﻿264: 
  Dr. 
  A. 
  M. 
  Tyndall 
  and 
  Miss 
  Searle 
  on 
  the 
  

  

  high 
  ionic 
  velocity. 
  But 
  if 
  this 
  is 
  coupled 
  with 
  a 
  huge 
  ionic 
  

   density 
  the 
  currents 
  would 
  greatly 
  exceed 
  those 
  which 
  are 
  

   observed. 
  

  

  Secondly, 
  Warner 
  attempts 
  to 
  obtain 
  support 
  for 
  the 
  

   theory 
  from 
  the 
  variation 
  of 
  discharge 
  current 
  with 
  the 
  

   initial 
  pressure 
  u 
  j3 
  " 
  for 
  a 
  constant 
  potential 
  difference 
  

   between 
  the 
  wire 
  and 
  the 
  tube. 
  Since, 
  however, 
  the 
  

   pressure 
  u 
  p\* 
  is 
  not 
  a 
  constant 
  and 
  its 
  variation 
  with 
  " 
  p 
  " 
  

   is 
  unknown, 
  it 
  is 
  impossible 
  that 
  the 
  curves 
  he 
  gives 
  can 
  

   furnish 
  us 
  with 
  any 
  information 
  on 
  the 
  subject. 
  

  

  Perhaps 
  it 
  may 
  be 
  well 
  to 
  show 
  that 
  the 
  ordinary 
  pressure 
  

   of 
  the 
  electric 
  wind 
  makes 
  no 
  appreciable 
  contribution 
  to 
  the 
  

   effect. 
  In 
  the 
  experiments 
  cited 
  above, 
  the 
  manometer 
  com- 
  

   municated 
  directly 
  with 
  a 
  hole 
  in 
  the 
  wall 
  of 
  the 
  metal 
  tube 
  

   receiving 
  the 
  current. 
  Now 
  the 
  discharge 
  sets 
  up 
  a 
  radial 
  

   gradient 
  of 
  pressure 
  between 
  the 
  wire 
  and 
  the 
  tube, 
  the 
  

   pressure 
  at 
  the 
  former 
  being 
  below, 
  and 
  at 
  the 
  latter 
  above, 
  

   atmospheric 
  pressure. 
  The 
  following 
  argument 
  gives 
  the 
  

   maximum 
  value 
  of 
  excess 
  pressure 
  which 
  the 
  wind 
  can 
  set 
  up 
  

   at 
  the 
  tube-wall. 
  Circulation 
  of 
  air 
  would 
  decrease 
  this 
  

   value. 
  

  

  Let 
  the 
  radii 
  of 
  the 
  wire 
  and 
  of 
  the 
  metal 
  tube 
  be 
  " 
  a 
  " 
  and 
  

   U 
  A" 
  respectively. 
  Consider 
  a 
  thin 
  cylindrical 
  layer 
  of 
  gas, 
  

   of 
  thickness 
  oY 
  and 
  radius 
  " 
  r" 
  coaxial 
  with 
  the 
  wire. 
  Let 
  

   a 
  discharge 
  current 
  of 
  "t," 
  per 
  unit 
  length 
  of 
  the 
  wire, 
  pass 
  

   uniformly 
  through 
  the 
  layer. 
  This 
  will 
  give 
  rise 
  to 
  the 
  

   transfer 
  of 
  a 
  small 
  quantity 
  of 
  gas 
  through 
  the 
  layer, 
  and 
  to 
  

   a 
  difference 
  in 
  pressure, 
  $P, 
  per 
  unit 
  area, 
  between 
  the 
  two 
  

   sides 
  of 
  the 
  layer. 
  

  

  Now 
  ~ 
  p 
  _ 
  iSr 
  ^ 
  

  

  where 
  It 
  is 
  the 
  specific 
  ionic 
  velocity. 
  

  

  This 
  difference 
  in 
  pressure 
  e 
  may 
  be 
  expressed 
  as 
  a 
  rise 
  of 
  

   pressure 
  Bp 
  per 
  unit 
  area 
  outside 
  the 
  layer, 
  and 
  a 
  fall 
  Bp 
  l 
  

   inside 
  it, 
  so 
  that 
  

  

  $P=8p 
  + 
  8p 
  f 
  . 
  

  

  Then 
  Bp(A 
  2 
  -r 
  2 
  ) 
  = 
  hp'(r 
  2 
  -a 
  2 
  ) 
  ; 
  

  

  £ 
  _ 
  ihr(r 
  2 
  — 
  a 
  2 
  ) 
  

   '"' 
  P 
  ~ 
  2irrk(A 
  2 
  -a 
  2 
  y 
  

  

  * 
  Ohattock, 
  Phil. 
  Mag. 
  [5] 
  vol. 
  xlviii. 
  p. 
  401. 
  

  

  