﻿A 
  Telemetrical 
  Spherometer 
  and 
  Focometer. 
  91 
  

  

  great 
  accuracy 
  is 
  required, 
  it 
  certainly 
  saves 
  an 
  enormous 
  

   amount 
  of 
  labour 
  in 
  cases 
  where 
  an 
  error 
  of 
  1 
  or 
  2 
  per 
  cent, 
  

   is 
  unimportant. 
  

  

  The 
  experience 
  gained 
  in 
  the 
  construction 
  of 
  the 
  present 
  

   instrument 
  shows 
  that 
  it 
  would 
  be 
  quite 
  feasible 
  to 
  increase 
  

   the 
  number 
  of 
  elements 
  to 
  several 
  hundred, 
  or 
  even 
  to 
  a 
  

   thousand, 
  with 
  a 
  proportional 
  increase 
  in 
  the 
  accuracy 
  of 
  the 
  

   integrations. 
  

  

  Finally, 
  it 
  is 
  well 
  to 
  note 
  that 
  the 
  principle 
  of 
  summation 
  

   here 
  employed 
  is 
  so 
  general 
  that 
  it 
  may 
  be 
  used 
  for 
  series 
  of 
  

   any 
  functions 
  by 
  giving 
  to 
  the 
  poiuts 
  p 
  the 
  motions 
  corre- 
  

   sponding 
  to 
  the 
  required 
  functions, 
  instead 
  of 
  the 
  simple 
  

   harmonic 
  motion 
  furnished 
  by 
  the 
  eccentrics. 
  A 
  simple 
  

   method 
  of 
  effecting 
  this 
  change 
  would 
  be 
  to 
  cut 
  metal 
  tem- 
  

   plates 
  of 
  the 
  required 
  forms 
  and 
  mount 
  them 
  on 
  a 
  common 
  

   axis. 
  In 
  fact, 
  the 
  harmonic 
  motion 
  of 
  the 
  original 
  machine 
  

   was 
  thus 
  produced. 
  

  

  VII. 
  A 
  Telemetrical 
  Spherometer 
  and 
  Focometer. 
  

   By 
  Prof. 
  W. 
  Stroud, 
  JD.Sc, 
  M.A* 
  

  

  HAYING- 
  been 
  engaged 
  for 
  the 
  past 
  eight 
  years 
  in 
  con- 
  

   junction 
  with 
  Prof. 
  Barr 
  in 
  the 
  construction 
  and 
  

   perfecting 
  of 
  naval 
  range-finders, 
  it 
  was 
  natural 
  that 
  I 
  should 
  

   turn 
  my 
  attention 
  to 
  the 
  possible 
  application 
  of 
  telemetrical 
  

   principles 
  to 
  physical 
  measurement. 
  

  

  One 
  very 
  obvious 
  application 
  is 
  to 
  the 
  determination 
  of 
  (1) 
  

   the 
  radius 
  of 
  curvature 
  of 
  a 
  concave 
  and 
  especially 
  of 
  a 
  convex 
  

   surface, 
  and 
  (2) 
  the 
  focal 
  length 
  of 
  a 
  convex 
  and 
  especially 
  

   of 
  a 
  concave 
  lens. 
  The 
  problem 
  of 
  finding 
  the 
  position 
  of 
  

   the 
  image 
  of 
  an 
  object 
  in 
  a 
  convex 
  mirror 
  or 
  a 
  concave 
  lens 
  

   is 
  essentially 
  a 
  range-finding 
  problem. 
  

  

  For 
  the 
  particular 
  purpose 
  in 
  view 
  the 
  most 
  suitable 
  form 
  

   of 
  range-finder 
  is 
  a 
  constant-range 
  instrument, 
  i. 
  e. 
  an 
  instru- 
  

   ment 
  (whose 
  optical 
  parts 
  are 
  rigidly 
  fixed) 
  which 
  can 
  be 
  

   translated 
  along 
  an 
  optical 
  bank 
  and 
  will 
  indicate 
  when 
  an 
  

   object 
  or 
  image 
  is 
  at 
  the 
  specified 
  range. 
  The 
  mode 
  of 
  action 
  

   of 
  the 
  instrument 
  will 
  thus 
  be 
  very 
  like 
  that 
  of 
  an 
  ordinary 
  

   short-focus 
  telescope 
  as 
  commonly 
  used 
  on 
  optical 
  banks, 
  but 
  

   a 
  short-focus 
  telescope 
  is 
  essentially 
  bad 
  as 
  a 
  range-finder, 
  

   and 
  that 
  for 
  the 
  following 
  reasons 
  : 
  — 
  

  

  (1) 
  As 
  is 
  well 
  known, 
  when 
  using 
  such 
  a 
  telescope 
  it 
  

   is 
  advisable 
  to 
  cover 
  up 
  the 
  middle 
  portion 
  of 
  the 
  objective 
  

  

  * 
  Communicated 
  by 
  the 
  Physical 
  Society 
  : 
  read 
  Oct. 
  29, 
  1897. 
  

  

  