334  The  Hon.  J.  W.  Strutt  on  the  Reflection  and 
transmitted  wave,  the  influence  of  opacity  is  altogether  different 
from  that  of  density.  According  to  a  method  used  by  me  in 
the  investigation  of  the  light  scattered  from  very  small  particles 
(as  in  the  sky)*,  we  may  suppose  that  the  incident  wave  passes 
on  undisturbed,  if  suitable  forces  are  imagined  to  act  on  the 
sether  in  the  metal  in  order  to  compensate  for  the  alteration  of 
optical  properties.  In  the  case  when  the  thickness  of  the  me- 
tallic plate  is  small  compared  to  the  internal  wave-length,  this 
point  of  view  possesses  considerable  advantages,  and  gives  a 
clear  insight  into  the  peculiarities  of  the  question.  The  forces 
which  we  must  suppose  to  act  in  the  region  of  the  metallic 
layer  divide  themselves  into  two  groups — one  dependent  on  va- 
riation of  density,  and  the  other  on  opacity.  The  first  set  cor- 
respond in  phase  with  the  acceleration  of  the  sether,  the  second 
with  the  velocity.  There  is  thus  a  difference  of  a  quarter  of  a 
period.  In  my  former  paper  I  showed  that  the  effect  of  a  force 
acting  at  any  point  is  to  produce  at  another,  distant  r  from  it,  a 
disturbance  whose  retardation  relative  to  the  force  is  r  simply. 
In  our  case  each  particle  of  the  plate  must  be  considered  to  be 
a  centre  from  which  a  disturbance  emanates ;  and  it  will  readily 
appear  that  the  phase  due  to  the  whole  system  of  forces  is  just 
a  quarter  of  a  period  behind  that  corresponding  to  that  element 
of  disturbance  which  suffers  least  retardation.  In  fact,  if  we 
divide  the  whole  plate  into  Huyghens's  zones,  we  know  that  the 
effect  of  the  whole  is  the  half  of  that  of  the  first  zone.  Now  the 
phase  of  the  disturbance  due  to  the  first  zone  is  the  mean  be- 
tween that  corresponding  to  its  centre  and  circumference,  of 
which  the  latter  is  half  a  period  behind  the  former.  Thus  the 
wave  produced  by  the  set  of  forces  due  to  the  alteration  of  den- 
sity is  a  quarter  of  a  period  behind  the  direct  wave  which  has 
been  supposed  to  pass  through  undisturbed.  The  effect  of  the 
disturbance  is  accordingly  a  maximum  on  the  phase  (calculated 
without  allowance  for  the  metallic  plate),  and  a  minimum  (to  the 
order  of  approximation  here  considered,  vanishing)  on  the  in- 
tensity. It  is  just  the  opposite  with  the  second  group  of  forces 
due  to  the  opacity,  which  are  originally  a  quarter  of  a  period 
behind  the  first.  The  disturbance  due  to  them  will  be  half  a 
period  behind  the  direct  wave  with  which  it  has  to  be  com- 
pounded, and  therefore  produces  a  maximum  effect  on  the  inten- 
sity and  a  vanishing  one  on  the  phase.  A  very  thin  film  can 
produce  no  effect  on  the  phase  of  the  transmitted  light  in  virtue 
of  its  opacity,  however  great,  but  acts  just  as  if  it  were  deprived 
of  its  absorbent  power  and  reduced  to  the  condition  of  an  ordi- 
nary transparent  plate.  Of  course  this  does  not  explain  the  ac- 
celeration of  phase  found  by  Quincke  ;  but  it  shows  at  least  that 
*  Phil.  Mag.  February  1871. 
