Flames  containing  Salt  Vapours  for  Alternating  Currents.    499 
In  the  same  way  in  FB  we  have 
When  #=D— 1% 
^  =  _X0     and     'Vr=V1  +  V8; 
ax 
so  that  we  get  for  V  at  a=D, 
Y=-X0D  +  2TrP(t12-t22). 
Now  t1A-tq  =  d,  so  that 
Y=-X0J)  +  27rpd('2t1-d) (1) 
The    force    acting   on    a   negative    ion    is    —  X0<>  — A-^1, 
where  A  is  a  constant  representing  the  viscous  resistance  to 
motion  with  unit  velocity.  Let  m  be  the  mass  of  a  negative 
ion ;  then  its  equation  of  motion  is 
■V7-            a~t-\       .  at-\  ,„. 
-X0.  =  m^-fA^ (2) 
If    '  ^^ 
The  current-density  inside  the  slab  is  given  by  the  equation 
1=-P17  + 
dh      K  dX 
dt      -iir  dt 
where  K  is  the  specific  inductive  capacity  of  the  medium 
between  the  plates  in  the  absence  of  ions.  Thus  K  is  unity, 
and 
dt        1  dX0  m 
Now  in  a  flame  containing  a  salt  vapour  the  fall  of 
potential  nearly  all  takes  place  near  the  electrodes,  so  that 
X0  is  probably  very  small,  even  when  rapidly  alternating 
1     1\ 
currents  are  used.     Consequently,  since  p  is  large,  - y-° 
may  be  neglected  in  comparison  with  —p~r,1.  Hence  (3) 
becomes  i=  —  ^-y1  approximately.  Substituting  in  (1)  the 
value  of  X0  got  from  (2)  we  get 
T7     tt     •       j.     r\/m  d~h  .  A  dt,\      _       j,_  7, 
V=V0sm^=D(-  — i+  -  d(l)  +  2wpd(-2t,-J). 
This  gives 
^T  ml)  d%     AD  d%      ,       ,du 
