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  483 
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  LV. 
  On 
  Focal 
  Lines, 
  and 
  Anchor-Ring 
  Wave-Fronts. 
  

   By 
  Prof. 
  J. 
  D. 
  Everett, 
  F.R.S* 
  

  

  WHEN 
  a 
  small 
  cone 
  of 
  rays 
  is 
  obliquely 
  incident 
  on 
  a 
  

   spherical 
  reflecting 
  or 
  refracting 
  surface, 
  the 
  rays 
  

   after 
  reflection 
  or 
  refraction 
  no 
  longer 
  compose 
  a 
  true 
  cone. 
  

   Instead 
  of 
  meeting 
  in 
  a 
  point 
  they 
  form 
  a 
  narrow 
  neck; 
  and 
  

   this 
  neck 
  is 
  flattened 
  in 
  two 
  places 
  called 
  the 
  primary 
  and 
  

   secondary 
  foci, 
  the 
  planes 
  of 
  flattening 
  being 
  at 
  right 
  angles 
  

   to 
  each 
  other. 
  Optical 
  writers 
  give 
  the 
  name 
  focal 
  lines 
  to 
  

   the 
  sections 
  of 
  the 
  pencil 
  made 
  at 
  these 
  two 
  places 
  by 
  planes 
  

   perpendicular 
  to 
  the 
  axis 
  of 
  the 
  pencil 
  ; 
  but 
  it 
  would 
  be 
  more 
  

   appropriate 
  to 
  give 
  the 
  name 
  to 
  the 
  sections 
  which 
  most 
  

   nearly 
  resemble 
  lines, 
  whatever 
  angle 
  they 
  may 
  make 
  with 
  

   the 
  axis 
  of 
  the 
  pencil. 
  

  

  Clearness 
  of 
  conception, 
  in 
  intricate 
  matters, 
  is 
  greatly 
  

   aided 
  by 
  sharply 
  defined 
  illustration 
  ; 
  and 
  I 
  wish 
  to 
  call 
  

   attention 
  to 
  a 
  case 
  (which 
  appears 
  to 
  have 
  been 
  hitherto 
  

   overlooked) 
  in 
  which 
  all 
  the 
  rays, 
  even 
  of 
  a 
  large 
  pencil, 
  

   pass 
  accurately 
  through 
  two 
  definite 
  lines 
  : 
  one 
  of 
  these 
  lines 
  

   being 
  a 
  circular 
  arc 
  cutting 
  the 
  pencil 
  at 
  right 
  angles 
  ; 
  and 
  

   the 
  other 
  being 
  a 
  straight 
  line, 
  which 
  may 
  have 
  any 
  inclina- 
  

   tion 
  to 
  the 
  axis 
  of 
  the 
  pencil. 
  

  

  The 
  case 
  is 
  that 
  in 
  which 
  the 
  wave-front 
  in 
  one 
  of 
  its 
  

   positions 
  is 
  a 
  tore 
  (or 
  anchor-ring). 
  

  

  A 
  tore 
  may 
  be 
  defined 
  as 
  the 
  surface 
  generated 
  by 
  the 
  

   revolution 
  of 
  a 
  circle 
  round 
  a 
  fixed 
  straight 
  line 
  in 
  its 
  plane 
  ; 
  

   this 
  line 
  we 
  shall 
  refer 
  to 
  as 
  the 
  axis 
  of 
  revolution. 
  A 
  lore 
  

  

  Fio-. 
  1. 
  

  

  has 
  also 
  what 
  may 
  be 
  called 
  a 
  circular 
  axis 
  — 
  the 
  circle 
  gene- 
  

   rated 
  by 
  the 
  motion 
  of 
  the 
  centre 
  of 
  the 
  revolving 
  circle. 
  

   In 
  the 
  figure 
  QOS 
  is 
  the 
  axis 
  of 
  revolution, 
  the 
  centre 
  of 
  

   the 
  tore, 
  and 
  OA 
  the 
  radius 
  of 
  the 
  circular 
  axis. 
  P 
  is 
  any 
  

  

  * 
  Communicated 
  by 
  the 
  Physical 
  Society: 
  read 
  February 
  28, 
  1902. 
  

  

  