﻿Theory 
  and 
  Planetary 
  Temperatures. 
  471 
  

  

  which 
  corresponds 
  very 
  nearly 
  with 
  the 
  depletion 
  for 
  a 
  solar 
  

   altitude 
  of 
  27°. 
  

  

  Bearing 
  in 
  mind 
  that 
  the 
  discussion 
  at 
  this 
  point 
  does 
  not 
  

   relate 
  to 
  the 
  line 
  and 
  hand 
  absorption 
  which 
  follow 
  different 
  

   laws, 
  the 
  value 
  of 
  l 
  — 
  t 
  r 
  , 
  or 
  the 
  atmospheric 
  depletion 
  by 
  

   diffraction 
  and 
  selective 
  or 
  scattering 
  reflexion, 
  may 
  be 
  

   approximately 
  as 
  follows 
  : 
  — 
  

  

  By 
  taking 
  the 
  spectral 
  energy-curves 
  given 
  in 
  my 
  reduction 
  

   of 
  the 
  Mount 
  Whitney 
  observations 
  *, 
  and 
  making 
  a 
  further 
  

   reduction 
  to 
  sea-level, 
  Professor 
  Lowell 
  obtains 
  f 
  for 
  the 
  

   light 
  reflected 
  by 
  the 
  air 
  from 
  sea-level 
  upwards, 
  the 
  

   fraction 
  0*74. 
  In 
  the 
  reduction 
  to 
  sea-level, 
  observations 
  

   made 
  at 
  different 
  places 
  and 
  times, 
  and 
  with 
  different 
  instru- 
  

   ments, 
  were 
  used, 
  which 
  is 
  objectionable, 
  but 
  unavoidable, 
  

   It 
  is 
  also 
  desirable 
  to 
  differentiate 
  the 
  depletion 
  in 
  the 
  

   infra-red 
  into 
  several 
  kinds. 
  I 
  do 
  not 
  know 
  that 
  0*74 
  is 
  too 
  

   large 
  for 
  the 
  air-reflexion 
  of 
  visible 
  rays, 
  but 
  we 
  shall 
  be 
  

   taking 
  a 
  lower 
  limit 
  if 
  we 
  make 
  it 
  0*6. 
  It 
  cannot 
  be 
  as 
  much 
  

   for 
  the 
  air 
  above 
  clouds. 
  As 
  clouds 
  hang 
  at 
  very 
  different 
  

   altitudes 
  in 
  the 
  air, 
  no 
  exact 
  statement 
  can 
  be 
  made 
  as 
  to 
  the 
  light 
  

   reflected 
  by 
  the 
  air 
  before 
  the 
  sun's 
  rays 
  reach 
  the 
  cloud 
  level. 
  

   Let 
  it 
  be 
  03, 
  and 
  the 
  reflexion 
  from 
  clouds 
  0'72, 
  as 
  has 
  been 
  

   given 
  bv 
  observation. 
  Then 
  the 
  light 
  reflected 
  from 
  a 
  cloudy 
  

   area 
  of 
  the 
  earth's 
  surface 
  will 
  be 
  0'3 
  + 
  (0'72 
  x 
  07) 
  =0-804, 
  

   giving 
  the 
  albedo 
  of 
  a 
  half-clouded 
  earth, 
  J(0"6-f 
  0'8) 
  = 
  0'7. 
  

   Only 
  a 
  small 
  amount 
  of 
  infra-red 
  radiation 
  is 
  reflected 
  by 
  the 
  

   air. 
  Let 
  us 
  say 
  0*2 
  for 
  clear 
  air, 
  and 
  0*1 
  for 
  the 
  air 
  above 
  

   clouds. 
  But 
  the 
  clouds 
  also 
  do 
  not 
  reflect 
  the 
  infra-red 
  rays 
  

   as 
  well 
  as 
  they 
  do 
  the 
  visible 
  rays 
  ; 
  for 
  I 
  have 
  been 
  able 
  to 
  

   determine 
  the 
  position 
  of 
  the 
  sun 
  bolometrically 
  through 
  

   clouds 
  so 
  thick 
  as 
  completely 
  to 
  hide 
  it 
  from 
  the 
  eye. 
  Allowing 
  

   that 
  clouds 
  may 
  reflect 
  the 
  infra-red 
  rays 
  half 
  as 
  well 
  as 
  the 
  

   luminous 
  ones, 
  infra-red 
  reflexion 
  from 
  a 
  cloudy 
  area 
  is 
  

   0-1 
  + 
  (036 
  x 
  0-9) 
  = 
  0-424. 
  One 
  third 
  of 
  the 
  rays 
  being 
  visible, 
  

   the 
  total 
  reflexion 
  over 
  cloud 
  is 
  

  

  (0-33 
  x 
  0-804) 
  + 
  (0-67 
  x 
  0'424) 
  =0549. 
  

  

  The 
  reflexion 
  by 
  clear 
  air 
  is 
  

  

  (0-33 
  x 
  0-6) 
  + 
  (0-67 
  x 
  02) 
  = 
  0-332 
  ; 
  

  

  and 
  the 
  mean 
  reflexion 
  from 
  a 
  half-clouded 
  earth 
  for 
  the 
  

   entire 
  spectrum 
  is 
  J(0'549 
  + 
  0*332) 
  = 
  0*44, 
  giving 
  t 
  r 
  = 
  0'56. 
  

  

  * 
  U.S. 
  Weather 
  Bureau 
  Publication 
  No. 
  254, 
  " 
  The 
  Solar 
  Constant," 
  

   fig. 
  1, 
  p. 
  21. 
  

  

  t 
  Proc. 
  American 
  Academy 
  of 
  Arts 
  and 
  Sciences, 
  vol. 
  xlii. 
  p. 
  656 
  

   March 
  1907. 
  

  

  