﻿24 
  On 
  the 
  Constitution 
  of 
  Atoms 
  and 
  Molecules 
  . 
  

  

  the 
  conditions 
  in 
  the 
  celestial 
  body 
  in 
  question 
  ; 
  for 
  on 
  

   account 
  of 
  the 
  enormous 
  rarefaction 
  of 
  the 
  matter 
  there 
  may 
  

   be 
  comparatively 
  few 
  collisions 
  to 
  disturb 
  the 
  stationary 
  

   states 
  and 
  to 
  cause 
  a 
  true 
  emission 
  of 
  light 
  corresponding 
  to 
  

   the 
  transition 
  between 
  different 
  stationary 
  states 
  ; 
  on 
  the 
  other 
  

   hand 
  there 
  will 
  in 
  the 
  solar 
  corona 
  be 
  intense 
  illumination 
  of 
  

   light 
  of 
  all 
  frequencies 
  which 
  may 
  excite 
  the 
  natural 
  vibrations 
  

   of 
  the 
  systems 
  in 
  the 
  different 
  stationary 
  states. 
  If 
  the 
  above 
  

   assumption 
  is 
  correct, 
  we 
  immediately 
  understand 
  the 
  entirely 
  

   different 
  form 
  for 
  the 
  laws 
  connecting 
  the 
  lines 
  discussed 
  by 
  

   Nicholson 
  and 
  those 
  connecting 
  the 
  ordinary 
  line-spectra 
  

   considered 
  in 
  this 
  paper. 
  

  

  Proceeding 
  to 
  consider 
  systems 
  of 
  a 
  more 
  complicated 
  

   constitution, 
  we 
  shall 
  make 
  use 
  of 
  the 
  following 
  theorem, 
  

   which 
  can 
  be 
  very 
  simply 
  proved 
  : 
  — 
  

  

  " 
  In 
  every 
  system 
  consisting 
  of 
  electrons 
  and 
  positive 
  

   nuclei, 
  in 
  which 
  the 
  nuclei 
  are 
  at 
  rest 
  and 
  the 
  electrons 
  move 
  

   in 
  circular 
  orbits 
  with 
  a 
  velocity 
  small 
  compared 
  with 
  the 
  

   velocity 
  of 
  light, 
  the 
  kinetic 
  energy 
  will 
  be 
  numerically 
  equal 
  

   to 
  half 
  the 
  potential 
  energy." 
  

  

  By 
  help 
  of 
  this 
  theorem 
  we 
  get 
  — 
  as 
  in 
  the 
  previous 
  cases 
  

   of 
  a 
  single 
  electron 
  or 
  of 
  a 
  ring 
  rotating 
  round 
  a 
  nucleus 
  — 
  

   that 
  the 
  total 
  amount 
  of 
  energy 
  emitted, 
  by 
  the 
  formation 
  of 
  

   the 
  systems 
  from 
  a 
  configuration 
  in 
  which 
  the 
  distances 
  apart 
  

   of 
  the 
  particles 
  are 
  infinitely 
  great 
  and 
  in 
  which 
  the 
  particles 
  

   have 
  no 
  velocities 
  relative 
  to 
  each 
  other, 
  is 
  equal 
  to 
  the 
  

   kinetic 
  energy 
  of 
  the 
  electrons 
  in 
  the 
  final 
  configuration. 
  

  

  In 
  analogy 
  with 
  the 
  case 
  of 
  a 
  single 
  ring 
  we 
  are 
  here 
  led 
  

   to 
  assume 
  that 
  corresponding 
  to 
  any 
  configuration 
  of 
  equili- 
  

   brium 
  a 
  series 
  of 
  geometrically 
  similar, 
  stationary 
  con- 
  

   figurations 
  of 
  the 
  system 
  will 
  exist 
  in 
  which 
  the 
  kinetic 
  

   energy 
  of 
  every 
  electron 
  is 
  equal 
  to 
  the 
  frequency 
  of 
  revo- 
  

   lution 
  multiplied 
  by 
  ~h 
  where 
  t 
  is 
  an 
  entire 
  number 
  and 
  h 
  

  

  Planck's 
  constant. 
  In 
  any 
  such 
  series 
  of 
  stationary 
  con- 
  

   figurations 
  the 
  one 
  corresponding 
  to 
  the 
  greatest 
  amount 
  of 
  

   energy 
  emitted 
  will 
  be 
  the 
  one 
  in 
  which 
  t 
  for 
  every 
  electron 
  

   is 
  equal 
  to 
  1. 
  Considering 
  that 
  the 
  ratio 
  of 
  kinetic 
  energy 
  

   to 
  frequency 
  for 
  a 
  particle 
  rotating 
  in 
  a 
  circular 
  orbit 
  is 
  

   equal 
  to 
  tt 
  times 
  the 
  angular 
  momentum 
  round 
  the 
  centre 
  of 
  

   the 
  orbit, 
  we 
  are 
  therefore 
  led 
  to 
  the 
  following 
  simple 
  

   generalization 
  of 
  the 
  hypotheses 
  mentioned 
  on 
  pp. 
  15 
  and 
  22. 
  

   " 
  In 
  any 
  molecular 
  system 
  consisting 
  of 
  positive 
  nuclei 
  and 
  

   electrons 
  in 
  which 
  the 
  nuclei 
  are 
  at 
  rest 
  relative 
  to 
  each 
  other 
  

   and 
  the 
  electrons 
  move 
  in 
  circular 
  orbits, 
  the 
  angular 
  momentum 
  

  

  