298       M.  0.  E.  Meyer  on  Anomalous  Dispersion  of  Light, 
logously  be  called  the  index  of  the  external  friction  of  the  aether 
on  the  ponderable  molecules. 
According  to  the  first  of  the  two  hypotheses,  we  have  there- 
fore to  put 
d^v  _  qd%        dv 
aW~Ud^     Kdt' 
This  equation  is  satisfied  by  the  function 
v=  [A  cos  (a*— px)  +B  sin  [at— /3x)]e-vx 
when  between  the  constants  a,  /3,  y  the  relations 
subsist.     Hence  we  obtain 
2{i*j32  =  a\\  +  x/l-f/cV-2), 
and  further,  for  the  determination  of  the  quotient  of  refraction 
n3  taking  as  unit  the  velocity  of  light  in  empty  space, 
Putting  now 
aT=27r, 
T  is  the  time  of  an  undulation  of  the  ray ;  this,  however,  with 
the  chosen  unit  of  velocity,  is  equal  to  the  wave-length  X  in 
vacuo, 
T=X, 
so  that  we  may  also  put 
aX=27r. 
We  have  therefore,  according  to  this  hypothesis, 
According  to  this  formula,  with  increasing  value  of  the  wave- 
length X  the  ratio  of  refraction  likewise  becomes  greater.  This 
law  is  exactly  the  opposite  of  the  ordinary  law  of  dispersion,  and 
therefore  comprehends  anomalous  dispersion. 
To  an  altogether  similar  result  we  are  conducted  by  the  other 
theory,  which  assumes  internal  friction  of  the  aether.  The  dif- 
ferential equation  here  is 
d2v        0  d2v  d2v 
»s-S=^(i+^+«8«-a). 
di*  ~r  dsfi^'dtdx* 
