﻿Spherometer 
  and 
  Foco 
  meter. 
  _ 
  95 
  

  

  range, 
  dU 
  the 
  error 
  in 
  R, 
  B 
  the 
  base, 
  and 
  dd 
  the 
  error 
  in 
  

  

  • 
  • 
  „ 
  7/1 
  dR 
  B 
  ■■ 
  , 
  ;• 
  , 
  B 
  . 
  ..- 
  n 
  

  

  angular 
  estimation, 
  then 
  ^=~W"W> 
  but 
  r 
  1S 
  practically 
  

  

  fixed, 
  as 
  its 
  maximum 
  value 
  =--, 
  where 
  8, 
  p 
  are 
  the 
  diameter 
  

  

  and 
  radius 
  of 
  the 
  surface 
  respectively. 
  Hence 
  as 
  dd 
  is 
  

   fixed 
  (=• 
  1 
  minute 
  of 
  arc 
  for 
  snapshot 
  naked-eye 
  work 
  and 
  

   == 
  J- 
  minute 
  when 
  great 
  care 
  is 
  taken) 
  , 
  dR 
  will 
  be 
  a 
  minimum 
  

   when 
  R 
  is 
  a 
  minimum. 
  To 
  determine 
  the 
  range 
  of 
  a 
  real 
  

   image 
  as 
  accurately 
  as 
  possible, 
  we 
  must 
  then 
  take 
  the 
  

   minimum 
  base 
  and 
  minimum 
  range 
  for 
  maximum 
  accuracy. 
  

   In 
  this 
  case 
  it 
  may 
  be 
  advisable 
  to 
  place 
  on 
  the 
  face 
  of 
  the 
  

   prism 
  a 
  convex 
  lens 
  whose 
  focal 
  length 
  is 
  equal 
  to 
  the 
  range 
  

   required. 
  

  

  In 
  the 
  case 
  of 
  the 
  lens 
  used 
  8 
  = 
  6 
  cm. 
  p 
  = 
  16 
  cm.; 
  so 
  that 
  

  

  dU=R.^.dd 
  = 
  2Bdd. 
  

  

  If, 
  then, 
  dd 
  = 
  j 
  i 
  minute 
  == 
  * 
  and 
  R=5 
  cm., 
  then 
  

  

  dR= 
  T 
  J- 
  - 
  mm. 
  

  

  In 
  order 
  to 
  compete 
  in 
  accuracy 
  with 
  this 
  a 
  spherometer 
  

   would 
  require 
  to 
  indicate 
  to 
  -^-Jq-q 
  mm. 
  In 
  short, 
  as 
  a 
  R.F. 
  

   could 
  be 
  constructed 
  to 
  work 
  at 
  much 
  shorter 
  ranges 
  than 
  

   even 
  5 
  cm., 
  there 
  can 
  be 
  no 
  question 
  that 
  for 
  concave 
  sphe- 
  

   rical 
  surfaces 
  the 
  telemetrical 
  method 
  is 
  more 
  accurate 
  than 
  the 
  

   spherometer. 
  

  

  In 
  this 
  way 
  (though 
  not 
  with 
  a 
  very 
  restricted 
  base, 
  for 
  I 
  

   did 
  not 
  realize 
  at 
  the 
  time 
  that 
  the 
  accuracy 
  would 
  be 
  much 
  

   increased 
  by 
  restricting 
  the 
  base 
  and 
  diminishing 
  the 
  range) 
  

   the 
  radius 
  of 
  curvature 
  was 
  found 
  to 
  be 
  15*81. 
  A 
  small 
  

   spherometer 
  gave 
  15'87 
  cm. 
  — 
  the 
  lens 
  face 
  was 
  too 
  small 
  for 
  

   the 
  large 
  spherometer 
  previously 
  mentioned 
  ; 
  the 
  radius 
  of 
  

   the 
  circle 
  of 
  contact 
  of 
  the 
  small 
  spherometer 
  was 
  only 
  1*5 
  cm., 
  

   and 
  as 
  the 
  instrument 
  was 
  home-made 
  and 
  only 
  ordinary 
  care 
  

   had 
  been 
  bestowed 
  on 
  cutting 
  the 
  screw, 
  I 
  attribute 
  the 
  dis- 
  

   crepancy 
  to 
  errors 
  in 
  the 
  spherometer. 
  

  

  The 
  second 
  face 
  when 
  measured 
  telemetrically 
  turned 
  out 
  to 
  

   be 
  very 
  slightly 
  concave, 
  the 
  mean 
  of 
  several 
  measurements 
  

   giving 
  a 
  radius 
  of 
  3300 
  cm. 
  

  

  The 
  thickness 
  of 
  the 
  lens 
  can 
  be 
  readily 
  got 
  on 
  the 
  optical 
  

   bank 
  in 
  this 
  way: 
  — 
  The 
  R.F. 
  stand 
  is 
  so 
  constructed 
  that 
  it 
  

   can 
  be 
  turned 
  through 
  180° 
  about 
  a 
  vertical 
  axis. 
  A 
  fine 
  

   wire 
  carrying 
  a 
  weight 
  at 
  its 
  lower 
  end 
  is 
  supported 
  about 
  the 
  

   middle 
  of 
  the 
  bank 
  and 
  readings 
  of 
  its 
  position 
  are 
  taken 
  with 
  

   the 
  R.F. 
  from 
  both 
  sides. 
  

  

  