﻿332 
  Dr. 
  G. 
  Johnstone 
  Stoney 
  on 
  

  

  the 
  light 
  whose 
  optical 
  effect 
  is 
  under 
  consideration. 
  Since 
  

   6=0-00001, 
  b 
  or 
  X/e 
  = 
  100000 
  \. 
  Hence 
  b 
  on 
  plane 
  Y 
  is 
  the 
  

   same 
  fraction 
  of 
  a 
  decimetre 
  as 
  X 
  is 
  of 
  a 
  micron, 
  which 
  is 
  

   convenient 
  inasmuch 
  as 
  wave-lengths 
  are 
  in 
  modern 
  science 
  

   always 
  recorded 
  as 
  fractions 
  of 
  a 
  micron. 
  

  

  What 
  corresponds 
  to 
  this 
  in 
  the 
  experimental 
  apparatus 
  is 
  

   that 
  the 
  concentration 
  image 
  seen 
  at 
  through 
  the 
  Steinheil 
  

   lens, 
  will 
  in 
  each 
  case 
  be 
  identically 
  the 
  same 
  concentration 
  

   image 
  as 
  would 
  be 
  formed 
  on 
  plane 
  Y 
  in 
  the 
  cosmical 
  

   apparatus, 
  but 
  on 
  a 
  scale 
  100 
  times 
  smaller. 
  Hence 
  in 
  

   measuring 
  the 
  details 
  of 
  its 
  spectra 
  we 
  are 
  to 
  use 
  a 
  b' 
  (or 
  

   pro-fr) 
  which 
  shall 
  be 
  the 
  hundredth 
  part 
  of 
  b. 
  Accordingly 
  

   6' 
  = 
  1000\ 
  and 
  is 
  the 
  same 
  fraction 
  of 
  a 
  millimetre 
  as 
  \ 
  is 
  

   of 
  a 
  micron. 
  This 
  enables 
  us 
  to 
  read 
  off 
  directly 
  upon 
  

   the 
  scale 
  at 
  C 
  the 
  length, 
  corresponding 
  to 
  each 
  wave-length, 
  

   of 
  any 
  required 
  multiple 
  of 
  b 
  f 
  . 
  

  

  20. 
  To 
  secure 
  these 
  convenient 
  numerical 
  relations 
  and 
  

   other 
  advantages 
  of 
  a 
  like 
  kind 
  the 
  following 
  arrangements 
  

   were 
  made. 
  D, 
  the 
  distance 
  of 
  the 
  planet 
  from 
  the 
  earth 
  

   varies 
  from 
  day 
  to 
  day, 
  but 
  has 
  to 
  be 
  represented 
  in 
  our 
  

   apparatus 
  by 
  a 
  D', 
  or 
  pro-D, 
  which 
  shall 
  not 
  vary. 
  This 
  

   fixed 
  distance 
  is 
  made 
  1 
  metre. 
  Again, 
  e, 
  the 
  length 
  which 
  

   at 
  the 
  distance 
  of 
  the 
  planet 
  subtends 
  the 
  angle 
  e 
  at 
  the 
  

   earth, 
  and 
  which 
  is 
  therefore 
  =eD, 
  will 
  vary 
  in 
  the 
  same 
  

   ratio 
  as 
  D, 
  but 
  in 
  the 
  experimental 
  apparatus 
  is 
  to 
  be 
  repre- 
  

   sented 
  by 
  a 
  fixed 
  length 
  at 
  z' 
  . 
  This 
  length 
  has 
  been 
  made 
  

   1 
  mm., 
  so 
  that 
  e' 
  = 
  lmm. 
  With 
  these 
  conventions, 
  since 
  e 
  = 
  e/D, 
  

   e' 
  (the 
  pro-e 
  or 
  representative 
  of 
  e) 
  must 
  ^e'/D' 
  ', 
  i. 
  e. 
  

   1 
  mm./l 
  metre, 
  which 
  =0'001. 
  Hence 
  the 
  standard 
  angle 
  

   e' 
  of 
  the 
  experimental 
  apparatus 
  is 
  exactly 
  100 
  times 
  the 
  

   standard 
  angle 
  e 
  of 
  the 
  astronomer. 
  

  

  To 
  attain 
  these 
  convenient 
  results 
  the 
  distance 
  D' 
  upon 
  

   our 
  apparatus 
  will 
  need 
  to 
  be 
  not 
  directly 
  the 
  distance 
  from 
  

   y' 
  at 
  C 
  to 
  z' 
  at 
  E, 
  but 
  that 
  distance 
  when 
  corrected 
  by 
  

   making 
  allowance 
  for 
  the 
  optical 
  effect 
  upon 
  it 
  of 
  lens 
  L/. 
  

   For 
  the 
  distance 
  has 
  to 
  be 
  made 
  such 
  that 
  1 
  mm. 
  at 
  z' 
  shall 
  

   subtend 
  the 
  angle 
  e' 
  or 
  0*001 
  at 
  y' 
  , 
  and 
  this 
  requires 
  that 
  

   the 
  distance 
  from 
  y' 
  to 
  the 
  optical 
  centre 
  of 
  lens 
  1/ 
  shall 
  be 
  

   slightly 
  more 
  than 
  one 
  metre. 
  In 
  the 
  author's 
  apparatus 
  it 
  

   is 
  made 
  l 
  m, 
  005, 
  and 
  the 
  object 
  z' 
  when 
  pushed 
  into 
  its 
  

   place 
  is 
  some 
  4 
  or 
  5 
  millimetres 
  to 
  the 
  right 
  of 
  the 
  optical 
  

   centre 
  of 
  lens 
  I/. 
  When 
  these 
  arrangements 
  were 
  made, 
  

   what 
  we 
  may 
  call 
  the 
  optical 
  distance 
  of 
  z' 
  from 
  y' 
  became 
  

   one 
  metre. 
  

  

  21. 
  The 
  lens 
  1/ 
  is 
  to 
  be 
  a 
  pro-L, 
  that 
  is 
  a 
  lens 
  which 
  shall 
  

   function 
  in 
  our 
  apparatus 
  in 
  the 
  way 
  in 
  which 
  we 
  have 
  asked 
  

  

  

  