Fluorescence  and  Lambert's  Law.  785 
intensity  of  the  surface  is  greatest  when  it  is  viewed  in  the 
normal  direction,  while  at  grazing  emergence  scarcely  any 
fluorescent  light  at  all  is  visible.  This  is  without  doubt  due 
to  refraction,  for  the  rays  which  emerge  at  grazing  incidence 
were  incident  upon  the  boundary  at  very  nearly  the  critical 
angle,  and  a  large  amount  of  energy  is  thus  lost  by  reflexion. 
It  is  moreover  clear  that  a  cone  of  rays  coming  from  a 
fluorescent  molecule  below  the  surface,  which  embraces  a  solid 
angle  equal  to  twice  the  critical  angle  for  the  glass,  is,  upon 
refraction  out  into  the  air,  spread  out  into  a  cone  of  180 
degrees,  that  is  over  a  hemisphere.  The  intensity  within  the 
medium  is  in  a  corresponding  degree  increased  by  total 
reflexion,  practically  doubled  in  fact  within  a  given  angular 
range.  To  prove  the  existence  of  this  reflexion  of  the  fluo- 
rescent layer  at  the  boundary  between  the  two  media,  it  is 
only  necessary  to  place  a  cube  of  quartz  in  front  of  and  against 
the  fluorescing  surface,  with  a  small  drop  of  glycerine  pressed 
out  between  the  two.  The  quartz  and  glycerine  are  both 
quite  transparent  to  the  radiations  from  the  spark  which 
excites  the  fluorescence  ;  consequently  all  changes  which  are 
observed  are  due  solely  to  the  alteration  of  the  refractivity  of 
the  medium  in  front  of  the  glass  surface.  The  intensity  of 
the  fluorescence  of  the  surface  in  contact  with  the  glycerine 
will  be  found  to  be  much  less  than  the  surrounding  surface, 
when  viewed  from  the  glass  side,  while  it  is  much  greater 
when  viewed  from  the  quartz  side.  A  more  complete  study 
could  be  made  if  the  refractive  index  of  the  medium  could 
be  made  the  same  on  both  sides  of  the  fluorescent  surface,  or 
varied  at  will  ;  but  it  is  difficult  or  impossible  to  find  suitable 
media  which  are  transparent  to  the  ultra-violet  waves  which 
excite  the  fluorescence.  If  we  try  to  get  round  this  difficulty 
by  using  media  which  fluoresce  under  the  influence  of  less 
easily  absorbed  radiations,  we  no  longer  have  the  fluorescence 
confined  to  the  necessary  shallow  layer. 
The  subject  of  fluorescence  in  its  connexion  with  Lambert's 
law  has  been  discussed  by  Lommel  in  a  paper  which  appeared 
in  Wiedemann's  Annalen  in  1880*. 
In  this  paper  Lommel  deduces  Lambert's  law  for  a  medium 
which  has  a  high  absorbing  power,  and  which  is  emitting 
light  in  virtue  of  its  high  temperature.  Applying  the  same 
method  to  a  partially  transparent  medium,  and  to  fluorescent 
media,  he  comes  to  the  conclusion  that  in  these  cases  the 
emission  is  not  proportional  to  the  cosine  of  the  angle,  but 
to  a  certain  function  of  the  cosine,  which  has  the  value  1  for 
normal  emission  and  0  for  an  emission  at  90  degrees. 
*  Wied.  Ann.  x.  p.  149  (1880). 
