Intelligence  and  Miscellaneous  Articles,  545 
case  of  rock-salt,  n  is  the  index  corresponding  to  the  rays  employed. 
It  appeared  to  me  to  require  to  be  taken  as  equal  to  1*49.  In  the 
case  of  glass,  the  value  of  n  which  satisfies  experiment  is  »=1'7; 
but  here  measurements  of  the  index  are  not  possible,  because  glass 
even  of  the  thickness  of  §  millim.  obstructs  the  passage  of  the  rays  em- 
ployed. If,  however,  we  suppose  that,  in  this  case  again,  n  retains 
its  ordinary  physical  signification,  we  must  conclude  that  in  glass 
the  extreme  obscure  rays  are  incomparably  more  refracted  than  the 
red  rays,  which  are  nevertheless  much  more  refrangible  than  the 
former  in  a  rock-salt  prism. 
These  facts  were  recorded  in  a  memoir  presented  to  the  Academy 
in  186S.  I  have  thought  it  necessary  to  mention  them  now  in  order 
to  compare  them  with  the  experiments  made  eighteen  months  since 
on  abnormal  dispersion,  and  with  those  which  M.  Leroux  had  pre- 
viously published  on  the  same  subject. 
The  study  of  reflection  at  the  surface  of  metals  leads  to  analogous 
consequences.  On  studying,  with  De  La  Provostaye,  the  reflection 
of  polarized  heat  at  metallic  surfaces,  we  have  recognized  that 
Cauchy's  formula?  very  well  represent  the  results  obtained  for  the 
two  principal  positions  of  the  plane  of  polarization. 
But  when  limited  to  the  case  in  which  the  plane  of  polarization 
is  parallel  with  that  of  incidence,  we  may  be  confident  that  the  for- 
mula  I2=  w.  0 ) {  very  well  represents  the  data  of  experiment, 
sin"(i  +  r) 
the  angle  r  being  always  connected  with  the  angle  of  incidence  by 
the  formula  sin  i=.n  sinr,  n  being  a  constant.  But  the  values  of  n 
are  in  general  very  considerable ;  for  the  rays  in  the  vicinity  of  the 
extreme  red  they  appeared  to  me  to  be  the  following  :  platinum, 
=  8;  speculum-metal,  =8"  7  ;  silver,  =20;  finally  n— 26  in  the  case 
of  rays  emitted  by  lamp-black  at  300°  and  reflected  by  speculum- 
metal.  This  enormous  increase  agrees  well  with  what  I  had  already 
found  in  studying  the  reflection  from  glass. 
When  the  rays  are  polarized  perpendicularly  to  the  plane  of  inci- 
tan0"*  (i — y") 
dence,  Fresnel's  formula  I2=t — *\  ,.  , — (  no  longer  represents  either 
tang"(2  +  r)  °        ■ 
the  metallic  reflection  or  that  of  rays  of  low  temperature  from  glass. 
But  the  considerations  from  which  that  formula  is  derived  require 
very  little  modification  in  order  to  yield  one  which  will  represent 
the  phenomena. 
Indeed,  let  us  suppose  that  the  vis  viva  of  the  refracted  pencil, 
instead  of  being  equal  to  the  difference  between  that  existing  in  the 
direct  and  that  existing  in  the  refracted  pencil,  differs  a  little  from 
that  excess,  and  we  shall  then  have  between  the  coefficients  of  vi- 
bration i,  v,  and  u  of  the  three  pencils  a  relation  of  the  form 
(1  —  ir)cos  i  sin  r=tr  cosr  sin  2(1—  3), 
c  representing  the  coefficient  of  the  corrective  term.  Now  I  have 
ascertained  that  by  the  introduction  of  this  term  we  arrive  at  a  final 
formula  which  well  represents  all  the  experiments  I  am  acquainted 
with,  provided  that  we  assign  to  3  a  value  of  the  form  It  tang2 (a* — r); 
Phil.  May.  S.  4.  No.  289.  Suppl.  Vol  4-3.  2  N 
