﻿Nodal-Slide 
  Method 
  of 
  Focometry. 
  25 
  

  

  coincide 
  with 
  H 
  2 
  , 
  then 
  Z=— 
  233, 
  m 
  = 
  0, 
  and 
  the 
  dis- 
  

   placement 
  under 
  the 
  same 
  conditions 
  would 
  have 
  been 
  

   0*0087 
  cm. 
  

  

  These 
  small 
  displacements 
  may 
  also 
  be 
  calculated 
  more 
  

   simply 
  by 
  using 
  the 
  approximate 
  formula 
  

  

  Ss=,^-M=-f.Sl 
  (5) 
  

  

  In 
  the 
  first 
  case 
  ^——2*6 
  and 
  85 
  = 
  0*0082, 
  in 
  the 
  second 
  

   case 
  / 
  9 
  =— 
  3*4 
  and 
  85 
  = 
  0*0062: 
  while 
  in 
  the 
  ordinary 
  

   nodal-slide 
  method 
  Z=-2'43 
  and 
  & 
  = 
  0-0087. 
  These 
  

   results 
  agree 
  closely 
  with 
  those 
  obtained 
  by 
  the 
  more 
  

   exact 
  formula. 
  Or, 
  to 
  put 
  the 
  matter 
  rather 
  differently, 
  

   if 
  we 
  suppose 
  the 
  smallest 
  observable 
  displacement 
  to 
  

   be 
  0*01 
  cm., 
  then 
  the 
  distances 
  through 
  which 
  the 
  axis 
  

   would 
  have 
  to 
  be 
  moved 
  from 
  the 
  nul 
  position 
  to 
  produce 
  

   this 
  displacement 
  would 
  be 
  1*20, 
  1*61, 
  and 
  1*15 
  mm. 
  in 
  the 
  

   three 
  cases 
  respectively. 
  These 
  examples 
  show^ 
  that 
  in 
  this 
  

   particular 
  case 
  the 
  nul 
  point 
  can 
  be 
  determined 
  with 
  greater 
  

   accuracy 
  by 
  the 
  ordinary 
  nodal-slide 
  method 
  than 
  by 
  the 
  

   general 
  method. 
  

  

  If, 
  however, 
  a 
  convergent 
  combination 
  forming 
  a 
  real 
  

   image, 
  as 
  in 
  fig. 
  1, 
  had 
  been 
  employed, 
  the 
  nul 
  point 
  

   would 
  lie 
  between 
  N 
  x 
  and 
  N 
  2 
  . 
  and 
  its 
  position 
  could 
  be 
  

   determined 
  with 
  greater 
  accuracy 
  by 
  the 
  general 
  method 
  

   than 
  by 
  the 
  ordinary 
  nodal-slide 
  method, 
  in 
  this 
  case 
  the 
  

   nul 
  point 
  is 
  indicated 
  by 
  O 
  , 
  which 
  is 
  the 
  point 
  of 
  inter- 
  

   section 
  of 
  QiQ 
  2 
  with 
  the 
  optic 
  axis. 
  

  

  Again, 
  if, 
  with 
  the 
  same 
  convergent 
  combination, 
  a 
  virtual 
  

   image 
  were 
  formed, 
  a 
  case 
  not 
  likely 
  to 
  arise 
  in 
  the 
  deter- 
  

   mination 
  of 
  focal 
  length, 
  the 
  magnification 
  would 
  be 
  positive 
  

   and 
  greater 
  than 
  unity. 
  The 
  nul 
  point 
  would 
  therefore 
  lie 
  

   on 
  the 
  side 
  of 
  Nj 
  remote 
  from 
  N 
  2 
  , 
  and 
  its 
  position 
  could 
  be 
  

   determined 
  by 
  the 
  general 
  method 
  with 
  greater 
  or 
  less 
  

   accuracy 
  than 
  by 
  the 
  ordinary 
  nodal-slide 
  metliod 
  according 
  

   as 
  it 
  is 
  at 
  a 
  distance 
  from 
  Nj 
  less 
  or 
  greater 
  than 
  a 
  

   respectively. 
  

  

  If 
  the 
  nodal 
  points 
  are 
  determined 
  by 
  either 
  of 
  the 
  two 
  

   direct 
  nodal-slide 
  methods, 
  which 
  will 
  here 
  be 
  distinguished 
  

   asthejirst 
  and 
  second 
  nul 
  methods 
  respectively, 
  the 
  principal 
  

   foci 
  and. 
  focal 
  lengths 
  may 
  be 
  most 
  readily 
  and 
  directly 
  

   found 
  by 
  measuring 
  the 
  distances 
  from 
  the 
  nul 
  point 
  of 
  the 
  

   object 
  in 
  the 
  first 
  method 
  and 
  of 
  the 
  image 
  in 
  the 
  second. 
  

  

  Xow 
  in 
  obtaining 
  the 
  position 
  of 
  the 
  image 
  there 
  will 
  be 
  

   a 
  certain 
  range 
  along 
  the 
  axis 
  within 
  which 
  the 
  object 
  may 
  

  

  