776  Prof.  J.  J.  Thomson  on  the 
Therefore  from  equation  (1)  we  have 
_  |ttN(X  +  XQQE2  +  MEe) 
~     $7rp(M*  +  mE)  -  mMp2    ? 
or  v/       PX 
where  p_      |7rN(mE2  +  MEg) 
~~  Jtt/3  (Me  +  mE)  -mMp2' 
In  consequence  of  the  motion  of  the  charged  corpuscles, 
the   current  is   no   longer  the   polarization-current   ~  — — , 
where  K0  is  the  specific  inductive  capacity  of  the  aether ;  but 
(dx  dP  \ 
E  —  —  e%  -j^  1 ; 
thus  u  the  total  current  parallel  is  given  by  the  equation 
_  Kp  dX      _3^  dX^ 
~~  4w    dt  4:7T     dt 
If  a,  /3,  7  are  the  components  of  the  magnetic  force, 
A  dp      dy 
dz       dy 
and  d§_=dX__dZ       d1  =  dY^_dX 
dt       dz      dx '      dt       dx       dy ' 
Hence,  since 
we  have 
dX  +  d^+dZ=() 
dx        dy       dz 
du  _  d2X      d2X      d2X  . 
dt       dx2       dy2        dz2  ' 
or  d2X      U2XX  _  d2X      d*X      d2X 
0  dt2         dt2         dx2       dy2       dz2' 
d?X  ,  _3P^  d2X  _  d2X      d2X      d2X 
K0    dt2    +   X_p    dt2     ~       dx2    +    ^2    +     dz2  ' 
Hence,  if  /a  is  the  refractive  index, 
3P 
I^P' 
At2  =  l  + 
or  /z2-l_p_       f7rN(mE2  +  mEe)  .  . 
tf  +  2         ~  ^(Me  +  mE)  -  mMp2'  '     "     '     ^  } 
