﻿and 
  Anchor-Bin 
  (j 
  Wave-Fronts. 
  485 
  

  

  Toric 
  wave-fronts 
  can 
  be 
  produced 
  by 
  constructing 
  a 
  con- 
  

   cave 
  reflector, 
  of 
  the 
  form 
  generated 
  by 
  making 
  an 
  ellipse., 
  

   or 
  any 
  portion 
  of 
  an 
  ellipse, 
  revolve 
  through 
  any 
  convenient 
  

   angle 
  round 
  an 
  ordinate 
  erected 
  at 
  one 
  focus 
  O 
  of 
  the 
  ellipse; 
  

   and 
  employing 
  it 
  to 
  reflect 
  rays 
  diverging 
  from 
  a 
  small 
  

   source 
  of 
  light 
  at 
  this 
  focus. 
  The 
  length 
  of 
  path 
  is 
  the 
  same 
  

   for 
  all 
  once-reflected 
  rays 
  from 
  O 
  to 
  the 
  circle 
  traced 
  by 
  the 
  

   other 
  focus 
  A, 
  and 
  will, 
  therefore, 
  be 
  the 
  same 
  for 
  all 
  such 
  

   rays 
  from 
  O 
  to 
  a 
  tore 
  having 
  this 
  circular 
  axis. 
  

  

  Figs. 
  2, 
  3, 
  4 
  represent 
  an 
  experimental 
  illustration. 
  Fig. 
  2 
  

  

  Fig. 
  2. 
  

  

  contains 
  an 
  axial 
  section 
  of 
  a 
  reflecting 
  surface 
  of 
  revolution; 
  

   the 
  section 
  being 
  made 
  up 
  of 
  portions 
  of 
  two 
  equal 
  ellipses 
  of 
  

   eccentricity 
  J. 
  O 
  and 
  A, 
  A' 
  are 
  points 
  corresponding 
  to 
  O 
  

   and 
  A 
  in 
  fig. 
  1. 
  A 
  point 
  source 
  at 
  O 
  is 
  provided 
  by 
  means 
  

   of 
  an 
  opaque 
  disk 
  pierced 
  with 
  a 
  small 
  hole 
  at 
  O 
  ; 
  the 
  disk 
  

   being 
  carried 
  by 
  an 
  axis 
  in 
  its 
  own 
  plane, 
  coinciding 
  with 
  a 
  

   diameter 
  of 
  the 
  bounding 
  circle 
  of 
  the 
  reflector, 
  as 
  shown 
  in 
  

   figs. 
  3, 
  4 
  (p. 
  486), 
  which 
  represent 
  the 
  reflector 
  supported 
  on 
  a 
  

   stand, 
  with 
  its 
  bounding 
  plane 
  vertical, 
  the 
  axis 
  of 
  rotation 
  of 
  

   the 
  disk 
  being 
  also 
  vertical. 
  By 
  rotation 
  round 
  this 
  axis 
  the 
  

   disk 
  can 
  be 
  made 
  to 
  face 
  a 
  source 
  of 
  light 
  at 
  its 
  own 
  level, 
  at 
  

   any 
  obliquity 
  to 
  the 
  bounding 
  plane. 
  In 
  fig. 
  2 
  a 
  beam 
  is 
  shown 
  

   focussed 
  on 
  the 
  hole 
  by 
  a 
  lens. 
  The 
  beam 
  may 
  be 
  furnished 
  

   by 
  a 
  lantern, 
  or 
  by 
  a 
  bright 
  lamp-flame 
  properly 
  screened. 
  

   Widening 
  the 
  angle 
  of 
  the 
  pencil 
  given 
  by 
  the 
  lens 
  lengthens 
  

   and 
  at 
  the 
  same 
  time 
  time 
  brightens 
  the 
  focal 
  lines. 
  

  

  The 
  primary 
  line 
  will 
  be 
  a 
  circle 
  having 
  A 
  A' 
  for 
  diameter, 
  

   and 
  will 
  be 
  always 
  real. 
  The 
  secondary 
  line 
  will 
  coincide 
  

   with 
  the 
  axis 
  of 
  revolution, 
  and 
  will 
  be 
  real 
  or 
  virtual 
  ac- 
  

   cording 
  to 
  the 
  position 
  of 
  the 
  area 
  of 
  incidence. 
  For 
  inci- 
  

   dence 
  at 
  the 
  extremity 
  of 
  the 
  ordinate 
  through 
  A, 
  the 
  reflected 
  

   ray 
  is 
  parallel 
  to 
  the 
  axis, 
  and 
  the 
  secondary 
  line 
  goes 
  off 
  to 
  

  

  