740  Prof.  J.  S.  Townsend  on  the  Field  of  Force 
the  experiments  that  have  been  made  that,  on  the  average, 
the  velocity  does  not  increase  mnch  more  rapidly  than  — 
for  the  forces  and  pressures  used  in  the  experiments.  P 
For  this  purpose,  it  is  necessary  to  examine  to  what  extent 
a  current  of  1*2  x  10~6  ampere  disturbs  the  uniformity  o£  the 
field.  The  effect  of  the  charge  is  greatest  near  the  negative 
electrode,  and  the  calculations  of  the  ratio  of  the  positive 
and  negative  currents  which  have  been  given  above  show 
that  the  stream  of  positive  ions  exceeds  that  of  the  negative 
ions  for  the  greater  part  of  the  distance  between  the  plates. 
The  quantity  n2  X  e  X  v  measured  in  electrostatic  units  is  of 
the  order  1*2  x  10-6  X  3  x  109  for  the  space  near  the  negative 
electrode,  as  nearly  all  the  current  is  carried  by  positive  ions; 
so  that  the   charge   n2xe   becomes   ,  v  being   the 
velocity  of  the  positive  ion. 
The  velocity  of  positive  ions  in  hydrogen  at  760  mms. 
pressure  under  a  force  of  1  volt  per  centimetre  is  6'7  cms. 
per  second*;  so  that  for  the  force  260-f-*8  volts  per  centi- 
metre and  a  pressure  of  1*37  millimetres  the  velocity  would 
be  1'2  X  106  cms.  per  second.  Near  the  negative  electrode 
the  positive  charge  would  be  3  x  10 ~3  electrostatic  units  per 
cubic  centimetre,  if  all  the  current  were  carried  by  the 
positive  ions. 
A  simple  calculation  shows  that  if  a  charge  of  3xl0-3 
electrostatic  units  per  cubic  centimetre  be  placed  in  a  layer  of 
the  gas  6  millimetres  wide  near  the  cathode,  the  potentials  in 
volts  at  different  distances  from  the  cathode  are : — 
Distance  from  1 
Cathode.      J 
0. 
•1. 
'2. 
•3. 
•4. 
•5. 
• 
*7. 
•8. 
1    Potential  =  — —  + 
'8 
0 
•36 
•62 
■77 
•80 
•70 
•51 
•25 
0 
y  being  the  potential-difference  between  the  plates,  which 
in  this  case  wras  256  volts. 
As  these  changes  are  so  small  the  current  might  have  been 
considerably  larger  without  having  much  influence  on  the 
potentials.  The  actual  potential  of  the  wire  at  2  millimetres 
from  the  negative  electrode  was  102  volts  ;  so  that  this  large 
increase  over  the  potential  64*62  is  most  probably  due  to  the 
fact  that  the  stream  of  positive  ions  is  so  much  greater  than 
that  of  negative  ions.     There  is  a  marked  difference  in  the 
*  Zelenev,  Phil.  Trans.  1900,  p.  193. 
