Number  of  Corpuscles  in  an  Atom.  Ill 
this  quantity,  we  see,  if  A,  is  the  wave-length  of  the  light, 
/*2-l_p    ,  p2M  m  1  3tt 
/*2  +  2       oi~    °  E'  *'  N(M+-nfii)  \2? 
(2) 
where  E'  and  /  are  the  values  of  E  and  e  in  electromagnetic 
measure.  This  is  the  expression  for  the  refractive  index  of 
a  monatomic  gas.  I  have  not  been  able  to  find  any  deter- 
minations of  the  dispersion  of  such  gases.  Lord  Rayleigh, 
however,  found  that  the  dispersion  of  helium  was  of  the  same 
order  as  that  of  diatomic  gases.  If  the  atoms  in  the  molecules 
of  a  diatomic  gas  are  not  charged,  the  preceding  expression  will 
hold  for  the  refractive  index  of  such  a  gas  ;  if,  however,  the 
atoms  carry  electrical  charges,  the  theory  subsequently  given 
shows  that  this  expression  has  to  be  modified.  We  know 
that  as  a  matter  of  fact  the  atomic  refraction  of  some  elements, 
oxygen  for  example,  depends  upon  the  kind  of  compound 
in  which  the  oxygen  is  found.  This  variation  may  be  ascribed 
to  the  charges  carried  by  the  atoms  in  the  molecules.  The 
atomic  refraction  of  hydrogen  seems,  however,  to  be  constant; 
and  1  shall,  in  the  absence  of  data  for  monatomic  gases,  apply 
the  preceding  formula  to  this  gas. 
From  Ketteler's  measurements  of  the  refractive  index  of 
hydrogen  for  light  of  different  wave-lengths,  we  find  that  for 
hydrogen  at  atmospheric  pressure 
g^  =  ^2-8014  xl0-*+2xl°~14 
z*2+2     3r5Ui4XiU    +     A2 
Comparing  this  with  the  equation 
/*2-l  _p    ,  p  2M  m  1  3tt 
/*a  +  2        0+    °  E'  e'  N(M  +  nm)  \2' 
we  find 
Mm  1  . 
6  x  10" 
EV  N(M  +  wm) 
but  m/e'  =  1/1-7  xlO7     and     W  =  'S; 
hence 
M       e' 
^—-^  =  1,  approximately; 
or,  since  E '  =  nef, 
Tfr -  =1,  approximately. 
M  +  nm  n  rr  J 
This  result  shows  (1)  that  n  cannot  differ  much  from  unity, 
and  (2)  that  M,  the  mass  of  the  carriers  of  positive  electricity, 
