﻿Doppler 
  Effect 
  in 
  Positive 
  Rays 
  in 
  Hydrogen. 
  895 
  

  

  The 
  formulae 
  of 
  transformation 
  for 
  the 
  convection 
  currents 
  

   and 
  vohime 
  density 
  of 
  electricit}^ 
  are 
  obtained 
  from 
  the 
  

   equation 
  * 
  

  

  p'ii\,' 
  dt/dz'd£ 
  + 
  pWoJ 
  dz'dMt' 
  + 
  p'lcj 
  d.v'dy'dt' 
  - 
  p'dx'dy'dz' 
  

   =piv^v 
  dydzdt 
  + 
  pWydzdxdt 
  4- 
  pwzdxdydt 
  — 
  pdxdydz, 
  

  

  where 
  {piVx^ 
  pici/, 
  pwz) 
  are 
  the 
  components 
  of 
  the 
  convection 
  

   currents, 
  p 
  the 
  volume 
  density 
  of 
  electricity. 
  Thus 
  

  

  r 
  ^.- 
  _ 
  ^/ 
  r 
  ^2 
  _ 
  ^,2 
  r 
  

  

  Since 
  {iL\v) 
  < 
  c 
  it 
  appears 
  that 
  p' 
  and 
  p 
  are 
  of 
  opposite 
  

   signs. 
  

  

  The 
  University, 
  Manchester. 
  

  

  XCYI. 
  The 
  Doppler 
  Effect 
  in 
  Positive 
  Rays 
  in 
  Hydrogen. 
  

   By 
  T. 
  RoYDS, 
  M.Sc, 
  1851 
  Exhibition 
  Science 
  Scholar'^. 
  

  

  LITTLE 
  is 
  known 
  of 
  the 
  cause 
  of 
  luminescence 
  of 
  the 
  

   canal 
  rays 
  and 
  of 
  the 
  origin 
  of 
  the 
  discrepancy 
  between 
  

   their 
  actual 
  velocity 
  and 
  that 
  calculated 
  from 
  the 
  potential 
  

   drop 
  through 
  which 
  they 
  have 
  fallen. 
  Some 
  explanation 
  of 
  

   these 
  would 
  probably 
  be 
  obtained 
  if 
  the 
  velocity 
  of 
  the 
  

   positive 
  rays 
  at 
  different 
  parts 
  of 
  the 
  discharge 
  were 
  compared 
  

   with 
  the 
  distribution 
  of 
  potential, 
  of 
  electric 
  force, 
  and 
  of 
  

   the 
  rate 
  of 
  change 
  of 
  the 
  latter. 
  Unfortunately 
  there 
  is 
  no 
  

   satisfactory 
  method 
  of 
  isolating 
  the 
  different 
  portions 
  between 
  

   the 
  cathode 
  and 
  the 
  negative 
  glow 
  for 
  the 
  observation 
  of 
  the 
  

   Doppler 
  effect. 
  At 
  one 
  poinc 
  of 
  the 
  discharge, 
  however, 
  a 
  

   comparison 
  is 
  possible, 
  namely, 
  at 
  the 
  point 
  where 
  the 
  

   cathode 
  glow 
  (Goldstein's 
  ^' 
  erste 
  Kathodenschicht 
  ") 
  com- 
  

   mences. 
  Since 
  the 
  canal 
  rays 
  mostly 
  start 
  from 
  the 
  negative 
  

   glow, 
  we 
  can 
  assume 
  that 
  the 
  commencement 
  of 
  the 
  cathode 
  

   glow 
  corresponds 
  to 
  the 
  minimum 
  Doppler 
  effect 
  when 
  the 
  

   cathode 
  is 
  viewed 
  from 
  the 
  anode 
  side. 
  That 
  the 
  cathode 
  

   glow 
  near 
  its 
  commencement 
  shows 
  the 
  Doppler 
  effect 
  was 
  

   proved 
  by 
  placing 
  the 
  discharge-tube 
  inclined 
  to 
  the 
  axis 
  of 
  

   the 
  collimator 
  until 
  light 
  from 
  only 
  the 
  first 
  portions 
  of 
  the 
  

   cathode 
  glow 
  fell 
  on 
  the 
  slit, 
  the 
  portions 
  nearer 
  the 
  cathode 
  

   being 
  screened 
  off 
  by 
  the 
  cylinder 
  carrying 
  the 
  cathode. 
  The 
  

  

  * 
  Proc. 
  London 
  Math. 
  Soc. 
  (2), 
  1909. 
  

   t 
  Communicated 
  hv 
  the 
  Author. 
  

  

  