﻿Telescopic 
  Vision. 
  955 
  

  

  the 
  mathematician's 
  point 
  o£ 
  view 
  will 
  be 
  infinite 
  in 
  number, 
  

   since 
  he 
  requires 
  to 
  be 
  able 
  to 
  push 
  matters 
  to 
  their 
  limit, 
  in 
  

   order 
  to 
  comply 
  with 
  the 
  requirements 
  of 
  mathematical 
  

   analysis 
  ; 
  but 
  when 
  our 
  object 
  is 
  either 
  to 
  interpret 
  ex- 
  

   periments, 
  or 
  to 
  deal 
  with 
  nature, 
  the 
  whole 
  range 
  of 
  

   wave-lengths 
  may 
  be 
  divided 
  into 
  groups, 
  d\, 
  d\ 
  2 
  , 
  &c, 
  each 
  

   of 
  a 
  sufficiently 
  small 
  range, 
  and 
  then, 
  as 
  explained 
  in 
  § 
  31, 
  

   a 
  single 
  u 
  £ 
  W 
  may 
  be 
  substituted 
  for 
  each 
  of 
  these 
  groups. 
  

   When 
  this 
  has 
  been 
  done 
  the 
  light 
  incident 
  upon 
  z' 
  from 
  any 
  

   one 
  of 
  the 
  das 
  will 
  consist 
  of 
  a 
  large 
  but 
  finite 
  number 
  of 
  

   ufW's, 
  of 
  different 
  wave-lengths 
  all 
  travelling 
  in 
  one 
  

   direction. 
  Let 
  m 
  be 
  the 
  number 
  of 
  these 
  ' 
  groups,' 
  i. 
  e. 
  of 
  

   the 
  d\'s, 
  within 
  the 
  visible 
  part 
  of 
  the 
  spectrum, 
  and 
  let 
  n 
  be 
  

   the 
  number 
  of 
  da's 
  in 
  disk 
  <x, 
  then 
  will 
  the 
  entire 
  of 
  the 
  

   visible 
  light 
  incident 
  upon 
  z 
  consist 
  of 
  mn 
  ufW's, 
  of 
  which 
  

   m 
  of 
  the 
  ufW's 
  of 
  different 
  wave-lenglhs 
  will 
  have 
  issued 
  

   from 
  each 
  da 
  — 
  together 
  with 
  traces 
  of 
  r 
  1 
  (residual 
  light), 
  too 
  

   faint 
  to 
  need 
  to 
  be 
  taken 
  into 
  account. 
  

  

  62. 
  The 
  visible 
  light 
  which 
  inhabitants 
  upon 
  the 
  earth 
  

   receive 
  from 
  a 
  white 
  star 
  is 
  of 
  the 
  same 
  kind 
  as 
  that 
  received 
  

   by 
  the 
  z' 
  of 
  our 
  experimental 
  apparatus 
  from 
  any 
  one 
  of 
  the 
  

   da's 
  of 
  the 
  source 
  of 
  light. 
  They 
  both 
  consist 
  of 
  the 
  same 
  

   u 
  f 
  W's, 
  of 
  different 
  wave-lengths, 
  with 
  in 
  addition 
  a 
  tiny 
  

   amount 
  of 
  residual 
  light, 
  which 
  is 
  too 
  faint 
  to 
  need 
  to 
  be 
  

   considered. 
  It 
  will 
  be 
  convenient 
  to 
  have 
  a 
  name 
  for 
  this 
  

   kind 
  of 
  light, 
  and 
  it 
  will 
  in 
  the 
  present 
  paper 
  be 
  called 
  a 
  

   stellade 
  ; 
  which 
  will 
  therefore 
  mean 
  light 
  of 
  the 
  same 
  kind 
  

   as 
  we 
  receive 
  from 
  a 
  star. 
  The 
  statement 
  at 
  the 
  end 
  of 
  the 
  

   last 
  paragraph 
  may 
  now 
  be 
  put 
  into 
  the 
  following 
  more 
  

   convenient 
  form 
  : 
  — 
  

  

  If 
  (7, 
  the 
  source 
  of 
  light, 
  is 
  divided 
  into 
  n 
  sufficiently 
  small 
  

   patches, 
  da 
  x 
  , 
  da 
  2 
  , 
  &c, 
  and 
  if 
  the 
  wave-lengths 
  present 
  within 
  

   the 
  visible 
  part 
  of 
  the 
  spectrum 
  are 
  divided 
  into 
  m 
  sufficiently 
  

   small 
  groups, 
  d\ 
  t 
  , 
  d\ 
  2 
  , 
  &c, 
  then 
  will 
  the 
  visible 
  light 
  which 
  

   is 
  thrown 
  by 
  disk 
  a 
  upon 
  object 
  z', 
  consist 
  of 
  n 
  stellades, 
  one 
  

   from 
  each 
  da, 
  advancing 
  along 
  the 
  n 
  directions 
  from 
  the 
  

   centres 
  of 
  the 
  da's 
  to 
  the 
  centre 
  of 
  z'\ 
  and 
  each 
  of 
  these 
  

   stellades 
  will 
  consist 
  of 
  ra 
  ufW's, 
  of 
  the 
  wave-lengths 
  that 
  

   correspond 
  to 
  the 
  middles 
  of 
  the 
  small 
  groups, 
  d\, 
  d\ 
  2 
  , 
  &c. 
  — 
  

   together 
  with 
  the 
  residual 
  light 
  referred 
  to 
  in 
  § 
  29, 
  which 
  is 
  

   so 
  very 
  faint 
  that 
  it 
  may 
  legitimately 
  be 
  disregarded. 
  

  

  This 
  resolution 
  of 
  the 
  light 
  incident 
  upon 
  z 
  into 
  n 
  stellades, 
  

   and 
  of 
  each 
  stellade 
  into 
  m 
  ufW's, 
  answers 
  the 
  first 
  of 
  the 
  

   three 
  inquiries 
  proposed 
  in 
  § 
  59, 
  viz. 
  : 
  How 
  is 
  the 
  light 
  in 
  its 
  

   first 
  stage, 
  i. 
  e. 
  between 
  a 
  and 
  z', 
  to 
  be 
  analysed 
  ? 
  

  

  63. 
  It 
  should 
  be 
  borne 
  in 
  mind 
  that 
  the 
  u 
  f 
  W's 
  into 
  which 
  

  

  