﻿326 
  Dr. 
  G. 
  Johnstone 
  Stoney 
  on 
  

  

  the 
  observation 
  is 
  made 
  ; 
  so 
  that 
  every 
  half-millimetre 
  any- 
  

   where 
  on 
  the 
  eidolon 
  will 
  exactly 
  represent 
  1" 
  upon 
  the 
  

   corresponding 
  part 
  of 
  the 
  planet. 
  Partly 
  for 
  this 
  reason 
  and 
  

   partly 
  because 
  a 
  power 
  of 
  about 
  400 
  is 
  (under 
  favourable 
  

   atmospheric 
  conditions) 
  the 
  best, 
  as 
  we 
  shall 
  see 
  farther 
  on, 
  

   for 
  bringing 
  out 
  the 
  full 
  capabilities 
  of 
  the 
  telescope 
  of 
  

   12-inch 
  aperture 
  which 
  the 
  author 
  was 
  in 
  the 
  habit 
  of 
  using, 
  

   he 
  made 
  a 
  practice 
  for 
  several 
  years 
  of 
  regarding 
  412 
  as 
  a 
  

   standard 
  of 
  magnification, 
  with 
  which 
  he 
  compared 
  the 
  

   various 
  magnifying 
  powers 
  he 
  had 
  occasion 
  to 
  employ. 
  Thus, 
  

   when 
  using 
  an 
  eyepiece 
  giving 
  magnification 
  140, 
  he 
  would 
  

   think 
  of 
  this 
  as 
  not 
  far 
  from 
  one-third 
  of 
  his 
  standard, 
  and 
  

   that 
  accordingly 
  each 
  half-millimetre 
  on 
  the 
  smaller 
  eidolon 
  

   of 
  the 
  planet 
  which 
  it 
  would 
  furnish 
  would 
  correspond 
  to 
  a 
  

   length 
  at 
  the 
  distance 
  of 
  the 
  planet 
  subtending 
  3". 
  This 
  was 
  

   very 
  convenient. 
  But 
  other 
  considerations 
  of 
  much 
  weight 
  

   have 
  since 
  convinced 
  the 
  author 
  that 
  it 
  would 
  be 
  still 
  better 
  

   for 
  astronomers 
  to 
  adopt 
  a 
  magnification 
  of 
  400 
  as 
  a 
  standard 
  

   unit, 
  and 
  to 
  make 
  a 
  practice 
  of 
  estimating 
  the 
  various 
  powers 
  

   they 
  use 
  as 
  multiples 
  or 
  fractions 
  of 
  that 
  number. 
  The 
  

   reason 
  for 
  this 
  recommendation 
  will 
  be 
  explained 
  farther 
  on. 
  

   Meanwhile 
  it 
  may 
  be 
  useful 
  to 
  call 
  attention 
  to 
  the 
  use 
  which 
  

   may 
  be 
  made 
  of 
  the 
  new 
  standard, 
  viz. 
  400, 
  in 
  estimating 
  

   magnitudes. 
  The 
  eidolon 
  of 
  a 
  planet 
  which 
  results 
  from 
  

   using 
  a 
  power 
  of 
  400 
  is 
  slightly 
  smaller 
  than 
  the 
  eidolon 
  

   which 
  would 
  be 
  yielded 
  by 
  412*53. 
  The 
  reduction 
  in 
  size, 
  

   however, 
  is 
  little 
  more 
  than 
  3 
  per 
  cent., 
  and 
  does 
  not 
  hinder 
  

   its 
  being 
  useful 
  for 
  the 
  observer 
  to 
  keep 
  in 
  mind 
  that 
  each 
  

   V 
  on 
  the 
  planet 
  will 
  now 
  be 
  represented 
  by 
  slightly 
  less 
  than 
  

   half 
  a 
  millimetre 
  on 
  the 
  eidolon, 
  where 
  ' 
  slightly 
  less 
  ' 
  means 
  

   roughly 
  speaking 
  3 
  per 
  cent, 
  less, 
  or 
  more 
  nearly 
  in 
  the 
  ratio 
  

   of 
  32 
  to 
  33, 
  or, 
  if 
  extreme 
  accuracy 
  is 
  required, 
  in 
  the 
  ratio 
  

   of 
  2" 
  to 
  2"*062648 
  — 
  the 
  latter 
  angle 
  being 
  the 
  angle 
  whose 
  

   circular 
  measure 
  is 
  exactly 
  0*00001. 
  This 
  last 
  mentioned 
  

   angle, 
  viz. 
  the 
  angle 
  0*00001, 
  is 
  of 
  special 
  and 
  frequent 
  use 
  

   to 
  the 
  observer 
  and 
  we 
  shall 
  call 
  it 
  angle 
  e 
  ; 
  and 
  the 
  length 
  

   which 
  at 
  the 
  distance 
  of 
  the 
  planet 
  would 
  subtend 
  angle 
  e, 
  

   we 
  may 
  call 
  the 
  length 
  e. 
  It 
  is 
  this 
  length 
  upon 
  the 
  planet 
  

   which 
  each 
  mm. 
  on 
  the 
  standard 
  eidolon 
  exactly 
  represents. 
  

  

  14. 
  Let 
  us 
  apply 
  this 
  way 
  of 
  regarding 
  events 
  to 
  what 
  

   will 
  happen 
  next 
  year. 
  Mars 
  will 
  come 
  closest 
  to 
  the 
  earth 
  

   on 
  1909, 
  Sept. 
  18. 
  On 
  that 
  day 
  its 
  semidiameter 
  will 
  have 
  

   become 
  12"*02. 
  Accordingly, 
  when 
  nearest 
  and 
  examined 
  

   with 
  a 
  power 
  of 
  400, 
  the 
  diameter 
  of 
  its 
  eidolon 
  will 
  be 
  about 
  

   3 
  per 
  cent, 
  less 
  than 
  12*02 
  millimetres, 
  i. 
  e. 
  it 
  will 
  be 
  11*8 
  mm. 
  

   in 
  diameter. 
  

  

  