Flames  containing  Salt  Vapours  for  Alternating  Currents.    497 
Two  parallel   vertical   platinum    disks   each    1*5    cms.   in 
11. 
diameter  were  used,  and  it  was  found  that  -=- — T   was  in- 
d2     d1 
dependent  of  the  distance  between  them  when  this  was  less 
than  3  or  4  millimetres. 
When  the j  were  10  millimetres   apart  ~r—~r  w^s   about 
double  its  value  between  0  and  4  mms.  This  increase  in  the 
apparent  capacity  is  no  doubt  due  to  the  fact  that  the  cross- 
section  of  flame  acted  on  by  the  P.D.  is  greater  when  the 
distance  between  the  electrodes  is  comparable  with  their 
diameter. 
We   may  therefore   conclude    that   —  — -    would    be    in- 
J  d2     dx 
dependent   of    the  distance  between  the   electrodes  if  they 
were  very  large.     This  is  in  agreement  with  the  results  for 
constant  P.D.'s,  for  which  the  current  is  independent  of  the 
distance  between  the  electrodes  when  thev  are  near  together. 
(4)    Theory  of  the  Conductivity  of  Ionized  Gases  for 
rapidly  alternating  Currents. 
It  will  be  convenient  now  to  describe  an  approximate 
theory  of  the  conductivity  of  ionized  gases  for  rapidly 
alternating  currents — a  theory  which  affords  an  explanation 
of  the  experimental  results  obtained  in  this  investigation. 
Suppose    a    large    parallel   plate-condenser  filled   with    a 
uniformly   ionized    gas,  and   let   the    distance    between    the 
plates  be  D  cms.     Let  the  potential-difference  between  the 
plates    be    given    by    the    formula    Y  =  V0  sin  pt,    and    let 
the    number    of    positive    or    negative    ions   per    c.c.    be    n, 
each  ion  carrying  a  charge    +<?.     In   a  Bunsen   flame   the 
cms. 
velocity  of  the  negative  ions  is  about  1000 "  for  one  volt 
J  te  sec. 
per  cm.,  while  the  velocity  of  the  positive  ions  under  the 
cms 
same  potential  gradient  is  only  about  GO  -:  Moreover, 
the  mass  of  the  positive  ions  is  probably  very  large  com- 
pared with  that  of  the  negative  ions.  Consequently,  in  a 
rapidly  alternating  electric  field  the  amplitude  of  vibrati 
of  the  negative  ions  will  be  large  compared  with  that  of  th 
positive  ions.  As  a  first  approximation,  therefore,  we  shall 
assume  that  the  positive  ions  do  not  move  at  all,  so  that  all 
the  current  is  carried  by  the  negative  ions.  We  shall  also 
suppose  that  all  the  negative  ions  move  in  the  same  way  with 
the  same  velocity,  so  that  the  number  of  negative  per  e.e. 
e 
