﻿of 
  Atoms 
  and 
  Molecules. 
  11 
  

  

  ordinary 
  helium 
  tubes 
  may 
  be 
  that 
  in 
  such 
  tubes 
  the 
  ionization 
  

   of 
  helium 
  is 
  not 
  so 
  complete 
  as 
  in 
  the 
  star 
  considered 
  or 
  in 
  the 
  

   experiments 
  o£ 
  Fowler, 
  where 
  a 
  strong 
  discharge 
  was 
  sent 
  

   through 
  a 
  mixture 
  of 
  hydrogen 
  and 
  helium. 
  The 
  condition 
  

   for 
  the 
  appearance 
  of 
  the 
  spectrum 
  is, 
  according 
  to 
  the 
  above 
  

   theory, 
  that 
  helium 
  atoms 
  are 
  present 
  in 
  a 
  state 
  in 
  which 
  

   they 
  have 
  lost 
  both 
  their 
  electrons. 
  Now 
  we 
  must 
  assume 
  

   that 
  the 
  amount 
  of 
  energy 
  to 
  be 
  used 
  in 
  removing 
  the 
  second 
  

   electron 
  from 
  a 
  helium 
  atom 
  is 
  much 
  greater 
  than 
  that 
  to 
  be 
  

   used 
  in 
  removing 
  the 
  first. 
  Further, 
  it 
  is 
  known 
  from 
  expe- 
  

   riments 
  on 
  positive 
  rays, 
  that 
  hydrogen 
  atoms 
  can 
  acquire 
  a 
  

   negative 
  charge 
  ; 
  therefore 
  the 
  presence 
  of 
  hydrogen 
  in 
  the 
  

   experiments 
  of 
  Fowler 
  may 
  effect 
  that 
  more 
  electrons 
  are 
  

   removed 
  from 
  some 
  of 
  the 
  helium 
  atoms 
  than 
  would 
  be 
  the 
  

   case 
  if 
  only 
  helium 
  were 
  present. 
  

  

  Spectra 
  of 
  other 
  substances. 
  — 
  In 
  case 
  of 
  systems 
  containing 
  

   more 
  electrons 
  we 
  must 
  — 
  in 
  conformity 
  with 
  the 
  result 
  of 
  

   experiments 
  — 
  expect 
  more 
  complicated 
  laws 
  for 
  the 
  line- 
  

   spectra 
  than 
  those 
  considered. 
  I 
  shall 
  try 
  to 
  show 
  that 
  the 
  

   point 
  of 
  view 
  taken 
  above 
  allows, 
  at 
  any 
  rate, 
  a 
  certain 
  

   understanding 
  of 
  the 
  laws 
  observed. 
  

  

  According 
  to 
  Rydberg's 
  theory 
  — 
  with 
  the 
  generalization 
  

   given 
  by 
  Ritz 
  *— 
  the 
  frequency 
  corresponding 
  to 
  the 
  lines 
  of 
  

   the 
  spectrum 
  of 
  an 
  element 
  can 
  be 
  expressed 
  by 
  

  

  v 
  = 
  F,.(t 
  1 
  )-F 
  s 
  2 
  ), 
  

  

  where 
  t 
  x 
  and 
  t 
  2 
  are 
  entire 
  numbers, 
  and 
  F,, 
  F 
  2 
  , 
  F 
  3 
  , 
  .... 
  are 
  

  

  functions 
  of 
  t 
  which 
  approximately 
  are 
  equal 
  to 
  -. 
  — 
  - 
  ^ 
  OJ 
  

  

  K 
  + 
  «i) 
  2 
  ' 
  

  

  K 
  is 
  a 
  universal 
  constant, 
  equal 
  to 
  the 
  factor 
  

  

  {j-Va 
  2 
  f 
  _ 
  * 
  

  

  outside 
  the 
  bracket 
  in 
  the 
  formula 
  (4) 
  for 
  the 
  spectrum 
  of 
  

   hydrogen. 
  The 
  different 
  series 
  appear 
  if 
  we 
  put 
  Tj 
  or 
  t 
  2 
  equal 
  

   to 
  a 
  fixed 
  number 
  and 
  let 
  the 
  other 
  vary. 
  

  

  The 
  circumstance 
  that 
  the 
  frequency 
  can 
  be 
  written 
  as 
  a 
  

   difference 
  between 
  two 
  functions 
  of 
  entire 
  numbers 
  suggests 
  

   an 
  origin 
  of 
  the 
  lines 
  in 
  the 
  spectra 
  in 
  question 
  similar 
  to 
  

   the 
  one 
  we 
  have 
  assumed 
  for 
  hydrogen; 
  i. 
  e. 
  that 
  the 
  lines 
  

   correspond 
  to 
  a 
  radiation 
  emitted 
  during 
  the 
  passing 
  of 
  the 
  

   system 
  between 
  two 
  different 
  stationary 
  states. 
  For 
  systems 
  

   containing 
  more 
  than 
  one 
  electron 
  the 
  detailed 
  discussion 
  

   may 
  be 
  very 
  complicated, 
  as 
  there 
  will 
  be 
  many 
  different 
  

   configurations 
  of 
  the 
  electrons 
  which 
  can 
  be 
  taken 
  into 
  con- 
  

   sideration 
  as 
  stationary 
  states. 
  This 
  may 
  account 
  for 
  the 
  

   different 
  sets 
  of 
  series 
  in 
  the 
  line 
  spectra 
  emitted 
  from 
  the 
  

   * 
  W. 
  Ritz, 
  Phys. 
  Zeitschr. 
  ix. 
  p. 
  521 
  (1908). 
  

  

  