Wave-Lengths  icitli  a  Modified  Apparatus.  689 
In  this  way,  by  a  process  of  exclusion  the  true  value  is 
ultimately  arrived  at. 
The  details  of  the  best  course  will  depend  somewhat  upon 
circumstances.  It  will  usually  be  convenient  to  take  first  a 
ratio  of  wave-lengths  not  differing  much  from  unity.  Thus 
in  my  actual  operations  the  mechanical  measure  of  the 
distance  between  the  plates  was  4*766  mm.,  and  the  first 
optical  observations  calculated  related  to  the  two  yellow  lines 
of  mercury.  The  ratio  of  wave-lengths,  according  to  the 
measurements  of  Fabry  and  Perot,  is  1*003650;  giving  after 
correction  for  the  measured  diameters  1' 003 641  as  the 
ratio  P'/P.  From  the  mechanical  measure  we  find  as  a 
rough  value  of  P,  P  =  16460.  Calculating  from  this,  we  get 
P'=  16519*92,  not  sufficiently  close  to  an  integer.  Adding 
22  to  P  we  find  as  corresponding  values 
P  =  16482,  P/  =  16542-00, 
giving  P  as  closely  as  it  can  be  found  from  these  obser- 
vations. This  makes  the  value  of  P  for  the  cadmium-red 
ring  observed  at  the  same  time  about  14824,  and  this  should 
not  be  in  error  by  more  than  +30. 
Having  obtained  an  approximate  value  of  P  for  the 
cadmium  red,  we  may  now  conveniently  form  a  table,  of 
which  the  first  column  contains  all  the  so  far  admissible 
(say  60)  integral  values  of  P.  The  other  columns  contain 
the  results  by  calculation  from  (5)  of  comparisons  between 
other  radiations  and  the  cadmium  red.  The  second  and  third 
columns,  for  example,  may  relate  to  cadmium  green  and 
cadmium  blue.  These  almost  suffice  to  fix  the  value  of  P 
but  any  lingering  doubt  will  be  removed  by  additional  columns 
relating  to  mercury  green  and  mercury  yellow  (more  re- 
frangible). An  extract  from  the  table  (p.  690)  may  make  the 
matter  clearer. 
Inasmuch  as  the  ratio  of  cadmium  red  to  cadmium  green  is 
1*2659650,  very  nearly  5  :  4,  only  every  fourth  number  for  red 
is  admissible  on  this  ground  alone.  If  we  consider  a  number 
such  as  14803  not  excluded  by  the  comparison  with  cadmium 
green,  we  see  that  while  it  would  pass  the  mercury  green  test, 
it  is  condemned  by  the  cadmium  blue  and  still  more  by  the 
mercury  yellow  test.  The  only  possible  value  of  P  is  found 
to  be  14814. 
The  criticism  may  probably  suggest  itself  that,  although 
other  values  of  P  may  be  excluded,  the  agreement  of  the  row 
containing  14814  writh  integers  is  none  too  good.  It  is  to 
be  remembered  that  these  observations  were  of  a  preliminary 
character,  and  were  taken  without  the  full  precautions  with 
