﻿24 
  Mr. 
  J. 
  A. 
  Tomkins 
  on 
  the 
  

  

  position 
  is 
  attained 
  when 
  the 
  axis 
  of 
  rotation 
  passes 
  through 
  

   the 
  first 
  nodal 
  point, 
  in 
  which 
  case 
  the 
  object, 
  real 
  or 
  virtual, 
  

   will 
  be 
  situated 
  at 
  the 
  first 
  principal 
  focus. 
  

  

  The 
  light 
  will 
  then 
  emerge 
  as 
  a 
  parallel 
  pencil, 
  and 
  the 
  

   image 
  can 
  be 
  viewed 
  through 
  a 
  telescope 
  focussed 
  for 
  parallel 
  

   rays, 
  as 
  in 
  one 
  of 
  the 
  well-known 
  methods 
  of 
  determining 
  

   the 
  focal 
  length 
  of 
  a 
  thin 
  lens. 
  A 
  further 
  advantage 
  of 
  this 
  

   position 
  is 
  that 
  the 
  nodal 
  points 
  are 
  determined 
  directly 
  as 
  

   in 
  the 
  ordinary 
  nodal-slide 
  method. 
  

  

  We 
  will 
  now 
  apply 
  these 
  formulae 
  to 
  the 
  example 
  given 
  in 
  

   Prof. 
  Anderson's 
  second 
  paper 
  (Phil. 
  Mag. 
  July 
  1917, 
  p. 
  76), 
  

   where 
  

  

  OPj 
  =a? 
  1 
  = 
  142cm.; 
  OP 
  2 
  = 
  2 
  / 
  1 
  = 
  9'4cm.; 
  and 
  ™i=ttL 
  = 
  0'0662. 
  

  

  OP 
  1 
  ' 
  = 
  ^ 
  2 
  =29-lcm.; 
  OP 
  2 
  '=y 
  2 
  = 
  8-3cm.; 
  and 
  ™ 
  2 
  =^ 
  = 
  0'285. 
  

  

  d 
  = 
  113'8cm.; 
  H 
  2 
  H 
  1 
  = 
  a 
  = 
  243cm. 
  

  

  The 
  distance 
  H^O 
  in 
  Prof. 
  Anderson's 
  figure 
  v 
  Phil. 
  Mag. 
  

   Jan. 
  1917, 
  p. 
  158), 
  in 
  which 
  the 
  principal 
  and 
  nodal 
  points 
  

   are 
  coincident, 
  is 
  given 
  by 
  

  

  which 
  is 
  but 
  a 
  particular 
  case 
  of 
  the 
  general 
  expression 
  

   obtained 
  by 
  Prof. 
  Anderson. 
  

  

  Hence 
  in 
  the 
  first 
  position 
  ILO= 
  — 
  z 
  = 
  — 
  2*60 
  cm. 
  

  

  r 
  1— 
  ra 
  x 
  

  

  and 
  in 
  the 
  second 
  position 
  ELO 
  = 
  — 
  — 
  — 
  — 
  = 
  — 
  3*40 
  cm. 
  

  

  1— 
  m 
  2 
  

  

  These 
  positions 
  in 
  relation 
  to 
  the 
  nodal 
  points 
  are 
  shown 
  to 
  

   scale 
  in 
  fig. 
  2. 
  

  

  Fig. 
  2. 
  

  

  <V 
  of 
  1h 
  2 
  hJ 
  

  

  Suppose 
  now 
  that 
  = 
  5° 
  = 
  0-0873 
  radian 
  and 
  that 
  the 
  axis 
  

   of 
  rotation 
  is 
  moved 
  1 
  mm. 
  from 
  the 
  nul 
  position 
  towards 
  the 
  

   object. 
  

  

  Then, 
  in 
  the 
  first 
  case, 
  l 
  x 
  r= 
  — 
  2-60 
  + 
  0-1 
  = 
  — 
  2*5 
  cm.; 
  

   m 
  1 
  = 
  0*0662; 
  and 
  the 
  displacement 
  of 
  the 
  image 
  calculated 
  

   by 
  equation 
  (1) 
  is 
  0'0083 
  cm. 
  In 
  the 
  second 
  case 
  we 
  have 
  

   l 
  2 
  =- 
  3-40 
  + 
  0-1 
  =-3-3 
  cm.; 
  m 
  2 
  = 
  0'285 
  and 
  the 
  dis- 
  

   placement 
  is 
  0-0062 
  cm. 
  If, 
  however, 
  the 
  ordinary 
  nodal- 
  

   slide 
  method 
  had 
  been 
  employed, 
  in 
  which 
  case 
  O 
  would 
  

  

  