330  The  Hon.  J.  W.  Strutt  on  the  Reflection  and 
of  A/  is  always  the  same.     Id  cases  where  the  influence  of  opa- 
city is  overwhelming,  tana=  —1. 
In  order  to  form  an  idea  of  the  sort  of  magnitudes  with  which 
we  are  dealing,  let  us  take  silver — an  extreme  case.  Exact 
measurements  of  the  percentage  of  light  reflected  at  perpendi- 
cular incidence  are  wanting  (so  far  as  I  know)  ;  but  De  la  Pro- 
vostaye  and  Desains  found  in  some  cases  a  reflection  of  dark 
heat  amounting  to  95  per  cent.  Using  this  in  our  formulae, 
we  find 
K-f -4  =  2cosa.39. 
it 
Now,  since  cos  a  can  never  be  less  than  —?=,  it  follows  that  ■=- 
V2  R 
can  be  neglected  in  comparison  with  R  ;  and  thus  11  =  80  cos  a ; 
R  cos  a  =  80  cos2 a;     R  sin  a  —  40  sin  2a. 
If  we  further  suppose  that  the  great  value  of  R  is  due  to  opacity, 
we  may  put  cos  a  =  — y=,  and 
R=40v/2,     Rcosa  =  40,     Rsina=— 40. 
Thus  A/=  — -  ;  otherwise  the  ratio  of  A/:  A,  is  still  smaller. 
40 
For  the  metals  it  is  probable  that  of  the  total  reflection  the 
greater  part  is  due  to  opacity;  in  other  cases  it  often  happens 
that  the  effect  of  opacity  is  only  a  slight  increase  of  the  reflec- 
tion that  would  otherwise  take  place.  Let  us  inquire  what  the 
strength  of  absorption  must  be. 
If  /x0  denote  the  refractive  index  which  the  medium  would 
possess  in  virtue  of  its  density  alone  ( —  J,  we  have 
R2  cos  2a  =  pj,      R2  sin  2a  =  — /*J  ~-; 
XJ  iC 
while  the  reflection  is  given  by 
Reflection  =  - — -jr-^ 
tan/+l 
and 
tan/=      1      (R  +  1 )  =      1     C_^o_  +  ^™*«) ; 
2  cos  a  \  R/      2  cos  a  Vv/ cos  2a  /i0      J 
from  which  it  appears  that,  when  a  is  small,  its  effect  depends 
on  a2. 
On  the  other  hand  the  factor  representing  the  absorption  is 
e     a  t  or  approximately  e     *       , 
