290     Prof.  Challis  an  the  Theory  of  the  Aberration  of  Light. 
produced  by  the  water.  Having  stated  these  experimental  re- 
sults, I  proceed  to  discuss  generally  the  Theory  of  Aberration, 
with  reference  more  especially  to  the  effect  of  a  water-column  in 
the  tube  of  the  telescope. 
It  will  be  proper  first  to  define  particularly  the  optical  centre 
and  axis  of  an  optical  instrument.  In  the  case  of  a  reflector 
having  a  circular  object-mirror,  the  surface  of  which  is  spherical, 
the  axis  is  perpendicular  to  the  mirror  at  its  middle  point ;  and 
this  point  is  the  optical  centre  of  the  instrument,  because  the 
axes  of  all  centrical  beams  from  points  of  the  object  pass  through 
it,  as  do  also  the  axes  of  all  the  corresponding  reflected  beams. 
In  a  refractor,  such  as  an  astronomical  or  a  Galilean  telescope, 
the  optical  centre  of  the  lens  on  which  the  centrical  beams  from 
the  points  of  the  object  are  immediately  incident  is  the  optical 
centre  of  the  instrument,  because  that  point  is  unique  in  the 
respect  that  the  straight  line  joining  the  foci  of  each  set  of  inci- 
dent and  refracted  centrical  beams  passes,  quam  proxime,  through 
it.  No  such  point  belongs  to  the  second  glass  of  a  compound 
object-glass,  nor  to  the  combination  of  the  two,  if  they  have  dif- 
ferent refractive  powers.  This  optical  centre,  or  its  position, 
will  be  designated  by  the  letter  0.  The  axis  of  a  refractor  cuts 
the  surfaces  of  all  the  lenses  and  mirrors  at  right  angles. 
Next  it  is  to  be  observed  that  any  aberration  that  may  be 
due  to  water  in  the  telescope-tube  is  not  produced  by  the  change 
of  direction  which  the  rays  undergo  by  ordinary  refraction  through 
the  water,  because  the  column,  supposed  to  be  symmetrical  with 
respect  to  the  axis  of  the  instrument,  only  acts  like  an  additional 
lens,  altering  the  focal  length  of  the  telescope  by  changing  the 
direction  of  the  rays,  just  as  the  second  lens  of  the  object-glass 
alters  it  by  being  combined  with  the  first.  There  is  no  more  rea- 
son to  attribute  any  aberrational  effect  to  the  refraction  pro- 
duced by  the  water  than  to  that  produced  by  the  second  lens, 
or  any  other  lens  of  the  instrument.  The  change  of  focal  length 
has  no  effect  on  the  amount  of  aberration,  for  the  reason  that 
aberration  is  sensibly  the  same  in  a  long  telescope  as  in  a 
short  one. 
In  refracting  telescopes  the  axis  of  a  pencil  of  rays  which  pro- 
ceeds from  an  external  point  P  and  eventually  forms  an  image  in 
the  field  of  view,  may  generally  be  assumed  to  be  coincident, 
before  incidence  on  the  object-lens,  with  the  axis  of  the  centrical 
beam  of  which  the  pencil  is  a  part,  and  consequently  to  pass 
through  0,  the  optical  centre  above  defined.  After  transmission 
through  the  first  glass,  the  pencil  would  form,  if  its  course  were 
not  changed  by  the  second  glass,  an  image  at  a  point  Q  on  the 
line  P  0  produced.  In  the  case  of  a  telescope  such  as  the  Gali- 
lean, the  axis  of  the  original  pencil  from  P  is  not  coincident  with 
