﻿of 
  Atoms 
  and 
  Molecules. 
  17 
  

  

  frequency 
  and 
  dimensions 
  of 
  the 
  systems 
  in 
  successive 
  

   stationary 
  states 
  will 
  diminish 
  without 
  limit 
  if 
  r 
  increases. 
  

   In 
  the 
  following 
  considerations 
  we 
  shall 
  for 
  the 
  sake 
  of 
  

   brevity 
  refer 
  to 
  the 
  two 
  kinds 
  of 
  states 
  in 
  question 
  as 
  

   " 
  mechanical- 
  " 
  states 
  ; 
  by 
  this 
  notation 
  only 
  emphasizing 
  

   the 
  assumption 
  that 
  the 
  motion 
  of 
  the 
  electron 
  in 
  both 
  cases 
  

   can 
  be 
  accounted 
  for 
  by 
  the 
  ordinary 
  mechanics. 
  

  

  Tracing 
  the 
  analogy 
  between 
  the 
  two 
  kinds 
  of 
  mechanical 
  

   states, 
  we 
  might 
  now 
  expect 
  the 
  possibility 
  of 
  an 
  absorption 
  

   of 
  radiation, 
  not 
  only 
  corresponding 
  to 
  the 
  passing 
  of 
  the 
  

   system 
  between 
  two 
  different, 
  stationary 
  states, 
  but 
  also 
  

   corresponding 
  to 
  the 
  passing 
  between 
  one 
  of 
  the 
  stationary 
  

   states 
  and 
  a 
  state 
  in 
  which 
  the 
  electron 
  is 
  free 
  ; 
  and 
  as 
  above, 
  

   we 
  might 
  expect 
  that 
  the 
  frequency 
  of 
  this 
  radiation 
  was 
  de- 
  

   termined 
  by 
  the 
  equation 
  E 
  = 
  Af, 
  where 
  E 
  is 
  the 
  difference 
  

   between 
  the 
  total 
  energy 
  of 
  the 
  system 
  in 
  the 
  two 
  states. 
  

   As 
  it 
  will 
  be 
  seen, 
  such 
  an 
  absorption 
  of 
  radiation 
  is 
  just 
  

   what 
  is 
  observed 
  in 
  experiments 
  on 
  ionization 
  by 
  ultra-violet 
  

   light 
  and 
  by 
  Rontgen 
  rays. 
  Obviously, 
  we 
  get 
  in 
  this 
  way 
  

   the 
  same 
  expression 
  for 
  the 
  kinetic 
  energy 
  of 
  an 
  electron 
  

   ejected 
  from 
  an 
  atom 
  by 
  photo-electric 
  effect 
  as 
  that 
  deduced 
  

   by 
  Einstein 
  *, 
  i. 
  e. 
  T 
  = 
  hv 
  — 
  W, 
  where 
  T 
  is 
  the 
  kinetic 
  energy 
  

   of 
  the 
  electron 
  ejected, 
  and 
  W 
  the 
  total 
  amount 
  of 
  energy 
  

   emitted 
  during 
  the 
  original 
  binding 
  of 
  the 
  electron. 
  

  

  The 
  above 
  considerations 
  may 
  further 
  account 
  for 
  ihe 
  

   result 
  of 
  some 
  experiments 
  of 
  R. 
  W. 
  Wood 
  f 
  on 
  absorption 
  

   of 
  light 
  by 
  sodium 
  vapour. 
  In 
  these 
  experiments, 
  an 
  

   absorption 
  corresponding 
  to 
  a 
  very 
  great 
  number 
  of 
  lines 
  in 
  

   the 
  principal 
  series 
  of 
  the 
  sodium 
  spectrum 
  is 
  observed, 
  and 
  

   in 
  addition 
  a 
  continuous 
  absorption 
  which 
  begins 
  at 
  the 
  head 
  

   of 
  the 
  series 
  and 
  extends 
  to 
  the 
  extreme 
  ultra-violet. 
  This 
  

   is 
  exactly 
  what 
  we 
  should 
  expect 
  according 
  to 
  the 
  analogy 
  in 
  

   question, 
  and, 
  as 
  we 
  shall 
  see, 
  a 
  closer 
  consideration 
  of 
  the 
  

   above 
  experiments 
  allows 
  us 
  to 
  trace 
  the 
  analogy 
  still 
  

   further. 
  As 
  mentioned 
  on 
  p. 
  9 
  the 
  radii 
  of 
  the 
  orbits 
  of 
  

   the 
  electrons 
  will 
  for 
  stationary 
  states 
  corresponding 
  to 
  high 
  

   values 
  for 
  t 
  be 
  very 
  great 
  compared 
  with 
  ordinary 
  atomic 
  

   dimensions. 
  This 
  circumstance 
  was 
  used 
  as 
  an 
  explanation 
  

   of 
  the 
  non-appearance 
  in 
  experiments 
  with 
  vacuum-tubes 
  of 
  

   lines 
  corresponding 
  to 
  the 
  higher 
  numbers 
  in 
  the 
  Balmer 
  

   series 
  of 
  the 
  hydrogen 
  spectrum. 
  This 
  is 
  also 
  in 
  conformity 
  

   with 
  experiments 
  on 
  the 
  emission 
  spectrum 
  of 
  sodium 
  ; 
  in 
  

   the 
  principal 
  series 
  of 
  the 
  emission 
  spectrum 
  of 
  this 
  substance 
  

  

  * 
  A. 
  Einstein, 
  Ann. 
  d. 
  Pfojs. 
  xvii, 
  p. 
  146 
  (1905). 
  

   t 
  R. 
  W. 
  Wood, 
  Physical 
  Optics, 
  p. 
  513 
  (1911). 
  

  

  PML 
  Mag. 
  S. 
  6. 
  Vol. 
  26. 
  No. 
  151. 
  July 
  1913. 
  C 
  

  

  