M.  0.  E.  Meyer  on  Anomalous  Dispersion  of  Light.       297 
aether  in  such  media.  This  resistance  must  depend  on  the  velo- 
city of  the  particles,  and  vanish  with  them.  On  the  supposition 
of  small  amplitude  and  consequently  little  velocity  of  the  oscilla- 
tions, the  assumption  that  these  resisting  forces  are  proportional 
to  the  velocities  appears  perfectly  safe. 
A  so  much  the  more  weighty  doubt,  however,  must  arise  as 
to  whether  the  seat  of  the  assumed  force  is  in  the  ponderable 
matter,  or  whether  the  force  upon  an  oscillating  aether- particle 
is  exerted  by  the  neighbouring  particles  of  aether.  In  the  first 
case  we  may  without  hesitation  regard  the  ponderable  particles 
as  motionless,  and  accordingly  we  have  to  suppose  this  force  pro- 
portional to  the  absolute  velocity  of  the  aether-particle  on  which 
it  operates.  In  the  other  case,  on  the  contrary,  considering  the 
force  a  reciprocal  operation  of  the  oscillating  particles  of  aether, 
tve  must  suppose  its  value  proportional  to  their  relative  velocities. 
The  latter  hypothesis  thus  leads  to  the  assumption  of  an  internal 
friction  in  the  luminous  aether  of  semitransparent  media,  while 
the  former  hypothesis  introduces  a  force  comparable  to  what  is 
called  the  external  friction  of  liquids. 
As  is  well  known,  the  differential  equation  for  a  plane  undu- 
latory  motion  is 
d2v       ^dH 
dF^fM  &' 
In  this,  v  denotes  the  displacement  which  exists  at  the  time  t, 
in  a  plane  at  the  distance  x  from  the  origin  of  the  undulations ; 
fi  is  a  constant.     The  equation  is  solved  by  the  formula 
r  =  Acos  (at— fix)  -fBsin  (at— fix), 
in  which  A,  B,  &,  fi  are  constant  quantities.  The  two  latter  are 
so  related  that 
and  this  relation  teaches  that  /j,  is  the  velocity  of  propagation  of 
the  wave.  Taking  as  unit  the  velocity  in  vacuo,  the  index  of 
refraction 
a.       fju 
After  the  new  hypothesis,  the  above  differential  equation  has  to 
be  completed  by  an  additional  term,  which  is  either 
dv  dsv 
—  fe-TT  or  v 
dt  dt  dx* 
according  to  whether  the  one  or  the  other  hypothesis  be  adopted. 
k  and  v  are  constant  quantities  of  positive  value;  the  latter  was 
named  by  Stokes*  the  index  of  friction ;  the  former  might  ana- 
*  Camb.  Phil.  Soc.  Tr.  vol.  ix.  pt.  2.  p.  17. 
