294     Prof.  Challis  on  the  Theory  of  the  Aberration  of  Light. 
Supposing  the  ray  to  suffer  retardation  by  passing  through 
the  lenses  and  through  a  column  of  water  in  the  telescope-tube, 
the  image  of  S  may  still  be  assumed  to  be  at  some  point  Wx 
in  S  0  produced,  although  at  a  different  distance  from  O.  Draw 
WY  0,  making  the  same  angle  with  OWj  as  in  the  case  of  no 
retardation.  Then,  by  reason  of  the  retardation,  the  optical 
centre  moves  through  a  space  0  02  greater  than  O  Ol9  and  thus 
there  would  appear  to  be  the  additional  aberration  Ox  Wj  02. 
But  M.  Hoek's  experiment  proves  that  this  amount  of  aberration 
is  exactly  neutralized  by  the  dragging  of  the  ray,  the  effect  of 
which  is  to  shift  the  position  of  the  image  from  Wx  to  a  point  W2 
such  that  WXW2  is  parallel  and  equal  to  Oi  02.  Accordingly  the 
instrumental  direction  of  the  star  isW202,  which  is  parallel  to 
Wj  0! ;  so  that  the  aberration  is  the  same  as  if  the  lenses  and  the 
water  had  no  effect.  This  agrees  with  the  result  of  the  Greenwich 
experiment. 
There  remains  the  question,  What  is  the  cause  of  the  dragging 
or  displacement  of  the  ray  ?  and  why  is  the  amount  of  displace- 
ment just  equal  to  the  increment  of  the  aberration  due  to  the 
lenses  and  the  water  ? 
According  to  the  view  I  take  of  the  Undulatory  Theory  of 
Light,  this  question  appears  to  admit  of  the  following  answer. 
I  have  constantly  maintained  that  the  propagation  of  light  is 
caused  to  be  slower  in  a  medium  than  in  vacuum  simply  by  the 
obstacle  to  the  free  movement  of  the  sether  due  to  the  reflex 
action  of  the  finite  atoms  of  the  medium,  the  effect  of  this  action 
at  any  given  point  being  the  result  of  reflections,  unaccompanied 
by  sensible  condensation,  from  a  vast  number  of  neighbouring 
atoms.  Thus  although  the  actual  elasticity  of  the  sether  may  be 
the  same  within  the  medium  as  outside,  there  is  by  this  action 
an  apparent  diminution  of  elasticity,  in  consequence  of  which 
the  relation  v=.dcr  between  the  velocity  v  and  condensation  <rof 
the  fluid  out  of  the  medium  is  changed  to  v=  —  a  within,  u, 
being  the  refractive  index  of  the  medium  and  a'  the  rate  of  pro- 
pagation of  light  in  vacuum.  But  this  being  the  case  when  the 
sether  is  in  motion  and  the  medium  at  rest,  there  must  be  a  cor- 
responding action  when  the  medium  is  in  motion  and  the  fluid 
at  rest.  The  two  actions  are  not,  however,  immediately  compa- 
rable one  with  the  other — because,  with  respect  to  movements 
communicated  to  the  aether  by  the  atoms  of  the  medium,  there 
is  no  parameter  of  the  same  order  as  A,  in  light-undulations,  on 
the  value  of  which  the  amount  by  which  the  propagation  is  re- 
tarded within  the  medium  depends,  being  greater  as  X  is  less. 
We  may,  however,  regard  the  impulsive  action  of  the  atoms  as 
an  extraneous  impressed  force,  which,  if  measured  in  the  same 
manner  as  the  elastic  force  of  the  sether,  will  be  proportional, 
