﻿474 
  Mr. 
  A. 
  0. 
  Allen 
  on 
  Graphical 
  Methods 
  

  

  K 
  

  

  L=3 
  

  

  1 
  " 
  1 
  (3+--I) 
  

  

  ( 
  x 
  - 
  sr) 
  I 
  1 
  - 
  n) 
  (i- 
  ^) 
  2 
  

  

  + 
  **»* 
  / 
  i/ 
  r 
  ; 
  

  

  «*(l 
  + 
  J) 
  ; 
  B- 
  -tf.-^ 
  -tf 
  .-^ 
  -*?(* 
  + 
  1 
  + 
  ^> 
  

  

  These 
  expressions 
  have 
  perhaps 
  a 
  forbidding 
  aspect 
  ; 
  but 
  

   it 
  is 
  to 
  be 
  noticed 
  that 
  owing 
  to 
  the 
  constant 
  occurrence 
  of 
  

  

  AT 
  and 
  - 
  along 
  with 
  integers, 
  the 
  computation 
  is 
  not 
  nearly 
  

  

  as 
  toilsome 
  as 
  it 
  looks; 
  even 
  L 
  and 
  S 
  yield 
  quite 
  readily. 
  

   The 
  expression 
  (1) 
  is 
  merely 
  an 
  expansion 
  of 
  Seidel's 
  first 
  

   term, 
  JSi. 
  His 
  second 
  term, 
  -JS 
  2 
  , 
  expands 
  into 
  a 
  form 
  which, 
  

   if 
  Si 
  is 
  zero, 
  contains 
  expression 
  (2) 
  as 
  a 
  factor; 
  so 
  that 
  the 
  

   expression 
  is 
  only 
  to 
  be 
  regarded 
  as 
  measuring 
  the 
  departure 
  

   from 
  the 
  sine-condition, 
  and 
  the 
  amount 
  of 
  coma, 
  provided 
  

   there 
  is 
  no 
  spherical 
  aberration; 
  and 
  the 
  meaning 
  of 
  Cheshire 
  2 
  s 
  

   "intersection-surface" 
  is 
  subject 
  to 
  the 
  same 
  limitation. 
  More 
  

   generally, 
  the 
  connexion 
  with 
  the 
  Seidel 
  terms 
  may 
  be 
  stated 
  

   thus 
  : 
  — 
  If 
  the 
  object-point 
  is 
  at 
  a 
  finite 
  distance, 
  and 
  at 
  a 
  height 
  

   y 
  x 
  above 
  the 
  axis, 
  then 
  the 
  spherical 
  aberration 
  of 
  a 
  ray 
  from 
  

  

  it, 
  striking 
  the 
  objective 
  at 
  height 
  h, 
  is 
  Q/i-~h) 
  3 
  (pi 
  +p 
  2 
  ) 
  3 
  - 
  ~h 
  

  

  