﻿194 
  Mr. 
  J. 
  H. 
  Vincent 
  on 
  the 
  

  

  normal 
  one 
  is 
  proved 
  by 
  its 
  obeying 
  the 
  formula 
  

  

  v 
  u 
  F 
  

  

  The 
  calculated 
  length 
  of 
  v 
  on 
  the 
  negative 
  was 
  3 
  99 
  cm. 
  

   It 
  actually 
  measured 
  4*05 
  cm. 
  

  

  Fig. 
  5. 
  — 
  Frequency 
  120. 
  

  

  This 
  is 
  from 
  a 
  negative 
  taken 
  with 
  the 
  first 
  form 
  of 
  apparatus. 
  

   The 
  source 
  is 
  placed 
  at 
  the 
  centre 
  of 
  curvature 
  of 
  the 
  circular 
  

   mirror 
  and 
  we 
  should 
  expect 
  to 
  find 
  no 
  focus 
  conjugate 
  to 
  

   the 
  source. 
  But 
  there 
  is 
  a 
  well-defined 
  centre 
  of 
  a 
  series 
  of 
  

   concentric 
  circles 
  ; 
  this 
  centre 
  is 
  distant 
  from 
  the 
  mirror 
  less 
  

   than 
  half 
  the 
  radius 
  of 
  curvature 
  ; 
  no 
  real 
  source 
  can 
  have 
  

   such 
  a 
  conjugate 
  focus 
  if 
  the 
  ripples 
  obey 
  the 
  ordinary 
  laws 
  

   of 
  reflexion. 
  For 
  a 
  normal 
  focus 
  to 
  be 
  formed 
  in 
  this 
  

   position 
  it 
  would 
  be 
  necessary 
  to 
  allow 
  a 
  series 
  of 
  circular 
  

   ripples 
  to 
  impinge 
  on 
  the 
  reflector 
  in 
  such 
  a 
  way 
  that 
  the 
  

   centre 
  of 
  the 
  contracting 
  circles 
  should 
  be 
  behind 
  the 
  mirror. 
  

   The 
  sides 
  of 
  the 
  trough 
  are 
  rectilinear, 
  and 
  the 
  virtual 
  images 
  

   of 
  the 
  source 
  due 
  to 
  the 
  sides 
  of 
  the 
  vessel 
  are 
  outside 
  the 
  

   trough. 
  

  

  From 
  figs. 
  1 
  and 
  2 
  we 
  see 
  that 
  no 
  casual 
  trepidation 
  is 
  

   likely 
  to 
  cause 
  curvilinear 
  waves. 
  Perhaps 
  these 
  spurious 
  

   foci 
  are 
  positions 
  of 
  maximum 
  disturbance 
  consequent 
  upon 
  

   the 
  interference 
  of 
  the 
  ripples 
  from 
  all 
  the 
  real 
  and 
  virtual 
  

   sources. 
  

  

  Fig. 
  6. 
  — 
  Frequency 
  236. 
  

  

  This 
  is 
  another 
  illustration 
  of 
  conjugate 
  foci. 
  The 
  reflector 
  

   was 
  accurately 
  elliptical. 
  It 
  does 
  not 
  look 
  so 
  in 
  the 
  figure, 
  

   owing 
  to 
  the 
  whole 
  of 
  the 
  enclosed 
  area 
  not 
  being 
  photographed, 
  

   due 
  to 
  slight 
  curvature 
  of 
  the 
  surface 
  near 
  the 
  boundary. 
  

   The 
  reflector 
  was 
  cut 
  out 
  of 
  thin 
  ebonite. 
  The 
  plate 
  was 
  

   floated 
  in 
  the 
  mercury 
  and 
  was 
  then 
  buoyed 
  up 
  by 
  under- 
  

   lying 
  chips 
  of 
  wood 
  until 
  the 
  mercury 
  surface 
  was 
  as 
  plane 
  

   as 
  could 
  be 
  arranged. 
  If 
  this 
  is 
  not 
  attended 
  to, 
  little 
  

   reflexion 
  occurs 
  at 
  the 
  edge. 
  

  

  The 
  source 
  can 
  be 
  distinguished 
  by 
  the 
  style 
  of 
  glass, 
  which 
  

   shows 
  as 
  a 
  black 
  mark 
  on 
  the 
  print. 
  The 
  image 
  is 
  approxi- 
  

   mately 
  at 
  the 
  other 
  focus 
  of 
  the 
  ellipse. 
  This 
  is 
  an 
  interesting 
  

   case 
  of 
  conjugate 
  foci 
  and 
  reminds 
  us 
  that 
  the 
  principle 
  of 
  

   least 
  time 
  is 
  really 
  the 
  principle 
  of 
  maximum 
  or 
  minimum 
  

   time. 
  

  

  Fig. 
  7. 
  — 
  Frequency 
  236. 
  

  

  If 
  the 
  source 
  is 
  placed 
  at 
  the 
  centre 
  of 
  the 
  ellipse, 
  the 
  

   surface 
  of 
  the 
  mercury 
  becomes 
  so 
  furrowed 
  by 
  the 
  large 
  

   number 
  of 
  ripples 
  going 
  in 
  different 
  directions 
  that 
  it 
  is, 
  

   regarded 
  as 
  a 
  whole 
  ; 
  almost 
  dark 
  on 
  the 
  ground 
  glass 
  of 
  the 
  

  

  