Wave-Lengths  with  a  Modified  Apparatus.  691 
factor,  we  denote  the  thicknesses  for  the  two  wave-lengths 
by  **a,  e\> ,  we  have 
P    "   ^A    V  ' 
and  accordingly  in  place  of  (5) 
F=XVA1+8-"8-J (6) 
But  although  I  was  prepared  to  find  the  calculated  values 
of  P'  differing  somewhat  from  integers,  I  was  disturbed  by  the 
amount  and  at  first  by  the  direction  of  the  difference.  For 
in  their  paper  of  1899  *  Fabry  and  Perot  remark  : — "  Le 
surface  optique  du  metal  pour  la  radiation  rouge  est,  par 
suite,  situee  un  peu  plus  profondement  dans  le  metal  que 
celle  cle  la  lumiere  verte,  et  a  une  distance  de  4  fiii."  At 
this  rate  ek  (red)  would  exceed  ek,  (green),  and  the  introduction 
of  the  new  factor  in  (6)  would  increase,  and  not  remove,  the 
discrepancy.  It  would  seem,  however,  that  the  passage  above 
quoted  is  in  error  and  inconsistent  with  the  discussion  given 
in  the  later  paper  t«  itself  indeed  embarrassed  by  several 
misprints  J. 
The  amount  of  the  correction  required  to  bring  the  number 
for  cadmium  green  up  to  an  integer — about  2J  parts  in  a 
million — is  2\  times  as  great  as  one  would  expect  from  Fabry 
and  Perot's  indications  §.  As  to  this,  it  may  be  observed 
that  the  wave-lengths  employed  in  the  calculation  of  the 
cadmium  radiations  are  those  of  Michelson,  and  were  obtained 
by  a  method  free  of  the  complication  now  under  discussion. 
If  these  are  correct,  as  there  is  no  reason  to  doubt,  and  if 
there  is  no  mistake  in  the  identification  of  the  ring — and 
there  can  be  none  here — it  follows  that  the  change  of  optical 
thickness  in  passing  from  red  to  green  is  determined  by  the 
numbers  given  and  may  be  used  to  correct  ratios  of  wave- 
lengths not  previously  known  with  precision. 
If  we  wish  to  make  the  results  of  the  present  method 
entirely  independent,  we  must  obtain  material  from  obser- 
vation sufficient  to  allow  the  variation  of  thickness  with  wave- 
length to  be  eliminated,  that  is,  we  must  use  the  same  silvered 
*  Ann.  cle  Chimie,  xvi.  p.  311. 
t  L.  c.  pp.  120-124. 
X  Of  these  it  may  be  worth  while  to  note  that  the  sign  of  0-6  pp  on 
p.  123,  line  5  should  apparently  be  —  instead  of  + . 
§  It  is  known  that  the  effect  depends  upon  the  thickness  of  the  silver 
films ;  perhaps  also  upon  the  process  used  in  silvering*  and  upon  the  con- 
dition of  the  surfaces  in  other  respects.  Surfaces  that  have  stood  some 
time  in  air  are  almost  certain  to  be  contaminated  with  layers  of  volatile 
areasv  matter. 
