﻿Experimental 
  Study 
  of 
  Optical 
  Systems. 
  57 
  

  

  an 
  absolute 
  destruction 
  o£ 
  aberration. 
  In 
  an 
  instrument 
  

   free 
  from 
  aberration 
  the 
  waves 
  arrive 
  at 
  the 
  focal 
  point 
  in 
  

   the 
  same 
  phase. 
  It 
  will 
  suffice 
  for 
  practical 
  purposes 
  if 
  the 
  

   error 
  of 
  phase 
  nowhere 
  exceeds 
  ^X. 
  This 
  corresponds 
  to 
  an 
  

   error 
  of 
  |\ 
  in 
  a 
  reflecting 
  and 
  ^X 
  in 
  a 
  (glass) 
  refracting 
  

   surface, 
  the 
  incidence 
  in 
  both 
  cases 
  being 
  perpendicular 
  "*. 
  

  

  In 
  the 
  case 
  of 
  larger 
  aberrations 
  (implying 
  by 
  that 
  word 
  

   the 
  effect 
  on 
  the 
  " 
  image 
  " 
  of 
  the 
  deviation 
  from 
  sphericity 
  of 
  

   the 
  wave-front) 
  the 
  writer 
  is 
  firmly 
  of 
  the 
  opinion 
  that 
  the 
  

   departure 
  (expressed 
  in 
  wave-lengths) 
  of 
  the 
  wave 
  surface 
  

   as 
  it 
  leaves 
  the 
  dioptric 
  element 
  from 
  a 
  spherical 
  wave 
  

   surface, 
  should 
  form 
  the 
  basis 
  of 
  all 
  statements 
  of 
  imper- 
  

   fections 
  of 
  definition, 
  and 
  believes 
  that 
  such 
  a 
  procedure, 
  

   besides 
  being 
  most 
  rational 
  according 
  to 
  our 
  present 
  know- 
  

   ledge, 
  is 
  at 
  the 
  same 
  time 
  very 
  convenient 
  in 
  application 
  by 
  

   the 
  manufacturer. 
  

  

  The 
  co-ordination 
  of 
  the 
  phenomena 
  observed 
  on 
  this 
  

   interferometer 
  with 
  the 
  image-forming 
  properties 
  of 
  the 
  

   optical 
  system 
  under 
  test 
  is 
  one 
  of 
  the 
  objects 
  of 
  Dr. 
  L. 
  

   SSilberstein's 
  investigations, 
  part 
  of 
  which 
  appear 
  in 
  another 
  

   paper 
  in 
  this 
  Magazine. 
  

  

  (c) 
  The 
  use 
  of 
  aspherical 
  surfaces. 
  

  

  In 
  spite 
  of 
  the 
  great 
  advances 
  in 
  the 
  technique 
  of 
  optical 
  

   manufacture 
  during 
  the 
  past 
  thirty 
  years, 
  the 
  definition 
  of 
  

   actual 
  optical 
  systems 
  still 
  leaves 
  ample 
  room 
  for 
  improvement. 
  

   Even 
  if 
  we 
  confine 
  our 
  remarks 
  to 
  the 
  best 
  makers, 
  it 
  is 
  only 
  

   in 
  certain 
  of 
  the 
  smaller 
  optical 
  instruments 
  that 
  the 
  imper- 
  

   fections 
  of 
  definition 
  are 
  inconsiderable, 
  and 
  even 
  then 
  only 
  on 
  

   the 
  best 
  part 
  of 
  the 
  field 
  of 
  view. 
  This 
  is 
  in 
  great 
  part 
  due 
  

   to 
  the 
  difficulty 
  with 
  a 
  limited 
  choice 
  of 
  suitable 
  dioptric 
  

   materials 
  (for, 
  although 
  extensive, 
  the 
  choice 
  is 
  not 
  as 
  varied 
  

   as 
  the 
  lens 
  designer 
  could 
  wish) 
  of 
  obtaining 
  the 
  results 
  

   desired 
  by 
  calculations 
  based 
  on 
  the 
  utilization 
  of 
  spherical 
  

   surfaces 
  alone. 
  

  

  If 
  we 
  look 
  for 
  the 
  reason 
  why 
  opticians 
  have 
  so 
  far 
  almost 
  

   entirely 
  limited 
  themselves 
  to 
  the 
  production 
  of 
  dioptric 
  

   elements 
  bounded 
  by 
  spherical 
  surfaces, 
  we 
  find 
  it 
  at 
  once 
  in 
  

   the 
  comparative 
  ease 
  with 
  which 
  such 
  surfaces 
  can 
  be 
  generated 
  

   with 
  precision. 
  But, 
  given 
  a 
  sufficient 
  incentive, 
  it 
  cannot 
  

   be 
  doubted 
  that 
  surfaces 
  other 
  than 
  spherical 
  could 
  be 
  

   produced. 
  Indeed 
  this 
  has 
  already 
  been 
  done 
  with 
  an 
  

  

  * 
  Scientific 
  Papers 
  of 
  John 
  William 
  Strutt, 
  Baron 
  Rayleigh, 
  vol. 
  ii. 
  

   Article 
  on 
  Optics, 
  Encyclopedia 
  Britannica, 
  xvii. 
  1884. 
  

  

  