292     Prof.  Challis  on  the  Theory  of  the  Aberration  of  Light. 
perceptible  change  in  the  position  of  its  optical  centre,  that  po- 
sition being  determined  by  refractions  at  surfaces  which  may 
be  regarded  as  plane  and  parallel.  Consequently  the  motion 
of  the  telescope  has  no  aberrational  effect.  In  fact,  the  experi- 
ment of  M.  Hoek  gave  no  indication  of  aberration  from  this 
cause,  although  it  was  well  adapted  for  detecting  it,  inasmuch 
as  the  sign  of  such  aberration  would  have  been  different  according 
as  the  telescope  was  directed  northward  or  southward. 
What  has  been  said  in  the  four  preceding  paragraphs  writh 
respect  to  a  refracting  telescope  is  applicable,  mutatis  mutandis, 
to  a  reflector. 
From  the  foregoing  general  considerations  I  proceed  to  the 
theory  of  aberration,  as  it  respects  especially  the  experiments 
made  with  water  in  the  tube  of  the  telescope.  In  speaking  of 
the  motion  of  the  telescope  or  of  its  optical  centre,  it  is  to  be 
understood  that  the  actual  motion  resolved  perpendicularly  to 
the  direction  of  the  pointing  of  the  telescope,  which  is  the  same 
as  the  product  of  the  earth's  motion  and  the  sine  of  the  "  earth's 
way,"  is  alone  taken  into  account,  the  part  resolved  along  the  di- 
rection of  vision  being  ineffective  as  regards  aberration. 
Taking,- first,  the  case  of  M.  Hoek's  experiment,  in  which  the 
telescope  was  directed  in  or  near  the  meridian,  both  northward 
and  southward,  about  noon  or  midnight,  to  an  object  which  could 
be  made  to  revolve  about  a  vertical  axis  with  the  telescope,  let 
0  and  P  (fig.  1)  be  the  positions  of  the  optical  centre  and  the 
object  at  a  given  instant,  and  let  the 
straight  line  joining  0  and  P  be  a  pro- 
longation of  the  axis  of  the  telescope. 
Then  the  ray  which  at  the  given  instant 
arrives  at  0  must  have  left  the  object 
when  it  had  a  position  P'  such  that  if 
the  earth's  motion  be  in  the  direction 
from  P'  to  P,  the  line  FP  is  to  F  0  as 
the  velocity  of  the  object  to  the  velocity 
of  light.   Although  the  direction  P'O  of 
the  incident  ray  is  inclined  to  the  axis- 
direction  0  P,  according  to  the  antece- 
dent argument  the  ray  forms  an  image 
which  may  be  assumed  to  be  at  some 
point  Wx  in  P'  0  produced.     Leaving 
at  first  out  of  account  any  retardations 
of  the  light  resulting  from  the  transmissions  through  the  water 
and  the  lenses,  while  the  light  is  propagated  from  O  to  W,  let 
the  object  move  from  P  to  a  point  Pj  in  P'  P  produced,  and  let 
the  optical  centre  move  through  an  equal  parallel  space  0  Ov 
We  shall  thus  have  the  ratio  of  Wx  0  to  0  01;  the  same  as  that 
wa    w2 
