﻿1010 
  Prof. 
  A. 
  W. 
  Conway 
  on 
  an 
  Electromagnetic 
  

  

  of 
  P 
  in 
  AA. 
  Thus 
  P 
  would 
  move 
  under 
  the 
  influence 
  of 
  the 
  

   original 
  vorticities, 
  already 
  allowed 
  for, 
  and 
  of 
  the 
  negative 
  

   vorticity 
  at 
  Q. 
  Under 
  the 
  latter 
  influence 
  it 
  would 
  move 
  

   parallel 
  to 
  AA 
  with 
  a 
  certain 
  velocity, 
  and 
  for 
  the 
  same 
  

   reason 
  Q 
  would 
  move 
  similarly, 
  so 
  that 
  PQ 
  would 
  remain 
  

   perpendicular 
  to 
  A 
  A. 
  To 
  take 
  account 
  of 
  both 
  walls 
  the 
  

   more 
  complicated 
  arrangement 
  shown 
  in 
  the 
  figure 
  is 
  neces- 
  

   sary, 
  in 
  which 
  the 
  points 
  P 
  represent 
  equal 
  positive 
  vorticities 
  

   and 
  Q 
  equal 
  negative 
  vorticities. 
  The 
  conditions 
  at 
  both 
  

   walls 
  are 
  thus 
  satisfied 
  ; 
  and 
  as 
  before 
  all 
  the 
  vortices 
  P, 
  Q 
  

   move 
  under 
  each 
  other's 
  influence 
  so 
  as 
  to 
  remain 
  upon 
  a 
  

   line 
  perpendicular 
  to 
  AA. 
  Thus, 
  to 
  go 
  back 
  to 
  the 
  original 
  

   form 
  of 
  the 
  problem, 
  P 
  moves 
  parallel 
  to 
  the 
  walls 
  with 
  

   a 
  constant 
  velocity, 
  and 
  no 
  change 
  ensues 
  in 
  the 
  character 
  

   of 
  the 
  motion 
  — 
  a 
  conclusion 
  which 
  will 
  appear 
  the 
  more 
  

   remarkable 
  when 
  we 
  remember 
  that 
  there 
  is 
  no 
  limitation 
  

   upon 
  the 
  magnitude 
  of 
  the 
  added 
  VDrticity. 
  

  

  The 
  same 
  method 
  is 
  applicable 
  — 
  in 
  imagination 
  at 
  any 
  

   rate 
  — 
  whatever 
  be 
  the 
  distribution 
  of 
  vorticities 
  between 
  the 
  

   walls, 
  and 
  the 
  corresponding 
  velocity 
  at 
  any 
  point 
  is 
  deter- 
  

   mined 
  by 
  quadratures 
  on 
  Helmholtz's 
  principle. 
  The 
  new 
  

   positions 
  of 
  all 
  the 
  vorticities 
  after 
  a 
  short 
  time 
  is 
  thus 
  

   found, 
  and 
  then 
  a 
  new 
  departure 
  may 
  be 
  taken, 
  and 
  so 
  on 
  

   indefinitelv. 
  

  

  XCI. 
  An 
  Electromagnetic 
  Hypothesis 
  as 
  to 
  the 
  Origin 
  of 
  

   Series 
  Spectra. 
  By 
  Arthur 
  W. 
  Conway, 
  M.A., 
  IJ.Sc, 
  

   Professor 
  of 
  Mathematical 
  Physics, 
  University 
  College, 
  

   Dublin 
  *. 
  

  

  Introduction. 
  

  

  ri~lHE 
  following 
  paper 
  is 
  an 
  attempt 
  to 
  picture 
  a 
  model 
  of 
  

   _L 
  an 
  atom 
  based 
  on 
  the 
  classical 
  electrodynamics 
  which 
  

   will 
  illustrate 
  some 
  of 
  the 
  properties 
  of 
  spectral 
  series. 
  The 
  

   principal 
  difficulties 
  in 
  explaining 
  a 
  frequency 
  formula 
  of 
  the 
  

   type 
  

  

  V 
  =A-B/(> 
  + 
  yu) 
  2 
  , 
  

  

  where 
  

  

  n 
  = 
  1, 
  2, 
  3 
  .... 
  , 
  

  

  are 
  three: 
  (i.) 
  The 
  formula 
  gives 
  the 
  frequency 
  and 
  not 
  the 
  

   square 
  of 
  the 
  frequency 
  ; 
  (ii.) 
  no 
  elastic 
  or 
  electrical 
  system 
  

   has 
  a 
  frequency 
  equation 
  of 
  this 
  type, 
  the 
  frequency 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

  

  