Flames  containing  Salt  Vapours  for  Alternating  Currents.    501 
capacity  when   salt  is  added  to  the  flame.     In  what  follows 
we  shall  speak  of  T — j  as  the  apparent  capacity. 
Thus  we  should  expect  the  apparent  capacity  per  unit  area 
to  vary  as  the  square  root  of  the  number  of  ions  per  c.c.,  and 
inversely  as  the  square  root  of  the  maximum  P.D.  applied, 
but  to  be  independent  of  the  distance  between  the  electrodes. 
The  experimental  results  are  in  surprisingly  good  agreement 
with  these  conclusions.  Thus  we  have  seen  that  the  apparent 
capacity  is  nearly  independent  of  the  number  of  alternations 
per  sec,  and  varies  as  the  square  root  of  the  steady  current 
conductivity.  For  small  E.M.F/s  the  conductivity  for 
steady  currents  is  proportional  to  the  number  of  ions  per  c.c. 
and  to  the  velocity  of  the  ions.  But  it  has  been  shown  * 
that  all  alkali-salts  in  flames  give  ions  having  the  same 
velocity,  so  that  the  conductivity  for  steady  currents  should 
vary  nearly  as  the  number  of  ions  per  c.c.  present.  Hence 
the  observed  apparent  capacity  A'aries  nearly  as  the  square 
root  of  the  number  of  ions  present.  The  apparent  capacity 
was  also  independent  of  the  distance  between  the  electrodes, 
provided  this  was  small  compared  with  their  diameters. 
Further,  we  have  seen  that  the  apparent  capacity  varies 
roughly  inversely  as  the  square  root  of  the  maximum  P.D., 
measured  by  the  length  of  the  spark-gap  in  the  primary  coil 
of  the  Tesla  transformer.  It  appears,  therefore,  that  the 
expression  \/p/$7rY0  does  represent  approximately  the  ob- 
served variations  of  the  apparent  capacity  of  the  electrodes 
in  the  flame  containing  salt  vapour. 
This  expression  has  been  obtained  by  neglecting  the  mass 
of  the  ions  and  the  resistance  to  their  motion  through  the 
flame-gases,  so  that  it  appears  that  the  amount  of  alternating- 
current  through  the  flame  is  determined  merely  by  the 
density  of  the  layer  of  positive  charge  left  in  the  gas  near 
the  electrodes  when  the  negative  ions  move  under  the  action 
of  the  applied  field. 
If  a  steady  P.D.  V  is  applied  to  two  electrodes  immersed 
in  ati  ionized  gas,  and  if  the  positive  ions  cannot  move,  it  is 
easy  to  see  that  a  current  will  only  pass  for  the  short  time 
required  for  the  accumulation  of  positive  charge  near  the 
negative  electrode  to  become  sufficient  to  make  the  electric 
force  near  the  positive  electrode  zero.  Thus  the  two  electrodes 
will  behave  like  a  condenser  when  the  P.D.  is  applied.  When 
a  rapidly  alternating  P.D.  is  applied  it  is  easy  to  see  that  men 
if  the  positive  ions  can  move,  provided  their  velocity  is  small 
*  IT.  A.  Wilson,  Phil.  Trans.  A.  L899. 
