﻿968 
  Dr. 
  G. 
  Johnstone 
  Stoney 
  on 
  

  

  when 
  the 
  pro-telescope 
  is 
  successively 
  made 
  to 
  correspond 
  to 
  

   astronomical 
  telescopes 
  with 
  apertures 
  of 
  40, 
  24, 
  and 
  12 
  

   metric 
  inches, 
  i.e. 
  with 
  apertures 
  of 
  100, 
  60, 
  and 
  30 
  centi- 
  

   metres. 
  

  

  82. 
  The 
  angular 
  diameter 
  of 
  Neptune 
  in 
  opposition 
  is 
  about 
  

   IX 
  e. 
  and 
  the 
  maximum 
  diameter 
  of 
  Mars 
  in 
  1909 
  will 
  be 
  

   11*655 
  €. 
  We 
  shall 
  firsl 
  deal 
  with 
  these 
  magnitudes 
  in 
  the 
  

   most 
  obvious 
  way. 
  which 
  is 
  also 
  the 
  way 
  besl 
  fitted 
  Eor 
  com- 
  

   putation 
  : 
  and 
  we 
  will 
  afterward- 
  indicate 
  another 
  way 
  of 
  

   dealing 
  with 
  them 
  which 
  is 
  more 
  convenient 
  to 
  the 
  experi- 
  

   mentalist. 
  The 
  firsl 
  or 
  more 
  obvious 
  course 
  is 
  to 
  imagine 
  

   round 
  openings 
  in 
  copper 
  foil 
  with 
  diameters 
  J 
  .1 
  mm. 
  and 
  

   11*655 
  mm. 
  to 
  be 
  placed 
  successively 
  at 
  z\ 
  and 
  to 
  illuminate 
  

   these 
  by 
  a 
  single 
  stellade 
  of 
  light 
  incident 
  upon 
  them 
  from 
  

   the 
  right. 
  They, 
  and 
  the 
  round 
  opening 
  1 
  mm. 
  in 
  diameter 
  

   with 
  which 
  we 
  have 
  been 
  already 
  experimenting, 
  would 
  any 
  

   of 
  them 
  produce 
  on 
  plane 
  Y 
  the 
  same 
  kind 
  of 
  concentration 
  

   image. 
  These, 
  however, 
  would 
  he 
  of 
  different 
  sizes, 
  their 
  

  

  linear 
  dimensions 
  being 
  inversely 
  as 
  the 
  linear 
  dimensions 
  of 
  

   the 
  openings 
  at 
  z 
  to 
  which 
  they 
  are 
  due. 
  Hence 
  we 
  can 
  

   deduce 
  the 
  sizes 
  of 
  the 
  other- 
  from 
  the 
  dimensions 
  given 
  

   in 
  §74; 
  where 
  we 
  found 
  that 
  the 
  concentration 
  image 
  

   presented 
  when 
  z 
  is 
  a 
  round 
  hole 
  1 
  mm. 
  in 
  diameter 
  

   furnished 
  the 
  values 
  i 
  

  

  t 
  x 
  — 
  0*854 
  mm., 
  t 
  2 
  = 
  1*589 
  mm., 
  t 
  3 
  = 
  2-2u'8 
  mm., 
  . 
  (3) 
  

  

  where 
  fa 
  /o. 
  and 
  / 
  :; 
  are 
  the 
  radii 
  of 
  dark 
  circles 
  which 
  separate 
  

   the 
  central 
  boss 
  of 
  light 
  and 
  the 
  first 
  three 
  of 
  the 
  appendage 
  

   rings 
  which 
  with 
  the 
  central 
  boss 
  form 
  the 
  whole 
  of 
  the 
  

   concentration 
  image 
  produced 
  by 
  light 
  of 
  wave-length 
  

   \ 
  = 
  0*7 
  of 
  a 
  micron. 
  This 
  wave-length 
  and 
  wave-lengths 
  

   shorter 
  than 
  it 
  are 
  all 
  that 
  we 
  need 
  take 
  into 
  account, 
  as 
  this 
  

   range 
  includes 
  all 
  tin- 
  brighter 
  parts 
  of 
  the 
  spectrum 
  of 
  white 
  

   light. 
  Accordingly 
  the 
  central 
  boss 
  and 
  its 
  two 
  inner 
  appen- 
  

   dage 
  rings 
  will 
  lie 
  within 
  a 
  circle 
  of 
  which 
  the 
  radius 
  is 
  

   2"2(ji< 
  mm. 
  Airy's 
  formulae 
  do 
  not 
  enable 
  us 
  to 
  calculate 
  the 
  

   radii 
  of 
  the 
  limiting 
  circles 
  that 
  lie 
  farther 
  out 
  ; 
  but 
  their 
  

   position 
  can 
  be 
  seen 
  and 
  measured 
  in 
  the 
  experimental 
  

   apparatus, 
  and 
  it 
  thus 
  appears 
  that 
  a 
  circle 
  with 
  a 
  radius 
  

   of 
  4*2 
  mm. 
  would 
  nearly 
  include 
  all 
  of 
  the 
  fifth 
  ring. 
  

   Appendage 
  rings 
  that 
  lie 
  farther 
  out 
  become 
  so 
  faint 
  that 
  

   they 
  need 
  not 
  be 
  taken 
  into 
  account 
  unless 
  we 
  are 
  considering 
  

   the 
  vision 
  of 
  a 
  much 
  brighter 
  object 
  than 
  a 
  planet. 
  We 
  may 
  

   therefore 
  safely 
  assume 
  that 
  the 
  whole 
  of 
  the 
  effective 
  part 
  

   of 
  the 
  concentration 
  image 
  is 
  bounded 
  by 
  a 
  circle 
  4'2 
  mm. 
  in 
  

   radius. 
  This 
  radius 
  we 
  shall 
  call 
  T. 
  

  

  