546  Intelligence  and  Miscellaneous  Articles. 
k  is  a  constant  depending  on  the  nature  of  the  rays  and  on  that  of 
the   mirror.      The   constant   n,   always    denned   by   the   relation 
sin  i= n  sin  r,  retains  the  value  deduced  from  the  experiments  in 
which  the  plane  of  polarization  is  parallel  with  that  of  incidence. 
The  final  formula  is  the  following  : — 
tang  (i— r), t  Ti   •_  cos  z* sm  ?  ^  tang2^'— r)~\ 
tang  (i + r)5  [_         cos  i  sin  i  -f  cos  r  sin  i  J 
cos  i  sin  i  h  tang2  (i — r) 
cos  i  sin  i-f-  cos  r  sin  r  * 
I  have  verified  this  formula  between  the  incidences  of  20°  and  75°. 
— Comptes  Rendus  de  V Acad,  des  Sciences,  April  22,  1872. 
PRIZE  QUESTION  PROPOSED  BY  THE  DANISH  ROYAL  SOCIETY  OF 
SCIENCES  FOR  THE  YEAR  1872. 
The  detailed  researches  of  which  the  spectra  of  the  planets  have 
been  the  subject  since  the  introduction  of  the  spectroscope  in  astro- 
nomical investigation  are  yet  far  from  having  led  to  satisfactorily 
accordant  results,  even  in  respect  of  the  principal  points.  At  this 
moment  we  know  positively  only  one  thing — namely,  that  the 
spectra  are  not  at  all  identical  wTith  that  of  the  solar  light ;  while 
great  uncertainty,  even  actual  contradiction,  prevails  when  the  po- 
sitions of  new  lines  and  zones  of  absorption  have  to  be  determined ; 
these  in  the  case  of  Uranus,  for  example,  seem  to  change  com- 
pletely the  character  and  nature  of  the  spectrum.  It  is  true  that 
these  researches,  in  order  to  have  all  the  precision  desirable,  de- 
mand observations  which  are  some  of  the  most  difficult  and  delicate 
in  astronomy  ;  but  the  above-mentioned  discordances,  and  notably 
those  which  belong  to  the  researches  previous  to  1868,  must  cer- 
tainly be  attributed  in  part  to  the  entire  absence  of  a  normal  general 
o 
spectrum-scale,  such  as  was  given  some  years  since  by  M.  Angstrom 
in  his  celebrated  work. 
In  the  conviction  that  the  analyzers  and  instruments  of  precision 
now  available  permit  the  spectroscopic  examination  of  the  planets 
Venus,  Mars,  Jupiter,  Saturn,  and  Uranus  in  such  a  manner  that 
doubts  shall  no  longer  be  possible  relative  to  the  position  and  spe- 
cial nature  of  the  principal  lines,  groups,  and  zones  in  each  of  these 
spectra,  the  Danish  Royal  Society  requests  a  description  of  the 
spectra  of  these  planets,  accompanied  by  a  critical  comparison  of 
the  results  obtained  anteriorly  by  Dr.  William  Huggins,  Father 
Secchi,  Dr.  Vogel,  and,  particularly  as  regards  Jupiter,  by  Mr. 
Le  Sueur  at  Melbourne,  and  offers  as  the  prize  its  gold  medal  toge- 
ther with  a  sum  of  money  representing  the  value  of  that  medal. 
The  memoirs  in  answer  to  this  must  be  sent  in  before  the  end  of 
October  1873,  addressed  to  Councillor  Japetus  Steenstrup,  Secre- 
tary of  the  Society.  They  may  be  written  in  Latin,  French,  English, 
German,  Swedish,  or  Danish.  The  memoirs  must  not  bear  the 
names  of  the  authors,  but  must  be  furnished  with  mottoes ;  and 
