688  Lord  Bayleigh  :   Some  Measurements  of 
Consider  first  the  cadmium  radiation  X.  It  gives  a  system  of 
rings.  Let  P  be  the  ordinal  number  o£  one  of  these  rings, 
for  example  the  first  counting  from  the  centre.  This  integer 
is  supposed  known.  The  order  of  interference  at  the  centre 
will  be  p=P  i-  e.  We  have  to  determine  this  number  e,  lying 
ordinarily  between  0  and  1.  The  diameter  of  the  ring  under 
consideration  increases  with  e ;  so  that  a  measure  of  the 
diameter  allows  us  to  determine  the  latter.  Let  e*  be  the 
thickness  of  the  plate  of  air.  The  order  of  interference  at 
the  centre  is  p  —  2ej\.  This  corresponds  to  normal  passage. 
At  an  obliquity  i  the  order  of  interference  is  p  cos  i.  Thus 
if  x  be  the  angular  diameter  of  the  ring  P,  p  cos  -J  x  —  F  ;  or 
since  x  is  small, 
P 
-*(»♦!> 
In  like  manner,  from  observations  upon  another  radiation  X1 
to  be  compared  with  X,  we  have 
P-: 
*-(>+?)■ 
whence  if  e  be  treated  as  an  absolute  constant, 
x=f  (1+«~r) (*> 
The  ratio  X/X1  is  thus  determined  as  a  function  of  the 
angular  diameters  a?,  x   and  of  the  integers  P,  P'. 
One  of  the  principal  variations  in  my  procedure  relates  to 
the  manner  in  which  P  is  determined.  MM.  Fabry  and 
Perot  f  say  : — "  L'etalon,  tine  fois  regie,  est  mesure  en 
fonction  des  longueurs  d'onde  du  cadmium,  par  les  methodes 
que  nous  avons  precedement  decrites  ;  l'emploi  de  interfero- 
metre  est  necessaire  pour  cela/"  I  wished  to  dispense  with  the 
sliding  interferometer,  and  there  is  no  real  difficulty  in 
determining  P  without  it.  For  this  purpose  we  use  a  modified 
form  of  (4),  viz. : — 
P'       X(.      x2      x'2\ 
expressing  P'/P  as  a  function  of  X/X\  regarded  as  known,  and 
of  the  diameters.  To  test  a  proposed  (integral)  value  of  P,  we 
calculate  P'  from  (5).  If  the  result  deviates  from  an  integer 
by  more  than  a  small  amount  (depending  upon  the  accuracy 
of  the  observations),  the  proposed  value  of  P  is  to  be  rejected. 
*  Now  with  an  altered  meaning. 
t  Loc.  at.  p.  112. 
