﻿High-Frequency 
  Spectra 
  of 
  the 
  Elements. 
  1033 
  

  

  have 
  an 
  experimental 
  verification 
  of 
  the 
  principle 
  of 
  the 
  

   constancy 
  o£ 
  angular 
  momentum 
  which 
  was 
  first 
  used 
  by 
  

   Nicholson 
  *, 
  and 
  is 
  the 
  basis 
  of 
  Bohr's 
  theory 
  of 
  the 
  atom. 
  

  

  It 
  is 
  evident 
  that 
  k 
  = 
  cr 
  n 
  . 
  If 
  then 
  & 
  = 
  1, 
  it 
  is 
  suggested 
  

   that 
  the 
  ring 
  contains 
  4 
  electrons, 
  for 
  o- 
  4 
  = 
  0*96. 
  

  

  We 
  are 
  now 
  justified 
  in 
  making 
  a 
  quantitative 
  comparison 
  

   between 
  the 
  frequency 
  of 
  a 
  and 
  that 
  of 
  the 
  fundamental 
  radia- 
  

   tion 
  from 
  such 
  a 
  ring 
  calculated 
  from 
  the 
  theory 
  of 
  Bohr. 
  

  

  We 
  have 
  obtained 
  the 
  experimental 
  result, 
  

  

  X 
  = 
  3-.. 
  (N-<7„)*. 
  

  

  On 
  his 
  theory, 
  making 
  the 
  assumption 
  that 
  the 
  ring 
  moves 
  

   as 
  a 
  whole 
  from 
  stationary 
  state 
  2 
  to 
  state 
  1, 
  the 
  frequency 
  

   of 
  the 
  principal 
  radiation 
  emitted 
  is 
  

  

  = 
  (t>-W^^-°^ 
  

  

  where 
  e 
  is 
  the 
  charge 
  on 
  an 
  electron, 
  m 
  its 
  mass, 
  and 
  h 
  

   Planck's 
  constant. 
  

  

  The 
  numerical 
  agreement 
  between 
  these 
  two 
  constants 
  

  

  v 
  and 
  — 
  -p 
  — 
  is 
  known 
  to 
  be 
  very 
  close, 
  while 
  Bohr's 
  

  

  explanation 
  of 
  the 
  Balmer 
  series 
  for 
  hydrogen 
  assumes 
  them 
  

   to 
  be 
  identical. 
  This 
  numerical 
  agreement 
  between 
  the 
  

   experimental 
  values 
  and 
  those 
  calculated 
  from 
  a 
  theory 
  

   designed 
  to 
  explain 
  the 
  ordinary 
  hydrogen 
  spectrum 
  is 
  

   remarkable, 
  as 
  the 
  wave-lengths 
  dealt 
  with 
  in 
  the 
  two 
  cases 
  

   differ 
  by 
  a 
  factor 
  of 
  about 
  2000. 
  The 
  assumption 
  that 
  the 
  

   whole 
  ring 
  takes 
  part 
  in 
  the 
  radiation 
  introduces, 
  however, 
  

   a 
  grave 
  difficulty 
  from 
  energy 
  considerations, 
  while 
  no 
  

   explanation 
  of 
  the 
  faint 
  line 
  /3 
  has 
  been 
  forthcoming. 
  

   Probably 
  further 
  experiments 
  will 
  show 
  that 
  the 
  theory 
  

   needs 
  some 
  modification. 
  

  

  The 
  results 
  hitherto 
  obtained 
  for 
  the 
  radiations 
  of 
  the 
  

   L 
  series 
  are 
  too 
  meagre 
  to 
  justify 
  any 
  explanation. 
  As 
  

   before, 
  the 
  line 
  of 
  longest 
  wave-length 
  is 
  the 
  most 
  pro- 
  

   minent, 
  a 
  result 
  similar 
  to 
  that 
  found 
  in 
  ordinary 
  light- 
  

   spectra. 
  The 
  wave-lengths 
  found 
  for 
  this 
  line 
  in 
  the 
  case 
  of 
  

   tantalum 
  and 
  platinum 
  suggest 
  that 
  possibly 
  the 
  frequency 
  

   is 
  here 
  

  

  =(i- 
  !*>»(*-*.)'. 
  

  

  Here 
  X 
  and 
  cr„ 
  are 
  unknown, 
  but 
  it 
  is 
  evident 
  from 
  the 
  

   periodic 
  system 
  that 
  N 
  Pt 
  — 
  N 
  Ta 
  = 
  5, 
  while 
  probably 
  a 
  n 
  remains 
  

  

  * 
  Monthly 
  Notes 
  Roy. 
  Astr. 
  Sec. 
  June 
  19] 
  2. 
  

   Phil 
  Mag. 
  S. 
  6. 
  Vol. 
  26. 
  No. 
  156. 
  Dec. 
  1913. 
  4 
  A 
  

  

  