﻿Phosphorus 
  Emanation 
  in 
  Spherical 
  Condensers. 
  89 
  

  

  the 
  initial 
  (t 
  = 
  0, 
  nearly) 
  contours 
  of 
  the 
  curves. 
  Tt 
  will 
  be 
  

   sufficient 
  to 
  report 
  the 
  results 
  graphically. 
  

  

  The 
  chart 
  figure, 
  6, 
  gives 
  the 
  relation 
  of 
  the 
  current 
  

   (8s/8t), 
  arbitrarily 
  in 
  scale 
  parts, 
  to 
  the 
  potential-difference 
  V 
  

   in 
  volts 
  per 
  centim., 
  or 
  strength 
  of 
  the 
  field. 
  The 
  graph 
  is 
  

   obviously 
  curved 
  so 
  that 
  Ohm's 
  law 
  is 
  departed 
  from, 
  but 
  the 
  

   curvature 
  is 
  small, 
  indicating 
  a 
  limit 
  as 
  yet 
  a 
  great 
  way 
  off. 
  

  

  These 
  results 
  are 
  now 
  to 
  be 
  compared 
  with 
  similar 
  data 
  for 
  

   condensers 
  larger 
  and 
  smaller, 
  the 
  diameters 
  chosen 
  being 
  

   2R=6'9 
  centims. 
  for 
  K8 
  and 
  2R 
  = 
  23*3 
  centims. 
  for 
  K 
  2, 
  

   respectively. 
  

  

  The 
  currents 
  here 
  obtained 
  are 
  also 
  graphically 
  reproduced 
  

   in 
  the 
  chart 
  figure 
  6, 
  where 
  the 
  abscissas 
  are 
  the 
  fields 
  in 
  

   volt. 
  /cm., 
  and 
  ordinates 
  are 
  the 
  currents 
  in 
  the 
  usual 
  arbitrary 
  

   measure. 
  The 
  relative 
  conductivity 
  of 
  the 
  three 
  condensers 
  

   is 
  maintained, 
  and 
  the 
  saturated 
  states 
  (maxima 
  of 
  the 
  curves) 
  

   are 
  in 
  all 
  cases 
  enormously 
  distant. 
  The 
  relative 
  curvatures 
  

   of 
  the 
  three 
  graphs 
  in 
  the 
  same 
  field 
  cannot 
  be 
  made 
  out. 
  

  

  11. 
  Observations 
  for 
  constant 
  V 
  and 
  for 
  constant 
  R 
  com- 
  

   pared. 
  — 
  I 
  shall 
  now 
  endeavour 
  to 
  compare 
  the 
  data 
  of 
  § 
  6 
  and 
  

   $ 
  10, 
  by 
  referring 
  them 
  either 
  to 
  the 
  same 
  radii 
  or 
  to 
  the 
  

   same 
  electric 
  fields. 
  The 
  latter 
  method 
  is 
  preferable 
  not 
  only 
  

   as 
  yielding 
  a 
  greater 
  range 
  of 
  data, 
  but 
  because 
  the 
  values 
  

   of 
  the 
  currents, 
  Ss/8t, 
  and 
  of 
  njK, 
  have 
  not 
  been 
  regarded 
  in 
  

   this 
  light. 
  To 
  begin 
  with 
  the 
  former, 
  figure 
  7 
  contains 
  the 
  

   values 
  of 
  8s/8t 
  varying 
  with 
  the 
  fields 
  as 
  taken 
  from 
  the 
  

   Tables 
  I., 
  II., 
  III., 
  in 
  wdnch 
  V 
  /R 
  varies 
  by 
  reason 
  of 
  varying 
  R. 
  

   These 
  data 
  though 
  vague, 
  eventually 
  lie 
  within 
  the 
  limits 
  

   marked 
  by 
  the 
  curves 
  R 
  and 
  R'. 
  In 
  the 
  same 
  chart 
  I 
  have 
  

   inserted 
  the 
  curve 
  F, 
  taken 
  from 
  fig. 
  (i, 
  in 
  which 
  V 
  /R 
  varies 
  

   by 
  reason 
  of 
  varying 
  V 
  . 
  It 
  is 
  the 
  curve 
  for 
  K 
  2 
  for 
  which 
  

   11 
  = 
  11*7 
  is 
  largest, 
  and 
  the 
  data 
  surest. 
  The 
  point 
  of 
  

   importance 
  is 
  clear 
  at 
  once 
  : 
  as 
  the 
  fields 
  grow 
  stronger 
  the 
  

   curve 
  F 
  lies 
  quite 
  above 
  the 
  curves 
  R. 
  If 
  therefore 
  high 
  

   fields 
  are 
  produced 
  by 
  diminishing 
  the 
  radius 
  of 
  the 
  condenser, 
  

   the 
  currents 
  may 
  be 
  upwards 
  of 
  20 
  per 
  cent, 
  or 
  30 
  per 
  cent, 
  

   too 
  small, 
  both 
  because 
  of 
  the 
  escape 
  of 
  ions 
  around 
  the 
  stem 
  

   -and 
  of 
  the 
  access 
  of 
  air. 
  Indeed 
  this 
  state 
  of 
  things 
  is 
  not 
  

   unexpected, 
  inasmuch 
  as 
  the 
  chief 
  object 
  of 
  the 
  investigation 
  

   with 
  spherical 
  condensers 
  was 
  the 
  avoidance 
  of 
  such 
  losses 
  of 
  

   ions 
  as 
  occur 
  in 
  plate-condensers. 
  Returning 
  for 
  additional 
  

   consideration 
  to 
  fig. 
  3, 
  it 
  appears 
  that 
  the 
  definitely 
  low 
  data 
  

   corresponding 
  to 
  the 
  radii 
  2 
  and 
  3 
  centimetres, 
  are 
  erroneously 
  

   much 
  too 
  low, 
  whence 
  it 
  follows 
  that 
  the 
  probability 
  of 
  a 
  

   •constant 
  ^K 
  is 
  enhanced. 
  

  

  12. 
  Conclusion. 
  — 
  Contrary 
  to 
  my 
  expectation 
  and 
  in 
  spite 
  

  

  