﻿of 
  Atoms 
  and 
  Molecules. 
  23 
  

  

  the 
  permanent 
  state 
  of 
  the 
  system 
  which 
  only 
  differ 
  from 
  

   those 
  given 
  by 
  the 
  equations 
  (3) 
  on 
  p. 
  5, 
  by 
  exchange 
  of 
  

   E 
  fovE-esn." 
  

  

  Tlie 
  question 
  of 
  stability 
  of 
  a 
  ring 
  of 
  electrons 
  rotating 
  

   round 
  a 
  positive 
  charge 
  is 
  discussed 
  in 
  great 
  detail 
  by 
  Sir 
  J. 
  

   J. 
  Thomson 
  *. 
  An 
  adaption 
  of 
  Thomson's 
  analysis 
  for 
  the 
  

   case 
  here 
  considered 
  of 
  a 
  ring 
  rotating 
  round 
  a 
  nucleus 
  of 
  

   negligibly 
  small 
  linear 
  dimensions 
  is 
  given 
  by 
  Nicholson 
  f- 
  

   The 
  investigation 
  of 
  the 
  problem 
  in 
  question 
  naturally 
  divides 
  

   in 
  two 
  parts 
  : 
  one 
  concerning 
  the 
  stability 
  for 
  displacements 
  

   of 
  the 
  electrons 
  in 
  the 
  plane 
  of 
  the 
  ring 
  ; 
  one 
  concerning 
  

   displacements 
  perpendicular 
  to 
  this 
  plane. 
  As 
  Nicholson's 
  

   calculations 
  show, 
  the 
  answer 
  to 
  the 
  question 
  of 
  stability 
  

   differs 
  very 
  much 
  in 
  the 
  two 
  cases 
  in 
  question. 
  While 
  the 
  

   ring 
  for 
  the 
  latter 
  displacements 
  in 
  general 
  is 
  stable 
  if 
  the 
  

   number 
  of 
  electrons 
  is 
  not 
  great 
  ; 
  the 
  ring 
  is 
  in 
  no 
  case 
  

   considered 
  by 
  Nicholson 
  stable 
  for 
  displacements 
  of 
  the 
  first 
  

   kind. 
  

  

  According, 
  however, 
  to 
  the 
  point 
  of 
  view 
  taken 
  in 
  this 
  

   paper, 
  the 
  question 
  of 
  stability 
  for 
  displacements 
  of 
  the 
  

   electrons 
  in 
  the 
  plane 
  of 
  the 
  ring 
  is 
  most 
  intimately 
  connected 
  

   with 
  the 
  question 
  of 
  the 
  mechanism 
  of 
  the 
  binding 
  of 
  the 
  

   electrons, 
  and 
  like 
  the 
  latter 
  cannot 
  be 
  treated 
  on 
  the 
  basis 
  of 
  

   the 
  ordinary 
  dynamics. 
  The 
  hypothesis 
  of 
  which 
  we 
  shall 
  

   make 
  use 
  in 
  the 
  following 
  is 
  that 
  the 
  stability 
  of 
  a 
  ring 
  of 
  

   electrons 
  rotating 
  round 
  a 
  nucleus 
  is 
  secured 
  through 
  the 
  

   above 
  condition 
  of 
  the 
  universal 
  constancy 
  of 
  the 
  angular 
  

   momentum, 
  together 
  with 
  the 
  further 
  condition 
  that 
  the 
  

   configuration 
  of 
  the 
  particles 
  is 
  the 
  one 
  by 
  the 
  formation 
  of 
  

   which 
  the 
  greatest 
  amount 
  of 
  energy 
  is 
  emitted. 
  As 
  will 
  be 
  

   shown, 
  this 
  hypothesis 
  is, 
  concerning 
  the 
  question 
  of 
  stability 
  

   for 
  a 
  displacement 
  of 
  the 
  electrons 
  perpendicular 
  to 
  the 
  plane 
  

   of 
  the 
  ring, 
  equivalent 
  to 
  that 
  used 
  in 
  ordinary 
  mechanical 
  

   calculations. 
  

  

  Returning 
  to 
  the 
  theory 
  of 
  Nicholson 
  on 
  the 
  origin 
  of 
  

   lines 
  observed 
  in 
  the 
  spectrum 
  of 
  the 
  solar 
  corona, 
  we 
  shall 
  

   now 
  see 
  that 
  the 
  difficulties 
  mentioned 
  on 
  p. 
  7 
  may 
  be 
  only 
  

   formal. 
  In 
  the 
  first 
  place, 
  from 
  the 
  point 
  of 
  view 
  considered 
  

   above 
  the 
  objection 
  as 
  to 
  the 
  instability 
  of 
  the 
  systems 
  for 
  

   displacements 
  of 
  the 
  electrons 
  in 
  the 
  plane 
  of 
  the 
  ring 
  may 
  

   not 
  be 
  valid. 
  Further, 
  the 
  objection 
  as 
  to 
  the 
  emission 
  of 
  the 
  

   radiation 
  in 
  quanta 
  will 
  not 
  have 
  reference 
  to 
  the 
  calculations 
  

   in 
  question, 
  if 
  we 
  assume 
  that 
  in 
  the 
  coronal 
  spectrum 
  we 
  are 
  

   not 
  dealing 
  with 
  a 
  true 
  emission 
  but 
  only 
  with 
  a 
  scattering 
  of 
  

   radiation. 
  This 
  assumption 
  seems 
  probable 
  if 
  we 
  consider 
  

   * 
  Loc. 
  cit. 
  t 
  Loc. 
  "cit. 
  

  

  