778  Prof.  J.  J.  Thomson  on  the 
the  part  of  the  refractivity  arising  from  the  coupling  of  two 
atoms  together  may  easily  be  comparable  with  the  part  due 
to  the  corpuscles  within  the  atom.  Thus,  to  take  the  case 
when  the  waves  are  so  long  that  we  may  neglect  the  term  in 
p2,  the  contribution  to  the  refractivity  due  to  the  coupling  is 
<K») w 
If  the  force  between  the  atoms  changed  as  slowly  as  the 
force  between  the  two  charges  E'  and  —  E'  at  a  distance  D, 
<£(D)  would  equal  2E'2/D3,  and  (1)  would  become 
N'D3 
If  we  compare  this  with  2NV,  the  value  due  to  the 
corpuscles  inside  the  atom,  a  being  the  radius  of  the  atom, 
we  see  that  unless  the  force  between  the  two  atoms  varies 
very  rapidly  with  the  distance,  a  considerable  part  of 
the  refractivity  may  be  due  to  the  coupling  between  the 
atoms. 
If  AP0is  the  part  of  (/x2-l)/(/a2  +  2)  when  X  is  infinite 
due  to  the  charges  on  the  atoms  in  the  diatomic  molecule, 
we  see  from  equation  (3)  that  the  part  of  (fju2—  l)/(/u,2  +  2) 
due  to  these  charges  is  approximately  equal  to 
AF0  ,  (AP0)  ^  g-,  (Mi  +  M2)  J^?>       •      •      W 
where  E/  is  the  value  of  the  charge  in  electromagnetic  units. 
In  the  case  of  a  molecule  consisting  of  two  charged  atoms, 
the  charge  on  the  negative  atom  will  be  due  to  the  presence 
on  the  atom  of  extra  corpuscles  which  can  move  freely  about. 
Thus,  if  M2  refers  to  the  negative  charge,  M2/E/  will  equal 
m/e-i,  where  m  is  the  mass  and  e  the  charge  on  a  corpuscle  ; 
for  the  positive  atom  M,  will  equal  the  mass  of  the  atom, 
while  Ej  will  equal  e1  if  the  atoms  are  monovalent,  2e1  if  they 
are  divalent,  and  so  on.  Comparing  the  part  of  the  coefficient 
of  1/A,2  which,  is  due  to  the  charge  on  the  atoms,  with  that 
(given  by  equation  (2))  due  to  the  corpuscles  inside  the 
atom,  we  see  that  the  factor  M2/E/  in  (5)  is  the  same  as 
mje'  in  (2)  ;  while  if  there  are  many  corpuscles  in  the  atom, 
the  factor  — ^  -^ ^p-  will  be  much  laro-er  than 
E/  Mx  +  Ma  *  E(M  +  nm) 
for  E/  will  only  be  a  small  multiple  of  e1}  while  E  is  equal 
to  neu  where  n  is  the  number  of  corpuscles  in  the  atom. 
Thus,  unless  AP0  is  very  small  compared  with  P0,  the  dis- 
