Prof.  Challis  on  the  Theory  of  the  Aberration  of  Light,     291 
the  axis  of  the  beam  incident  on  the  object-lens,  and  conse- 
quently does  not  pass  through  0,  the  optical  centre.  Yet,  as  is 
known  from  optics,  if  it  were  not  diverted  from  its  course  by  the 
second  lens,  it  would  form  an  image  at  some  point  Q  in  P  0 
produced.  Supposing,  therefore,  0  A  to  represent  the  direction 
of  the  pointing  of  the  axis  in  the  case  of  any  refracting  telescope, 
according  to  optics  the  course  of  the  ray  from  the  point  P  to 
the  point  where  the  image  of  P  is  formed  in  the  field  of  view  is 
made  up  of  rectilinear  parts  determined  as  to  position  by  the 
lenses  or  mirrors  of  the  instrument,  and  inclined  to  the  axis  by 
angles  having  to  the  angle  POA  certain  constant  ratios  independent 
of  the  particular  position  of  P.  Now,  from  what  has  been  argued 
respecting  the  water-column,  this  theorem  is  as  applicable  to  the 
part  of  the  course  which  lies  within  the  water  as  to  the  other 
parts,  and  is  therefore  true  with  respect  to  the  inclinations  of 
those  rays  to  the  axis  wThich  finally  form  the  image  in  the  field 
of  view  of  the  telescope. 
When  fixed  or  movable  micrometer-wires  or  graduated  scales 
are  placed  in  the  field  of  view  so  as  to  be  distinctly  visible  toge- 
ther with  the  image  of  the  object  for  the  purpose  of  taking  mea- 
sures, the  usual  mode  of  determining  the  value  in  arc  of  the  mi- 
crometer-revolution, or  scale-interval,  by  transits  of  a  star  (as 
was  done  in  the  Greenwich  experiments),  gives  the  means  of  con- 
verting the  final  inclinations  of  the  rays  to  the  axis  into  the 
inclinations  POA  corresponding  to  celestial  arcs,  and  virtually 
transfers  the  image  in  the  field  of  view  to  a  point  Q'  in  P  0  pro- 
duced, the  distance  of  which  from  0  is  very  nearly  the  same  as 
that  of  the  actual  image.  As  far  as  aberration  is  concerned,  it 
makes  no  difference  whether  we  take  the  actual  position  of  the 
image  or  the  virtual  position  in  P  0  produced.  For  the  sake  of 
simplicity  I  shall  always  suppose  the  image  to  be  in  the  virtual 
position. 
It  has  been  supposed  that  the  direction  of  a  ray  refracted  by 
the  object-glass  of  a  telescope  may  be  in  some  degree  altered  by 
the  motion  which  the  glass  has  relative  to  the  course  of  the  inci- 
dent ray  in  consequence  of  the  earth's  orbital  motion.  But 
since  the  refraction  at  any  small  portion  of  a  curved  surface 
takes  place  ultimately  as  if  that  portion  coincided  with  a  tan- 
gent-plane, the  curvature  only  determining  the  degree  of  con- 
vergence of  the  refracted  pencil,  it  follows  that  the  direction  of 
the  refracted  ray  is  not  altered  by  the  motion  of  the  surface,  even 
if  there  be  physical  reasons  for  concluding  that  the  change  of 
direction  from  that  of  incidence  to  that  of  refraction  is  not  in- 
stantaneous, but  occupies  a  very  small  interval  of  time,  provided 
always  that  there  is  no  sensible  angular  motion  of  the  refracting 
surface.     Hence  also  the  motion  of  the  object-lens  produces  no 
U2 
