﻿22 
  

  

  Mr. 
  J„ 
  A. 
  Tomkins 
  on 
  the 
  

  

  the 
  nodal 
  points, 
  because 
  small 
  errors 
  are 
  multiplied 
  by 
  the 
  

   numerical 
  value 
  of 
  d, 
  the 
  distance 
  through 
  which 
  the 
  com- 
  

   bination 
  is 
  moved, 
  which 
  may 
  be 
  large. 
  He 
  also 
  described 
  

   another 
  method 
  which 
  gave 
  satisfactory 
  values 
  for 
  this 
  

   distance. 
  In 
  a 
  third 
  paper 
  (Phil. 
  Mag. 
  Sept. 
  1917, 
  p. 
  174) 
  

   he 
  gave 
  some 
  further 
  properties 
  of 
  this 
  point, 
  which 
  he 
  terms 
  

   the 
  nul 
  point. 
  There 
  are, 
  however, 
  two 
  possible 
  sources 
  of 
  

   error 
  mentioned 
  by 
  Prof. 
  Anderson, 
  viz. 
  (1) 
  want 
  of 
  pre- 
  

   cision 
  in 
  determining 
  whether 
  there 
  is 
  any 
  displacement 
  of 
  

   the 
  image, 
  and 
  (2) 
  error 
  in 
  determining 
  its 
  position, 
  which 
  

   seem 
  to 
  call 
  for 
  further 
  consideration. 
  

  

  With 
  reference 
  to 
  the 
  first 
  it 
  is 
  to 
  be 
  noted 
  that 
  in 
  the 
  

   ordinary 
  nodal-slide 
  method 
  there 
  is 
  one, 
  and 
  only 
  one,, 
  

   possible 
  axis 
  of 
  rotation 
  of 
  the 
  lens 
  system, 
  viz. 
  that 
  passing 
  

   through 
  the 
  second 
  nodal 
  point, 
  whereas 
  in 
  the 
  general 
  

   method 
  described 
  by 
  Prof. 
  Anderson 
  there 
  is 
  an 
  infinite, 
  or 
  

   doubly 
  infinite, 
  number 
  of 
  possible 
  axes. 
  The 
  object 
  of 
  this 
  

   communication 
  is 
  to 
  investigate 
  the 
  best 
  position, 
  if 
  any, 
  for 
  

   the 
  nul 
  point, 
  and 
  to 
  compare 
  the 
  results 
  with 
  those 
  obtained 
  

   by 
  the 
  ordinary 
  nodal-slide 
  method. 
  

  

  For 
  the 
  purpose 
  of 
  observing 
  the 
  displacement 
  of 
  the 
  image 
  

   the 
  best 
  position 
  will 
  be 
  that 
  for 
  which 
  a 
  given 
  small 
  dis- 
  

   placement 
  of 
  the 
  axis 
  from 
  the 
  nul 
  position 
  will, 
  for 
  a 
  given 
  

   small 
  rotation 
  of 
  the 
  lens 
  system, 
  produce 
  the 
  greatest 
  

   displacement 
  of 
  the 
  image. 
  

  

  To 
  determine 
  this 
  it 
  is 
  necessary 
  first 
  to 
  find 
  an 
  expression 
  

   for 
  the 
  displacement 
  of 
  the 
  image 
  due 
  to 
  a 
  small 
  rotation 
  

   about 
  any 
  axis. 
  

  

  Fig. 
  1. 
  

  

  Pig. 
  1 
  shows 
  the 
  displacement 
  produced 
  by 
  a 
  convergent 
  

   combination 
  in 
  the 
  general 
  case 
  in 
  which 
  the 
  first 
  and 
  last 
  

   media 
  are 
  different, 
  and 
  in 
  which, 
  therefore, 
  the 
  principal 
  

   and 
  nodal 
  points 
  are 
  not 
  coincident. 
  PiQi 
  and 
  P 
  2 
  Qo 
  are 
  the 
  

   object 
  and 
  image 
  respectively, 
  Hj 
  and 
  H 
  2 
  the 
  principal 
  

  

  