532 
Mr.  J.  Walker  on  Talbot's  Lh 
centre  of  the  system  and  consequently  of   these  minima  on 
passing  from  one  wave-length  to  the  next*. 
The  case  of  the  minima  of  an  odd  order  is,  however, 
different ;  for  as  the  wave-length  alters,  there  is  not  only  a 
shift  due  to  the  dispersion  of  the  light,  but  also  a  dispersion 
due  to  the  varying  displacement  caused  by  the  change  in  the 
retardation  introduced  by  the  plate,  and  if  these  balance  one 
another,  the  bands  corresponding  to  different  wave-lengths 
will  be  superposed  and  will  therefore  be  rendered  visible. 
It  is  clear  then  that  the  plate  must  be  so  placed  that  the 
dispersion  of  the  bands  that  it  produces  must  oppose  the 
dispersion  of  the  light  introduced  by  the  prism  or  the  grating. 
Thus  the  retardation  of  phase  caused  by  the  plate  increasing 
with  decreasing  wave-length,  the  plate  must  be  placed  over 
the  right  or  the  left  half  of  the  aperture,  according  as  the 
dispersion  in  the  focal  plane  of  the  telescope  from  red  to  blue 
is  from  right  to  left  or  from  left  to  right. 
2.  The  following  analysis  of  what  takes  place  may  perhaps 
tend  to  make  the  foregoing  explanation  somewhat  clearer. 
Let  us  suppose  that  the  light,  falling  normally  upon  the 
aperture,  is  nearly  monochromatic,  as  is  the  case  when  a 
small  portion  of  the  spectrum  is  considered,  and  that  the  slit 
of  a  spectroscope  is  placed  in  the  focal  plane  of  the  telescope 
in  a  direction  perpendicular  to  the  bands  of  the  diffraction 
pattern. 
Then  the  light  will  be  drawn  out  into  a  short  spectrum, 
and  the  aperture  being  uncovered,  this  will  be  traversed  by 
bands  running  along  it,  that  are  nearly  straight  and  parallel 
to  the  sides  of  the  spectrum  (fig.  1). 
Fis.  1.  Fig.  2. 
a-\a,b2     4^4^ 
A 
*&*&»%>"£>*** 
X-SX 
\\ 
\\ 
\ 
A-Qj 
When  half  of  the  aperture  is  covered  by  the  retarding 
plate,  the  bands  (a)  of  an  even  order  will  retain  their  positions, 
*  The  slight  change  in  the  distance  between  the  minima  as  the  wave- 
length alters,  may  he  left  out  of  account  when  a  small  region  of  the 
spectrum  is  considered. 
