INTERFERENCE  METHODS  IN  SPECTROSCOPY     333


Red  Green


Green.  Fed

I


If  mw  happens  to  be  a  whole  number  K,  then  the  coin-
cidence will  be  exact,  and  the  appearance  will  be  as  in
Fig.  131.
Generally,  we  put  mw  =  K  +  6,  K.  being  a  whole  number
and  6  lying  between  o  and  i.  When
^  is  =  o  or  I,  then  the  coincidence  is
exact,  as  in  Fig.  131  ;  and  when  6  has
some  intermediate  value,  the  coincidence
is  inexact,  as  in  Fig.  130.  If  a  and
a*  are  the  distances  AB,  B'A'  in  Fig.
130  (strictly  speaking  the  differences  in
path  denoted  by  the  distances  AB  and
B'A'),  then—


Fig.  131.
6  =


a  -\-  a


It  is  possible  when  \  and  A.'  are  not  too   close   to  measure
6  from  the  observations  on  a  coincidence.
Clearly  from  the  above  P  is  inversely  proportional  to  the
difference  between  X  and  'S! ;  if  P  corresponds  to  four  or  five
fringes  one  can  observe  the  coincidences  with  accuracy.  When
P  is  about  fifteen  fringes,  observations  of  6  are  more  difiScult ;
but  when  P  is  very  large,  as  with  the  D  rays  of  sodium,  it  is
better  to  observe  the  regions  of  complete  disagreement  of  the
fringes,  for  in  this  case  the  observations  are  impossible  on  the
coincidences,  as  the  fringes  belonging  to  the  two  systems
are  so  alike  in  colour  and  are  so  confused  with  one  another.
The  condition  of  complete  disagreement  is,  however,  easily
estimated,  and  then,  of  course,  we  have —

A  =  (»«  +  J)P.
In  all  interference  measurements  the  standards  of  reference
are  the  red,  green,  and  blue  radiations  of  cadmium,  determined
by  Michelson  to  have  the  following  wave-lengths —

^K  =  6438-4722  A.U.
