Number  of  Corpuscles  in  an  Atom.  775 
Index  of  Refraction  of  a  Collection  of  Atoms . 
If  an  atom  consisting  of  corpuscles  dispersed  through  a 
sphere  of  uniform  positive  electrification  is  in  the  path  of  a 
wave  of  light,  the  electric  force  in  the  wave  will  displace  the 
corpuscles  in  the  atom;  the  motion  of  these  charged  corpuscles 
will  produce  a  magnetic  field  in  addition  to  that  in  the  wave 
before  it  struck  the  corpuscle ;  the  existence  of  this  field  will 
alter  the  velocity  of  propagation  of  the  wave  by  an  amount 
which  we  shall  attempt  to  calculate. 
Index  of  refraction  of  a  monatomic  gas  whose  atoms  contain 
as  much  positive  as  negative  electricity. — Consider  an  element 
of  volume  so  small  that  throughout  it  the  electric  force  in  the 
wave  may  be  regarded  as  constant.  Throughout  this  volume 
the  atoms  will  all  be  affected  by  the  electric  force  in  the 
same    way. 
If  %r,  r)r,  %r  are  the  displacements  parallel  to  the  axes  of 
x,  y,  z  of  the  rth  corpuscle  of  an  atom,  x  the  displacement 
of  the  centre  of  the  sphere  of  positive  electrification,  e  the 
negative  charge  on  a  corpuscle,  E  the  charge  of  positive  elec- 
trification in  the  sphere,  X  the  number  of  atoms  per  unit 
volume ;  then  X',  Y' ,  Z',  the  components  of  the  electric  force 
due  to  the  displacement  of  the  corpuscles,  are  given  by  the 
equations 
X'  =  f7rN(E^-2<ey 
Y'=t^N(Ey-2^r)L5      ....     (1) 
Z'=f-7rN(E,-2<)J 
the  summation  is  for  all  the  corpuscles  in  one  atom. 
The  equations  of  motion  for  the  corpuscles  and  sphere  of 
positive  electrification  are 
m  ^  =  -(X+X0E+f^%~fr), 
where  m  is  the  mass  of  a  corpuscle  and  M  that  of  the  sphere 
of  positive  electrification. 
If  all  the  quantities  vary  as  e*-^,  we  get  from  these  equations 
_  (X  +  XQEm 
X~  |77/o(Me  +  mE)--mMp2' 
-,  = (X  +  XQEM 
^r  *Trp(Me  +  mill )  -  mf 
