﻿90 
  Prof. 
  C. 
  Barns 
  on 
  the 
  Behaviour 
  of 
  the 
  

  

  of 
  the 
  labour 
  spent 
  upon 
  them, 
  the 
  results 
  for 
  spherical 
  

   condensers 
  have 
  not 
  enabled 
  me 
  to 
  give 
  a 
  decisive 
  answer 
  to 
  

   the 
  question 
  at 
  issue. 
  The 
  difficulty 
  encountered 
  and 
  which 
  

   occurs 
  here 
  in 
  accentuated 
  form, 
  is 
  the 
  same 
  which 
  has 
  

   hampered 
  me 
  throughout 
  the 
  present 
  research, 
  namely 
  the 
  

   elusive 
  variability 
  of 
  the 
  ionizer. 
  Moreover, 
  as 
  the 
  conditions 
  

  

  determining 
  it 
  exist 
  immediately 
  at 
  the 
  surface 
  of 
  the 
  active 
  

   phosphorus, 
  I 
  do 
  not 
  see 
  how 
  they 
  are 
  to 
  be 
  put 
  under 
  

   control 
  ; 
  merely 
  keeping 
  the 
  air 
  around 
  the 
  phosphorus 
  at 
  

   constant 
  temperature, 
  &c, 
  is 
  not 
  a 
  sufficient 
  check 
  on 
  the 
  

   behaviour 
  of 
  the 
  surface 
  itself. 
  

  

  In 
  several 
  respects, 
  nevertheless, 
  definite 
  advances 
  have 
  

   been 
  made. 
  It 
  has 
  been 
  shown 
  that 
  the 
  best 
  results 
  can 
  be 
  

   reached 
  with 
  large 
  spherical 
  condensers 
  (say 
  20 
  centims., 
  or 
  

   more, 
  in 
  diameter), 
  in 
  which 
  changes 
  of 
  field 
  are 
  produced 
  by 
  

   applying 
  larger 
  potential-differences 
  while 
  the 
  apparatus 
  itself 
  

   is 
  left 
  quite 
  without 
  interference. 
  

  

  Finally, 
  to 
  ascertain 
  in 
  how 
  far 
  the 
  present 
  experiments 
  

   agree 
  as 
  a 
  whole 
  with 
  the 
  results 
  for 
  plate-condensers, 
  where 
  

   a 
  theoretically 
  different 
  method 
  is 
  involved, 
  it 
  suffices 
  to 
  

   compute 
  the 
  value 
  of 
  n^ 
  the 
  number 
  of 
  particles 
  per 
  cubic 
  

   centim. 
  at 
  1 
  centim. 
  from 
  the 
  centre 
  of 
  the 
  condenser. 
  Since 
  

   ?z 
  1 
  K 
  / 
  in 
  fig. 
  3 
  is 
  of 
  the 
  order 
  of 
  *0012, 
  or 
  when 
  referred 
  to 
  

   natural 
  logarithms 
  ?z 
  1 
  K 
  = 
  *0026, 
  and 
  since 
  n 
  1 
  K 
  = 
  47T0U/C, 
  if 
  

   we 
  insert 
  J. 
  J. 
  Thomson's 
  value 
  of 
  <? 
  = 
  2"3/10 
  19 
  and 
  put 
  U 
  of 
  

   the 
  order 
  of 
  1 
  cm./sec, 
  C^G'7/10 
  11 
  farads, 
  it 
  follows 
  that 
  

   iii 
  = 
  &b 
  xlO 
  4 
  . 
  The 
  result 
  agrees 
  very 
  well 
  with 
  the 
  datum 
  

   w 
  =5"5xl0 
  4 
  , 
  as 
  determined 
  from 
  plate-condensers 
  by 
  the 
  

   totally 
  different 
  method 
  there 
  pursued. 
  If 
  in 
  both 
  cases 
  

   U= 
  I'5 
  cm./sec. 
  be 
  assumed, 
  the 
  numbers 
  will 
  be 
  7^ 
  = 
  4*3 
  x 
  10 
  4 
  

   and 
  /* 
  = 
  3'G 
  X 
  10 
  1 
  , 
  respectively. 
  In 
  either 
  case 
  the 
  saturation 
  

   is 
  that 
  existing 
  at 
  the 
  surface 
  of 
  the 
  phosphorus. 
  They 
  thus 
  

   agree 
  with 
  the 
  datum 
  for 
  the 
  unsaturated 
  emanation 
  n 
  = 
  2x 
  10 
  4 
  , 
  

   obtained 
  by 
  a 
  third 
  method 
  from 
  tubular 
  condensers. 
  Finally, 
  

   all 
  are 
  in 
  accord 
  with 
  J.J. 
  Thomson's 
  value 
  for 
  ionized 
  air 
  

   n 
  = 
  4: 
  x 
  10 
  4 
  , 
  resulting 
  from 
  a 
  method 
  theoretically 
  different 
  

   from 
  that 
  of 
  my 
  papers. 
  

  

  13. 
  Summary. 
  — 
  With 
  the 
  present 
  paper 
  I 
  have 
  given 
  a 
  

   brief 
  but 
  systematic 
  account 
  of 
  the 
  bulk 
  of 
  my 
  work 
  with 
  the 
  

   phosphorus 
  emanation, 
  the 
  purpose 
  throughout 
  being 
  to 
  map 
  

   out 
  roughly 
  the 
  phenomena 
  in 
  which 
  1 
  am 
  interested, 
  as 
  

   a 
  preliminary 
  to 
  the 
  more 
  rigorous 
  study 
  of 
  the 
  subject 
  

   which 
  I 
  am 
  now 
  beginning. 
  The 
  results 
  as 
  a 
  whole 
  are 
  

   eventually 
  to 
  be 
  tributary 
  to 
  an 
  investigation 
  on 
  the 
  colours 
  

   of 
  cloudy 
  condensation, 
  particularly 
  in 
  those 
  regions 
  within 
  

   which 
  Lord 
  Rayleigb/s 
  theory 
  must, 
  in 
  any 
  case, 
  cease 
  to 
  be 
  

   applicable. 
  

  

  