770  Prof.  J.  J.  Thomson  on  tie 
opposite  to  the  force  exerted  on  them  by  the  electric  force  in 
the  light-wave.  The  displacement  of  the  corpuscles  relatively 
to  the  sphere  of  positive  electricity  will  polarize  the  atom,  and 
the  collection  of  polarized  atoms  will  increase  the  specific 
inductive  capacity,  and  therefore  the  refractive  index  of  the 
medium.  If  the  mass  of  either  the  positive  electricity  or  of 
the  corpuscles  were  zero,  then,  however  short  the  time  for 
which  the  electric  force  in  the  light-wave  acted,  the  corpuscles 
and  the  positive  electricity  would  adjust  themselves  in  exactly 
the  same  way  as  if  the  electric  force  were  continuous  ;  so  that 
the  specific  inductive  capacity  and  the  refractive  index  would 
be  the  same  for  short  waves  as  for  long,  and  there  would  be 
no  dispersion.  If,  however,  the  masses  of  both  the  positive 
electricity  and  the  corpuscles  are  finite,  the  relative  displace- 
ment of  the  corpuscles  and  the  positive  electricity  will  depend 
upon  the  period  of  the  electric  force  •  and  since  the  specific 
inductive  capacity  and  refractive  index  depend  upon  this 
displacement,  the  refractive  index  of  the  medium  will  depend 
upon  the  period  of  the  electric  force,  and  there  will  be 
dispersion. 
In  the  latter  part  of  the  paper  the  expression  for  the 
refractive  index  of  a  monatomic  gas  is  investigated ;  and  it 
is  shown  that  if  p,  is  the  refractive  index  of  such  a  gas  for 
light  of  frequency  p,  then 
p?— 1_       |-7rNE(Mg  +  mE) 
^+2      f7r/>(Me  +  mE)-Mmp2'     '     '     '     W 
where  N  is  the  number  of  atoms  in  unit  volume  of  the  gas, 
m  the  mass  of  a  corpuscle,  M  the  mass  of  the  sphere  of 
positive  electrification,  e  the  charge  on  a  corpuscle,  E  the 
whole  charge  on  the  sphere  of  positive  electrification,  p  the 
density  of  the  electrification  in  this  sphere  ;  e,  E,  and  p  are 
expressed  in  electrostatic  measure. 
If  the  term  in  p2  is  small,  equation  (1)  may  be  written 
M3-1_NE/        Mm     f       3E  \ 
p.2  +  2     '    p   V        E    eM  +  nmATrpT 
since  JZ  =  ne,  where  n  is  the  number  of  corpuscles  in  the 
atom.     If  a  is  the   radius  of  the  sphere  of  positive  electri- 
fication,  E  =  |-7r^oa3,  i.  e.  =N|7ra3  =  volume  of  the  atoms 
per  cubic  centimetre  of  gas  ;  this  is  the  value  of  p?  —  1/(a?  +  2 
when  p  =  Q,  i.  e.  for  infinitely  long  waves.     Writing  P0  for 
