Refraction  of  Light  by  intensely  Opaque  Matter.         337 
D  =  I ^ — —  H o tab  +  cubes  in  o, 
™     .      R2e-2'"(flS)2      1  +  E26-2-  .  .         .      .     , 
D'  =  1 ^ — £ ^ eao  -f  cubes  in  6 ; 
.  D'-D ssRVS2! sin  2a-wS(l  +  R2 cos 2a), 
D'  +  D  =  2-RVS2cos2a-R2sm2a.«S$ 
,      -flS(l+R2cos2a)-f-R2sm2a.a2g2 
.-.  tan*-   2_Bi2C082a.fl«S«-R2sin2«.flS 
tfS(l-fR2cos2a)f1   ,    R2sin2«.flS/l  1 
Rg8Jn2«.fl8/l  1  \1 
+  """"      2  Vj5      l  +  R2cos2a/J- 
As  a  first  approximation, 
and  the  transmitted  wave  is 
e'=.-^(l  +  R2cos2«); 
tH*-**8"^-1 '>«*}. 
(amplitude)  e* 
so  that  the  retardation  is  = 8,  independent  of  the 
opacity,  as  we  have  already  seen  it  ought  to  be. 
The  second  term  in  the  approximate  value  of  e'  has  a  contrary 
effect  to  the  first,  because  sin  2a  is  negative.  Moreover  sin  2a 
is  numerically  large.  This  may  account  for  the  acceleration  of 
phase  observed  by  Quincke— though  if  this  explanation  be  cor- 
rect, there  must  always  be  a  retardation  when  the  film  is  thin 
enough.  It  may  happen  that,  in  virtue  of  the  great  opacity  of 
silver,  its  elimination  by  a  reduction  of  the  thickness  may  be 
impracticable  without  at  the  same  time  bringing  the  retardation 
due  to  density  below  the  point  at  which  it  could  be  detected. 
Terling  Place,  Witham, 
January  18,  1872. 
Postscript. — Since  the  above  was  written  there  has  appeared  a 
paper  by  0.  E.  Meyer,  entitled  "An  Attempt  to  account  for 
Anomalous  Dispersion  of  Light"*,  in  which  the  author  arrives 
at  an  expression  for  the  refractive  index  equivalent  to  that  found 
above  as  the  value  of  R  cos  «,  namely 
Rcos 
Considering  h  constant,  he  sees  in  this  an  explanation  of  anoma- 
*  Pogg.  Ann.  vol.  cxlv.  p.  80,  translated  in  Phil.  Mag.  vol.  xliii.  p.  295. 
Phil  Mag.  S.  4.  Vol.  43.  No,  287.  May  1872.  Z 
