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  Aberration 
  is 
  usually 
  given 
  as 
  proportional 
  to 
  the 
  sine 
  of 
  the 
  

   angle 
  between 
  the 
  ray 
  and 
  the 
  direction 
  of 
  motion 
  of 
  the 
  earth, 
  

   but 
  in 
  this 
  case 
  a 
  refers 
  to 
  the 
  wave-front 
  and 
  not 
  to 
  the 
  ray, 
  so 
  

   that 
  cos 
  a 
  is 
  the 
  function 
  that 
  should 
  be 
  used, 
  and 
  it 
  can 
  easily 
  

   be 
  shown 
  that 
  the 
  numerical 
  value 
  of 
  the 
  aberration 
  is 
  equal 
  to 
  

   T)'£ 
  cos 
  a. 
  The 
  last 
  two 
  terms 
  of 
  the 
  equation, 
  therefore, 
  cancel 
  

   one 
  another, 
  and 
  the 
  equation 
  reduces 
  to 
  the 
  usual 
  well-known 
  

   form. 
  

  

  William 
  B. 
  Caetmel, 
  

   Fellow 
  in 
  Physics, 
  

   University 
  of 
  Nebraska, 
  

  

  Lincoln, 
  Nebr. 
  

  

  University 
  College, 
  Sheffield, 
  

   March 
  20, 
  1902. 
  

  

  Me. 
  Caetmel 
  seems 
  to 
  suppose 
  that 
  I 
  have 
  attempted 
  to 
  give 
  

   an 
  explanation 
  of 
  a 
  term 
  in 
  the 
  expression 
  for 
  the 
  position 
  of 
  

   the 
  central 
  fringe, 
  whereas 
  I 
  have 
  introduced 
  the 
  term 
  because, 
  

   for 
  the 
  reasons 
  given 
  in 
  §§ 
  4, 
  15, 
  it 
  appeared 
  to 
  be 
  called 
  for. 
  

   I 
  do 
  not 
  see 
  that 
  Mr. 
  Cartmel 
  has 
  met 
  that 
  argument. 
  I 
  may 
  say 
  

   that 
  before 
  the 
  paper 
  was 
  published 
  I 
  had 
  a 
  good 
  deal 
  of 
  discussion 
  

   with 
  Dr. 
  Larmor 
  on 
  this 
  very 
  point. 
  His 
  argument 
  was 
  based 
  on 
  

   the 
  minimum 
  path 
  for 
  relative 
  rays, 
  and 
  he 
  suggested 
  that 
  the 
  

   effect 
  might 
  be 
  counteracted 
  by 
  the 
  action 
  of 
  the 
  drift 
  in 
  altering 
  

   the 
  refraction 
  through 
  the 
  lenses 
  of 
  the 
  instrument. 
  This 
  is 
  the 
  

   only 
  way 
  I 
  can 
  see 
  out 
  of 
  the 
  difficulty 
  ; 
  but 
  even 
  then 
  this 
  action 
  

   could 
  only 
  be 
  produced 
  between 
  the 
  object-glass 
  and 
  the 
  image, 
  

   whereas 
  the 
  effect 
  itself 
  depends 
  principally 
  on 
  the 
  distance 
  of 
  

   the 
  object-glass 
  from 
  the 
  place 
  observed. 
  

  

  The 
  correction 
  of 
  cos 
  a 
  for 
  sin 
  a 
  in 
  the 
  aberration 
  effect 
  was 
  

   noticed, 
  but 
  overlooked 
  in 
  the 
  final 
  revise. 
  I 
  cannot, 
  however, 
  

   follow 
  Mr. 
  Cartmel 
  in 
  his 
  statement 
  that 
  it 
  can 
  be 
  shown 
  that 
  it 
  

   will 
  numerically 
  cancel 
  the 
  former 
  effect. 
  In 
  fact, 
  if 
  so 
  the 
  matter 
  

   may 
  be 
  looked 
  at 
  from 
  the 
  opposite 
  point 
  of 
  view 
  as 
  completely 
  

   annulling 
  any 
  aberration 
  effect 
  — 
  which 
  would 
  be 
  a 
  curious 
  result 
  

   in 
  itself— 
  besides 
  verifying 
  the 
  reality 
  of 
  the 
  effect 
  he 
  calls 
  in 
  

   question. 
  

  

  The 
  aberration 
  displacement 
  at 
  the 
  focal 
  plane 
  of 
  the 
  instrument 
  

   would 
  be 
  F 
  £ 
  cos 
  a, 
  w 
  hereas 
  that 
  due 
  to 
  what 
  I 
  have 
  called 
  the 
  cos 
  a 
  

   effect 
  would 
  be 
  (d-f-F)£ 
  cos 
  a, 
  where 
  "F 
  is 
  the 
  focal 
  length 
  of 
  the 
  

   object-glass 
  and 
  d 
  its 
  distance 
  from 
  the 
  observed 
  fringe. 
  As 
  a 
  

   matter 
  of 
  fact, 
  if 
  the 
  curves 
  of 
  the 
  observations 
  published 
  be 
  

   plotted 
  for 
  a 
  complete 
  revolution 
  of 
  the 
  instrument, 
  they 
  show 
  

   evidence 
  of 
  both 
  a 
  cos 
  a 
  and 
  a 
  cos 
  2 
  a 
  effect. 
  But 
  too 
  much 
  stress 
  

   should 
  not 
  be 
  laid 
  on 
  this. 
  W. 
  M. 
  Hicks. 
  

  

  