  

   1 
  c.c. 
  of 
  air 
  to 
  the 
  ionization 
  produced 
  in 
  it 
  in 
  consequence 
  of 
  

   that 
  absorption, 
  a 
  and 
  b 
  having 
  the 
  same 
  values 
  as 
  before. 
  

   (It 
  will 
  be 
  seen 
  from 
  the 
  Zn 
  and 
  Cu 
  curves 
  that 
  there 
  is 
  

   a 
  departure 
  from 
  this 
  linear 
  relationship 
  for 
  very 
  penetrating 
  

   beams.) 
  

  

  When 
  a 
  secondary 
  homogeneous 
  Rontgen 
  beam 
  falls 
  nor- 
  

   mally 
  upon 
  a 
  tertiary 
  radiator, 
  the 
  amount 
  of 
  energy 
  absorbed 
  

   per 
  sec. 
  per 
  unit 
  area 
  of 
  its 
  surface 
  in 
  a 
  layer 
  of 
  thickness 
  So; 
  

   at 
  a 
  distance 
  x 
  below 
  the 
  surface 
  is 
  IX 
  1^-?^', 
  where 
  I 
  is 
  the 
  

   energy 
  crossing 
  unit 
  area 
  of 
  the 
  surface 
  per 
  second 
  at 
  the 
  

   depth 
  .V 
  below 
  the 
  surface 
  and 
  Xi 
  is 
  the 
  absorption 
  coefficient 
  

   by 
  the 
  substance 
  of 
  the 
  tertiary 
  radiator 
  of 
  the 
  secondary 
  

   beam. 
  If, 
  however, 
  we 
  confine 
  our 
  attention 
  to 
  the 
  absorp- 
  

   tion 
  which 
  is 
  directly 
  involved 
  in 
  the 
  process 
  of 
  emission 
  of 
  

   tertiary 
  rays, 
  we 
  must 
  substitute 
  X^ 
  for 
  Xi, 
  where 
  X' 
  is 
  the 
  

   increase 
  in 
  the 
  value 
  of 
  the 
  absorption 
  coefficient, 
  and 
  the 
  

   amount 
  of 
  energy 
  so 
  absorbed 
  per 
  second 
  in 
  this 
  layer 
  is 
  

   IX'Sx. 
  [The 
  values 
  of 
  V 
  are 
  given 
  in 
  Table 
  Y.] 
  

  

  But 
  the 
  amount 
  of 
  energy 
  emitted 
  as 
  tertiary 
  radiation 
  

  

  * 
  Barkla 
  & 
  Sadler, 
  Phil. 
  Mag. 
  Oct. 
  1908, 
  pp. 
  650-584. 
  

  

  