Number  of  Corpuscles  in  an  Atom.  Ill 
For  very  long  waves,  when  the  term  mMp2  may  be 
neglected,  we  have 
p       frrNE. 
or,  since  E  =  |7rpa3,  where  a  is  the  radius  of  the  sphere  of 
positive  electrification, 
IL2-  1 
^2  +  2      ° 
This  is  the  value  given  by  Mossotti's  theory  when  the 
atoms  are  assumed  to  be  perfectly  conducting  spheres  of 
radius  a. 
Case  of  a  diatomic  molecule,  the  atoms  carrying  electrical 
charges  equal  in  magnitude  and  opposite  in  sign. — In  this  case 
the  refractivity  P  will  contain  a  term  due  to  the  motion  of 
the  charged  atoms  relatively  to  each  other  under  the  electric 
field  due  to  the  light-wave.  We  can  calculate  this  term  as 
follows  : — Let  M1?  M2  be  the  masses  of  the  two  atoms,  E'  the 
charge  on  the  first  atom,  —  E'  that  on  the  other.  Let  xx 
be  the  displacement  of  the  centre  of  the  first  atom,  x2  that  of 
the  other.     The  equations  of  motion  will  be  of  the  form 
M15L=XE'-«^(D)(^1-iB2), 
M2^=-XE'-<^(D)(.,2-.,1), 
where  (/>(D)  is  a  function  of  1),  the  distance  between  the 
atoms,  the  value  of  this  function  depending  on  the  law  of 
force.     If  the  variables  as  before  vary  as  elP\  we  find 
%,= 
M2E'X 
(M1  +  M2)0(D)-M1M2ps 
M,E'X 
Xt  -      (Mi  +  MS)£(D)  -  MxMap2 ' 
The  contribution  to  P  of  the  motion  due  to  the  coordinates 
#1?  £c2  is  proportional  to 
\       at  dt  J 
or  to 
(Mi  +  MaM^-MiM^8'    •    •     •    '    W 
where  W  is  the  number  of  these  diatomic  molecules  per  unit 
volume.      The  consideration  of  this  expression  shows  that 
Phil.  Mag.  S.  6.  Vol.  11.  No.  M.  June  1906.  3  E 
