﻿round 
  the 
  locus 
  of 
  a 
  Lens, 
  at 
  Various 
  Apertures. 
  43 
  

  

  the 
  curves 
  are 
  more 
  conveniently 
  drawn 
  by 
  the 
  help 
  o£ 
  (22 
  a). 
  

   Formulse 
  (10'), 
  or 
  (10 
  a), 
  etc. 
  may, 
  now 
  and 
  then, 
  be 
  used 
  for 
  

   a 
  control 
  of 
  the 
  length 
  I 
  of 
  arc 
  attained. 
  

  

  In 
  this 
  manner 
  four 
  curves 
  have 
  been 
  drawn 
  on 
  milli- 
  

   metrated 
  paper 
  and 
  are 
  reproduced 
  in 
  the 
  annexed 
  fig. 
  3. 
  

  

  Fig. 
  3, 
  

  

  The 
  curves 
  marked 
  [1], 
  [10], 
  [20], 
  and 
  [30], 
  correspond 
  to 
  

  

  10 
  3 
  /< 
  

   2r 
  

  

  = 
  1, 
  10, 
  20, 
  and 
  30. 
  

  

  1 
  

  

  If, 
  for 
  example, 
  n 
  = 
  l"5, 
  and 
  r= 
  - 
  10 
  6 
  \ 
  (say, 
  \ 
  = 
  i 
  micron, 
  

  

  and 
  ?' 
  = 
  5*55 
  . 
  .. 
  cm.), 
  then 
  these 
  curves 
  will 
  correspond, 
  by 
  

   (21) 
  and 
  (19), 
  to 
  points 
  of 
  the 
  focal 
  plane 
  whose 
  distances 
  

   from 
  the 
  focus 
  are 
  p 
  = 
  X, 
  10X, 
  20X, 
  and 
  30X, 
  respectively. 
  

   Similarly 
  for 
  any 
  other 
  plano-convex 
  lens. 
  The 
  circlets 
  on 
  

  

  