Refraction  of  Light  by  intensely  Opaque  Matter.         323 
ance  of  these  facts  from  the  point  of  view  of  theoretical  optics ; 
but  it  lies  beside  the  object  of  the  present  paper  to  go  further 
into  the  question  here. 
That  a  sufficient  opacity  is  as  competent  as  a  high  optical 
density  to  produce  an  abundant  reflection  is  evident  without  any 
analysis.  So  long  as  the  medium  into  which  the  light  seeks  to 
penetrate  remains  nearly  at  rest,  the  greater  part  of  the  motion 
must  be  thrown  back  without  any  regard  to  the  cause  of  the  ap- 
proximate quiescence.  Whether  the  sluggishness  be  due  to  a 
great  inertia  or  a  correspondingly  great  friction  is  in  this  respect 
of  no  importance.  In  order,  however,  to  account  for  the  reflec- 
tion from  silver  (90  or  95  per  cent.)  without  opacity,  a  very  high 
optical  density  would  be  required,  much  higher  than  we  have 
any  reason  to  think  at  all  likely.  On  the  other  hand,  we  know 
that  the  opacity  of  metals  to  light  is  very  great. 
In  this  connexion  it  is  interesting  to  note  that  some,  and  pro- 
bably many,  non-metallic  substances  possess  a  quasi- metallic 
reflecting-power  for  dark  radiation.  De  la  Provostaye  and  Des- 
ains  long  ago  remarked  on  the  large  percentage  of  dark  heat 
reflected  from  glass,  which  was  much  in  excess  of  that  calculated 
from  FresnePs  formula?  with  the  known  refractive  index.  The 
observation  seems  to  have  remained  uninterpreted;  but  we  can- 
not well  be  wrong  in  attributing  the  extra  reflection  to  an  opa- 
city to  the  rays  of  dark  heat,  which,  always  great,  rises  some- 
where in  the  spectrum  to  such  a  magnitude  as  to  damp  the 
entering  rays  within  a  few  wave-lengths  of  the 'surface.  No- 
thing but  direct  experiment  can  inform  us  what  substances  are 
sufficiently  opaque  to  exercise  an  abnormal  reflection ;  for  the 
stoppage  of  radiant  heat  by  a  plate  of  ordinary  thickness  may 
well  be  complete  to  sense,  and  yet  not  sufficiently  sudden  to  give 
any  material  assistance  in  reflection.  I  am  glad  therefore  to  be 
able  to  refer  to  the  experiments  of  the  late  Professor  Magnus 
(PoggendorfFs  Annalen,  vol.  cxxxix.),  in  which  he  investigates 
the  proportion  of  heat  reflected  by  plates  of  various  substances, 
the  incident  radiation  being  derived  from  moderately  heated 
plates  of  the  same  or  of  a  different  material. 
First  let  us  see  what  fraction  of  the  incident  radiation  (unpo- 
larized)  would  be  reflected  from  the  surface  of  a  substance  having 
a  refractive  index  of  To — about  that  of  glass.  If  6  be  the  angle 
of  incidence,  and  I  the  corresponding  fraction,  I  find  by  calcula- 
tion from  FresnePs  formulae  the  following  : — 
0  =  0 
1  =  -040 
0  =  33° 
1  =  -0-12 
0  =  45° 
Ic=050 
(9  =  62° 
I  =  -100 
Y2 
