in  a  Discharge  between  Parallel  Plates.  741 
curves  obtained  experimentally  when  the  current  rises  to 
3  x  10-5  amperes. 
It  may  be  deduced  from  the  calculations  which  are  given 
above  that  in  this  case  the  charge  on  the  positive  ions  must 
produce  a  large  effect  on  the  distribution  of  force  in  the  field, 
and  the  experiments  show  that  the  potential  of  the  wire  at 
2  millimetres  from  the  negative  electrode  changes  from  102 
to  147  volts. 
It  will  be  noticed  that  the  curve  corresponding  to  a  current 
of  6  x  10— 6  ampere  lies  a  little  above  the  curve  for  1*2  x  10-6 
ampere,  and  the  calculations  show  that  the  charge  in  the  gas 
would  begin  to  produce  increases  of  2  or  3  volts  in  that 
case. 
The  numbers  which  have  been  given  for  the  increases  of 
potential  are  not  very  accurate.     They  must  be  considered 
as  indicating  the  order  of  effects  w7hich  would  be  produced 
under  the  assumptions  that  have   been  made  in  calculating 
the  velocity.     The  velocity  1*2  xlO6  which  has   been  found 
is  the  final  velocity  that  a  positive  ion  attains  under  these 
conditions,  and  the  estimate  of  the  effect  of  the  charge  has 
been  made  on  the  supposition  that  a  positive  ion  travels  along 
its  whole  path  in  the  gas  with  this  mean  velocity.     As  a 
matter  of  fact,  it  would  be  more  correct  to  consider  the  ion  as 
starting  from   rest  from  the  place  where  it  is  generated,  so 
that  the  ions  take  a  longer  time  to  traverse  their  paths,  and 
consequently  the  charge  in  the  gas  has  been  underestimated. 
It  is  interesting  to  find  how  long  it  takes  an  ion  to  traverse 
X 
6  millimetres  if  it  starts  from  rest  when  —  has  the  value  233, 
as  in  these  experiments.  P 
The  equation  of  motion  of  a  body  of  mass  m  and  charge  e 
in  an  electric  field  of  intensity  X  is 
k  being  a  constant  depending  on  the  retardation  of  the  ion. 
eX 
The  final  velocity    -r-  has   been   estimated  at  1*2  x  106  cms. 
per  second,  X  being  1*1  approximately  in  electrostatic  units. 
Experiments  on  diffusion  at  the  higher  pressures  show  that 
m  is  roughly  30  times  the  mass  of  a  molecule  of  oxygen  ; 
so   that   the   value   of   —    in    the   above   equation   becomes 
3*6  x  10~12.  When  these  values  of  the  constant  are  sub- 
stituted, the  solution  of  the  equation  becomes 
#=12  X  105x  £-4-8[l-e-2,5xl05x']. 
