742  Prof.  J.  S.  Townsend  on  tie  Field  of  Force 
The  time  required  for  the  ion  to  travel  6  millimetres  may 
be  obtained  by  substituting  for  x  the  value  '6,  and  it  is  thus 
found  to  be  approximately  2'2  X  10~6  seconds.  This  is  more 
than  four  times  the  length  of  time  5  x  10-7  seconds  required 
to  travel  the  distance  6  millimetres  at  the  uniform  velocity 
1*2  x  106  cms.  per  second.  It  must,  however,  be  borne  in 
mind  that  it  requires  some  time  for  a  large  group  of  molecules 
to  collect  round  a  positive  ion,  and  during  the  first  part  of  its 
path  the  ion  is  travelling  with  a  mass  practically  equal  to 
the  mass  of  a  molecule  of  hydrogen.  It  is  quite  conceivable 
that  during  the  short  time  of  the  order  10~7  second  the 
positive  ion  moves  as  if  it  had  a  comparatively  small  mass, 
and  possibly  the  value  5  X  10-7  seconds  is  a  more  correct 
estimate  of  the  time  required  to  travel  a  distance  of  6 
millimetres. 
These  considerations  show  that  it  is  very  difficult  to  make 
an  accurate  calculation  of  the  charge  in  the  gas  even  for  a 
field  of  force  that  is  practically  uniform ;  nevertheless  it  is 
of  interest  to  see  that  the  experimental  results  are  in  fair 
agreement  with  the  rough  indications  given  by  the  theory. 
The  theory  shows  that  the  potentials  at  2,  4,  6,  and  8 
millimetres  from  the  negative  electrode  ought  to  be  the  same 
as  the  potentials  at  1,  2,  3,  and  4  millimetres  respectively 
from  the  negative  electrode  when  the  pressure  of  the  gas  is 
doubled  and  the  distance  between  the  plates  reduced  from  8 
to  4  millimetres.  It  was  found  that  the  potentials  were  107, 
155,  205,  and  260  at  the  distances  mentioned  when  the 
pressure  of  the  hydrogen  was  1"37  millimetres  and  the  distance 
between  the  plates  8  millimetres;  and  for  the  pressure  2*74 
millimetres  with  the  plates  4  millimetres  apart,  the  potentials 
were  108,  154,  202,  and  257  at  the  corresponding  reduced 
distances. 
6.  Further  experiments  were  made  at  a  pressure  of  2*74 
millimetres  with  the  plates  8  millimetres  apart.  The  results 
are  shown  by  the  curves,  fig.  3.  The  velocity  of  the 
positive  ions  is  much  slower  in  this  case  as  the  potential 
required  to  maintain  a  small  current  rises  only  to  316  volts  as 
compared  with  256  volts  at  the  lower  pressure.  In  order 
that  the  field  of  force  should  not  be  apprecially  influenced 
by  the  charge,  it  is  necessary  to  use  smaller  currents  since 
the  charge  in  the  gas  is  inversely  proportional  to  the  velocity. 
It  was  found  that  the  field,  as  indicated  by  the  potential  of 
the  wire,  did  not  vary  for  currents  between  2  X  10 ~6  and 
2  x  10-7  ampere,  so  that  for  these  small  currents  the  charge  is 
too  small  to  make  an  appreciable  effect  on  the  field  of  force. 
It  will  be  seen  that  for  a  current  of  4  x  10~6  ampere  a  large 
