P.O.W,, 
w,  0SW8. 
Prof.  Challis  on  the  Theory  of  the  Aberration  of  Light.     293 
of  0  P-  to  P'  P;  so  that  Wj  Op  which  is  necessarily  the  instru- 
mental direction  of  the  object  at  the  instant  the  image  is  seen  at 
W,,  is  parallel  to  0  P  and  points  to  Pp  the  position  of  the  ob- 
ject at  that  instant.     Hence  there  is  no  aberration. 
Supposing,  now,  the  ray  to  be  retarded  by  passing  through  the 
lenses  and  the  water,  the  argument  above  referred  to  shows  that 
the  image  of  the  object  may  still  be  assumed  to  beat  some  point 
ytx  in  P'O  produced,  although  the  distance  0  W1  will  not  be 
the  same  as  before.  Draw  Pj  Ol  W,  parallel  to  P  0.  Then 
during  the  passage  of  the  light  from  0  to  W,  the  object  moves 
through  a  space  P  P2  greater  than  P  P„  and  the  optical  centre 
through  a  space  0  02  equally  greater  than  0  0^  Thus  the  in- 
strumental line  of  collimation  is  Wj  0^,  which  does  not  point 
to  P2 ;  and  consequently,  if  P2  02  W2  be  drawn  parallel  to 
there  is  a  forward  aberration  equal  to  the  angle 
But  M.  Hoek  found  no  aberration,  the  reading  of 
the  micrometer  for  bisection  of  the  object  being,  quam  proxime, 
the  same  whether  the  telescope  was  directed  northward  or  south- 
ward ;  whereas  if  such  aberration  existed^  it  would  have  had  op- 
posite signs  in  the  two  positions  of  the  telescope.  To  account 
for  this  fact  it  is  necessary  to  admit  that  the  ray,  after  passing 
through  0,  is  dragged  by  the  water  and  the  lenses,  so  that  the 
image  is  formed  at  a  point  Wa  such  that  W1W2  =  0,  02  =  P1P2. 
The  instrumental  direction  of  vision  thus  becomes  W2  02  pointing 
to  the  object  P2;  and  hence  there  is  no  aberration.  I  shall  pre- 
sently endeavour  to  give  a  theory  of  this  dragging  of  the  ray. 
In  the  case  of  the  Greenwich  experiment,  in  which  the  tele- 
scope was  directed  to  a  star,  let  0  (fig.  2)  be  the  position  of  the 
optical  centre  at  any  instant,  and  let 
OS,  pointing  to  the  star,  be  in  the  direc- 
tion of  the  prolongation  of  the  axis. 
Then  the  pencil  of  rays  which,  starting 
from  S,  arrives  at  0  at  the  same  instant 
that  the  optical  centre,  moving  in  the 
direction  from  0'  to  0,  arrives  at  the 
same  point,  proceeds  to  form  an  image 
at  some  point  W2  in  S  0  produced.  In 
the  case  of  no  retardation  by  the  lenses 
and  the  water,  let  the  optical  centre 
move  from  0  to  0lf  while  the  light  by 
which  the  image  is  seen  at  V?l  is  pro- 
pagated from  0  to  Wj.  Then,  since 
"\Vj  0,  is  the  instrumental  direction  of 
the  star  at  the  instant  of  the  bisection 
of  its  image  at  Wv  the  aberration  is  the 
angle  OWjO,,  the  value  of  which  is 
that  given  by  the  usual  formula  of  correction  for  aberration. 
