﻿466 
  MR 
  WILLIAM 
  SWAN 
  ON 
  THE 
  

  

  On 
  the 
  other 
  hand, 
  rays 
  proceeding 
  to 
  the 
  eye 
  from 
  the 
  edge 
  of 
  the 
  sun 
  in 
  the 
  

   direction 
  B 
  b, 
  will 
  pass 
  obliquely 
  through 
  the 
  stratum, 
  which, 
  from 
  its 
  small 
  thick- 
  

   ness, 
  may 
  be 
  regarded 
  as 
  a 
  lamina, 
  bounded 
  by 
  parallel 
  planes 
  perpendicular 
  to 
  

   B 
  b. 
  The 
  thickness 
  b 
  b' 
  of 
  the 
  medium 
  traversed 
  by 
  the 
  rays, 
  will 
  therefore 
  be 
  

  

  t 
  sec 
  B 
  b 
  C 
  = 
  t 
  cosec 
  a, 
  

   where 
  a 
  is 
  the 
  angle 
  B 
  C 
  b 
  ; 
  and 
  the 
  number 
  of 
  rays 
  that 
  escape 
  absorption 
  will 
  be 
  

  

  V 
  ml 
  

  

  W 
  

  

  Then, 
  putting 
  h 
  L 
  , 
  h.,, 
  for 
  the 
  apparent 
  brightnesses 
  of 
  the 
  sun's 
  disc 
  at 
  A 
  and 
  

   B, 
  as 
  seen 
  from 
  the 
  earth, 
  the 
  ratio 
  of 
  h 
  2 
  to 
  h 
  l 
  will 
  be 
  that 
  of 
  the 
  numbers 
  of 
  rays 
  

   transmitted 
  at 
  the 
  points 
  b' 
  a' 
  ; 
  or, 
  

  

  i, 
  ivr* 
  cosec 
  "■ 
  , 
  in 
  

  

  'h 
  _ 
  ivi 
  _ 
  M 
  J 
  (cosec 
  «—l) 
  

  

  Now, 
  the 
  nearer 
  a 
  b 
  is 
  to 
  the 
  surface 
  of 
  the 
  sun, 
  the 
  smaller 
  is 
  a, 
  and 
  for 
  a 
  

   small 
  angle, 
  cosec 
  a 
  will 
  be 
  very 
  large 
  ; 
  hence, 
  for 
  a 
  stratum 
  near 
  the 
  surface, 
  

   since 
  M 
  is 
  less 
  than 
  unity, 
  the 
  ratio 
  of 
  h 
  1 
  to 
  h. 
  2 
  will 
  be 
  very 
  great. 
  ' 
  On 
  the 
  other 
  

   hand, 
  as 
  the 
  distance 
  of 
  the 
  stratum 
  from 
  the 
  surface 
  increases, 
  cosec 
  a 
  approaches 
  

   to 
  unity, 
  and 
  h 
  x 
  becomes 
  nearly 
  equal 
  to 
  h,. 
  

  

  It 
  thus 
  appears 
  that 
  the 
  effect 
  of 
  the 
  oblique 
  transmission 
  of 
  the 
  lateral 
  rays 
  

   through 
  the 
  sun's 
  atmosphere 
  in 
  increasing 
  the 
  absorption 
  of 
  those 
  rays, 
  and 
  hence 
  

   diminishing 
  the 
  apparent 
  brightness 
  of 
  the 
  sun's 
  limb, 
  as 
  compared 
  with 
  his 
  centre, 
  

   is 
  very 
  great 
  in 
  the 
  case 
  of 
  those 
  strata 
  of 
  the 
  atmosphere 
  which 
  are 
  near 
  his 
  sur- 
  

   face 
  ; 
  but 
  that 
  it 
  rapidly 
  diminishes, 
  as 
  the 
  strata 
  are 
  more 
  and 
  more 
  removed 
  from 
  

   the 
  surface 
  of 
  the 
  sun. 
  Hence, 
  even 
  if 
  we 
  suppose 
  the 
  solar 
  atmosphere 
  equally 
  

   dense 
  and 
  equally 
  absorptive 
  throughout 
  its 
  whole 
  extent, 
  the 
  diminished 
  bright- 
  

   ness 
  of 
  the 
  sun's 
  limb 
  contrasted 
  with 
  that 
  of 
  his 
  centre, 
  would 
  be 
  due 
  chiefly 
  to 
  

   the 
  action 
  of 
  those 
  portions 
  of 
  the 
  atmosphere 
  which 
  are 
  near 
  his 
  surface. 
  But, 
  

   besides 
  this, 
  from 
  the 
  necessarily 
  rapid 
  diminution 
  of 
  their 
  density, 
  the 
  absorp- 
  

   tive 
  action 
  of 
  the 
  successive 
  strata 
  of 
  the 
  solar 
  atmosphere 
  on 
  light 
  must 
  quickly 
  

   diminish, 
  as 
  their 
  height 
  above 
  the 
  surface 
  increases 
  ; 
  and 
  this 
  will 
  conspire, 
  with 
  

   the 
  continually 
  lessening 
  obliquity 
  with 
  which 
  the 
  sun's 
  lateral 
  rays 
  traverse 
  the 
  

   higher 
  strata 
  of 
  his 
  atmosphere, 
  so 
  as 
  to 
  render 
  their 
  action 
  in 
  causing 
  the 
  di- 
  

   minished 
  brightness 
  of 
  the 
  sun's 
  limb 
  probably 
  insensible. 
  

  

  Since, 
  then, 
  the 
  observed 
  darkness 
  of 
  the 
  sun's 
  limb, 
  is 
  due 
  chiefly 
  to 
  a 
  com- 
  

   paratively 
  thin 
  layer 
  of 
  atmosphere 
  near 
  his 
  surface, 
  the 
  very 
  notable 
  amount 
  

   of 
  that 
  darkness 
  renders 
  it 
  necessary 
  for 
  us 
  to 
  regard 
  those 
  portions 
  of 
  the 
  atmo- 
  

   sphere 
  as 
  very 
  highly 
  absorptive. 
  The 
  thin 
  envelope 
  of 
  cloud 
  which 
  has 
  been 
  

   supposed 
  to 
  surround 
  the 
  sun, 
  near 
  his 
  surface, 
  is 
  precisely 
  such 
  an 
  agent 
  as 
  

   would 
  produce 
  the 
  phenomenon 
  now 
  under 
  consideration; 
  and 
  we 
  may 
  thus, 
  

   perhaps, 
  regard 
  the 
  diminished 
  brightness 
  of 
  the 
  sun's 
  limb 
  as 
  a 
  corroborative 
  

   proof 
  of 
  the 
  existence 
  of 
  such 
  an 
  envelope. 
  

  

  