﻿of 
  Atoms 
  and 
  Molecules. 
  7 
  

  

  objections, 
  however, 
  may 
  be 
  raised 
  against 
  the 
  theory. 
  These 
  

   objections 
  are 
  intimately 
  connected 
  with 
  the 
  problem 
  of 
  the 
  

   homogeneity 
  of 
  the 
  radiation 
  emitted. 
  In 
  Nicholson's 
  cal- 
  

   culations 
  the 
  frequency 
  of 
  lines 
  in 
  a 
  line-spectrum 
  is 
  identified 
  

   with 
  the 
  frequency 
  of 
  vibration 
  of 
  a 
  mechanical 
  system 
  in 
  a 
  

   distinctly 
  indicated 
  state 
  of 
  equilibrium. 
  As 
  a 
  relation 
  from 
  

   Planck's 
  theory 
  is 
  used, 
  we 
  might 
  expect 
  that 
  the 
  radiation 
  

   is 
  sent 
  out 
  in 
  quanta 
  ; 
  but 
  systems 
  like 
  those 
  considered, 
  in 
  

   which 
  the 
  frequency 
  is 
  a 
  function 
  of 
  the 
  energy, 
  cannot 
  emit 
  

   a 
  finite 
  amount 
  of 
  a 
  homogeneous 
  radiation 
  ; 
  for, 
  as 
  soon 
  as 
  the 
  

   emission 
  of 
  radiation 
  is 
  started, 
  the 
  energy 
  and 
  also 
  the 
  

   frequency 
  of 
  the 
  system 
  are 
  altered. 
  Further, 
  according 
  to 
  

   the 
  calculation 
  of 
  Nicholson, 
  the 
  systems 
  are 
  unstable 
  for 
  

   some 
  modes 
  of 
  vibration. 
  Apart 
  from 
  such 
  objections 
  — 
  which 
  

   may 
  be 
  only 
  formal 
  (see 
  p. 
  23) 
  — 
  it 
  must 
  be 
  remarked, 
  that 
  

   the 
  theory 
  in 
  the 
  form 
  given 
  does 
  not 
  seem 
  to 
  be 
  able 
  to 
  

   account 
  for 
  the 
  well-known 
  laws 
  of 
  Balmer 
  and 
  Bydberg 
  

   connecting 
  the 
  frequencies 
  of 
  the 
  lines 
  in 
  the 
  line-spectra 
  

   of 
  the 
  ordinary 
  elements. 
  

  

  It 
  will 
  now 
  be 
  attempted 
  to 
  show 
  that 
  the 
  difficulties 
  in 
  

   question 
  disappear 
  if 
  Ave 
  consider 
  the 
  problems 
  from 
  the 
  

   point 
  of 
  view 
  taken 
  in 
  this 
  paper. 
  Before 
  proceeding 
  it 
  may 
  

   be 
  useful 
  to 
  restate 
  briefly 
  the 
  ideas 
  characterizing 
  the 
  calcu- 
  

   lations 
  on 
  p. 
  5. 
  The 
  principal 
  assumptions 
  used 
  are 
  : 
  

  

  (1) 
  That 
  the 
  dynamical 
  equilibrium 
  of 
  the 
  systems 
  in 
  the 
  

  

  stationary 
  states 
  can 
  be 
  discussed 
  by 
  help 
  of 
  the 
  

   ordinary 
  mechanics, 
  while 
  the 
  passing 
  of 
  the 
  systems 
  

   between 
  different 
  stationary 
  states 
  cannot 
  be 
  treated 
  

   on 
  that 
  basis. 
  

  

  (2) 
  That 
  the 
  latter 
  process 
  is 
  followed 
  by 
  the 
  emission 
  

  

  of 
  a 
  homogeneous 
  radiation, 
  for 
  which 
  the 
  relation 
  

   between 
  the 
  frequency 
  and 
  the 
  amount 
  of 
  energy 
  

   emitted 
  is 
  the 
  one 
  given 
  by 
  Planck's 
  theory. 
  

  

  The 
  first 
  assumption 
  seems 
  to 
  present 
  itself 
  ; 
  for 
  it 
  is 
  

   known 
  that 
  the 
  ordinary 
  mechanics 
  cannot 
  have 
  an 
  absolute 
  

   validity, 
  but 
  will 
  only 
  hold 
  in 
  calculations 
  of 
  certain 
  mean 
  

   values 
  of 
  the 
  motion 
  of 
  the 
  electrons. 
  On 
  the 
  other 
  hand, 
  

   in 
  the 
  calculations 
  of 
  the 
  dynamical 
  equilibrium 
  in 
  a 
  stationary 
  

   state 
  in 
  which 
  there 
  is 
  no 
  relative 
  displacement 
  of 
  the 
  

   particles, 
  we 
  need 
  not 
  distinguish 
  between 
  the 
  actual 
  

   motions 
  and 
  their 
  mean 
  values. 
  The 
  second 
  assumption 
  is 
  

   in 
  obvious 
  contrast 
  to 
  the 
  ordinary 
  ideas 
  of 
  electrodynamics, 
  

   but 
  appears 
  to 
  be 
  necessary 
  in 
  order 
  to 
  account 
  for 
  experi- 
  

   mental 
  facts. 
  

  

  In 
  the 
  calculations 
  on 
  page 
  5 
  we 
  have 
  further 
  made 
  \\±v 
  

  

  