﻿Phosphorus 
  Emanation 
  in 
  Spherical 
  Condensers. 
  87 
  

  

  so 
  tbufc 
  the 
  current 
  increases 
  with 
  R, 
  which 
  is 
  not 
  admissible. 
  

   Neither 
  of 
  these 
  cases, 
  moreover, 
  would 
  be 
  open 
  to 
  com- 
  

   putation 
  directly, 
  and 
  they 
  are 
  thus 
  without 
  immediate 
  

   interest. 
  

  

  This 
  may 
  be 
  treated 
  in 
  a 
  slightly 
  different 
  manner, 
  however, 
  

   by 
  supposing 
  the 
  number, 
  n, 
  just 
  found 
  to 
  be 
  correctly 
  

   evaluated 
  and 
  then 
  introducing 
  the 
  ion 
  velocity, 
  U, 
  instead 
  of 
  

   the 
  absorption 
  velocity, 
  k, 
  in 
  the 
  usual 
  way, 
  and 
  they 
  then 
  

   become 
  suggestive. 
  If 
  1/A 
  is 
  replaced 
  by 
  n 
  l? 
  the 
  number 
  of 
  

   ions 
  per 
  cubic 
  centimetre 
  at 
  a 
  distance 
  of 
  1 
  centim. 
  from 
  the 
  

   centre, 
  the 
  above 
  concentration 
  n 
  at 
  a 
  distance 
  r 
  may 
  be 
  

   written, 
  

  

  m/ra 
  = 
  r( 
  (k'/k) 
  n 
  x 
  {l 
  — 
  r) 
  + 
  r). 
  

  

  If 
  decay 
  is 
  ignored, 
  rc=rc 
  1 
  /r 
  2 
  , 
  as 
  is 
  otherwise 
  clear, 
  is 
  inde- 
  

   pendent 
  of 
  k 
  also. 
  

  

  Now 
  if 
  the 
  electric 
  conduction 
  is 
  determined 
  by 
  the 
  number 
  

   of 
  ions 
  which 
  reach 
  the 
  external 
  shell 
  (r 
  = 
  r), 
  

  

  -dQ/dt 
  = 
  - 
  GdV/dt 
  = 
  4ttR 
  2 
  U 
  (V/R)n*. 
  

  

  It 
  is 
  understood 
  that 
  this 
  number 
  is 
  not 
  appreciably 
  modified 
  

   by 
  the 
  occurrence 
  of 
  the 
  field 
  so 
  that 
  when 
  decay 
  is 
  absent 
  

   (&' 
  = 
  0), 
  n 
  = 
  n 
  l 
  jR 
  c 
  *, 
  as 
  above 
  deduced. 
  Hence 
  

  

  -(dV/dt)/V 
  = 
  -d(\og 
  Y)ldt 
  = 
  4,ireV?i 
  1 
  /CR. 
  

  

  Here 
  the 
  first 
  member 
  is 
  equivalent 
  to 
  — 
  d(logs)/dt, 
  S 
  being 
  

   the 
  deflexion 
  of 
  the 
  electrometer, 
  and 
  is 
  obtainable 
  from 
  the 
  

   observations 
  directly, 
  47reU/C 
  is 
  a 
  constant, 
  n 
  v 
  expresses 
  the 
  

   waning 
  intensity 
  of 
  the 
  phosphoric 
  source 
  of 
  ionization, 
  and 
  

   R 
  is 
  the 
  external 
  radius 
  of 
  the 
  condenser. 
  The 
  equation 
  

   therefore 
  admits 
  of 
  being 
  tested. 
  The 
  integral 
  of 
  the 
  equation 
  

   found 
  for 
  the 
  potential 
  gradient 
  becomes 
  

  

  y_y 
  6 
  -(47reU» 
  1 
  'CR)f 
  

  

  which 
  is 
  compatible 
  with 
  the 
  data 
  of 
  tables 
  1-3. 
  In 
  these 
  

   tables 
  I 
  have 
  therefore 
  inserted 
  data 
  for 
  

  

  n 
  1 
  K=(47reU/C),7i 
  1 
  , 
  

   obtained 
  from 
  

  

  -(dV/dt)/Y.n 
  

  

  for 
  each 
  case. 
  To 
  facilitate 
  computation, 
  n 
  x 
  K 
  is 
  left 
  in 
  

   common 
  logarithms 
  and 
  written 
  nj$ 
  y 
  so 
  that 
  

  

  2-3w 
  1 
  &'=w 
  1 
  K. 
  

  

  9. 
  Comparison 
  of 
  data. 
  — 
  The 
  values 
  so 
  found, 
  i. 
  e., 
  

  

  ^K'^R^logV)/^, 
  

  

  