﻿152 
  ANNUM, 
  REPORT 
  SMITHSONIAN 
  INSTITUTION, 
  1922. 
  

  

  tinuously 
  from 
  its 
  source 
  and 
  being 
  absorbed 
  continuously 
  by 
  mate- 
  

   rial 
  in 
  ils 
  path, 
  (hose 
  emitting 
  and 
  absorbing 
  agents 
  being 
  known 
  to 
  

   be 
  electrons. 
  Yet 
  there 
  is 
  evidence 
  that 
  radiant 
  energy 
  is 
  absorbed 
  

   or 
  emitted 
  as 
  if 
  in 
  discrete 
  units 
  equal 
  to 
  /m, 
  where 
  n 
  is 
  the 
  fre- 
  

   quency 
  of 
  vibration 
  of 
  the 
  radiation. 
  

  

  Such 
  considerations 
  have 
  given 
  rise 
  l<> 
  the 
  quantum 
  theory, 
  which 
  

   has 
  been 
  remarkably 
  successful 
  as 
  a 
  statement 
  of 
  the 
  conditions 
  

   under 
  which 
  an 
  electron 
  will 
  OT 
  will 
  not 
  radiate 
  and 
  of 
  the 
  condi- 
  

   tions 
  under 
  which 
  it 
  may 
  be 
  in 
  equilibrium 
  in 
  an 
  atom. 
  Little 
  

   progress 
  has, 
  however, 
  been 
  made 
  in 
  explaining 
  the 
  quantum 
  laws, 
  

   and, 
  until 
  this 
  is 
  done, 
  it 
  will 
  probably 
  be 
  impossible 
  fully 
  to 
  under- 
  

   stand 
  the 
  forces 
  which 
  hold 
  the 
  parts 
  of 
  atoms 
  together. 
  

  

  Spectral 
  series. 
  — 
  In 
  the 
  apparently 
  complicated 
  spectra 
  of 
  chemi- 
  

   cal 
  elements, 
  some 
  of 
  which 
  contain 
  hundreds 
  of 
  bright 
  lines 
  in 
  the 
  

   visible 
  spectrum 
  alone, 
  there 
  have 
  been 
  discovered 
  remarkable 
  rela- 
  

   tionships 
  between 
  the 
  frequencies 
  of 
  vibration 
  of 
  the 
  different 
  spec- 
  

   tral 
  lines 
  of 
  an 
  element 
  and 
  between 
  corresponding 
  lines 
  of 
  different 
  

   elements. 
  These 
  relationships 
  may 
  be 
  expressed 
  by 
  series 
  formulae^ 
  

   of 
  which 
  the 
  following 
  formula 
  for 
  the 
  vibration 
  frequencies 
  of 
  the 
  

   various 
  kinds 
  of 
  light, 
  or 
  spectral 
  lines, 
  due 
  to 
  hydrogen 
  atoms 
  is 
  

   an 
  example: 
  

  

  n-JV| 
  

  

  \r 
  2 
  in 
  2 
  / 
  

  

  Here 
  n 
  is 
  the 
  number 
  of 
  vibrations 
  per 
  section, 
  N 
  is 
  a 
  universal 
  con- 
  

   stant 
  3.29025 
  ( 
  10) 
  15 
  and 
  r 
  and 
  m 
  are 
  integers 
  which 
  may 
  have 
  any 
  

   value 
  between 
  1 
  and 
  infinity. 
  Thus, 
  if 
  r 
  = 
  1 
  and 
  m 
  = 
  2, 
  3, 
  4, 
  .. 
  . 
  ., 
  

   each 
  value 
  of 
  m 
  gives 
  a 
  frequency 
  corresponding 
  to 
  a 
  spectral 
  line 
  in 
  

   the 
  extreme 
  ultraviolet. 
  These 
  lines 
  constitute 
  a 
  spectral 
  series. 
  

   Similarly 
  if 
  r 
  = 
  2 
  and 
  m 
  = 
  3, 
  4, 
  5, 
  etc., 
  we 
  get 
  a 
  scries 
  of 
  lines 
  in 
  the 
  

   visible 
  and 
  near 
  ultraviolet 
  spectrum. 
  If 
  r 
  = 
  3 
  and 
  m 
  = 
  4, 
  5, 
  6, 
  etc., 
  

   we 
  get 
  a 
  series 
  of 
  lines 
  in 
  the 
  infra 
  red. 
  The 
  frequencies 
  of 
  these 
  

   lines 
  agree 
  with 
  the 
  measured 
  frequencies 
  with 
  an 
  accuracy 
  of 
  about 
  

   one 
  part 
  in 
  a 
  hundred 
  thousand. 
  

  

  For 
  elements 
  other 
  than 
  hydrogen, 
  there 
  are 
  added 
  to 
  r 
  and 
  m 
  

   certain 
  constants 
  characteristic 
  of 
  the 
  element, 
  but 
  r 
  and 
  m 
  still 
  take 
  

   various 
  integral 
  values. 
  

  

  A 
  study 
  of 
  the 
  absorption 
  or 
  refraction 
  of 
  light 
  by 
  a 
  medium 
  leads 
  

   to 
  the 
  possibility 
  of 
  calculating 
  the 
  number 
  of 
  atoms 
  in 
  the 
  absorb- 
  

   ing 
  substance 
  which 
  are, 
  at 
  any 
  given 
  instant, 
  capable 
  of 
  emitting 
  

   light 
  of 
  any 
  given 
  frequency. 
  By 
  such 
  methods 
  we 
  learn 
  that 
  only 
  

   a 
  small 
  fraction 
  of 
  the 
  atoms 
  are, 
  at 
  any 
  instant, 
  taking 
  part 
  in 
  the 
  

   emission 
  of 
  light 
  and 
  that 
  the. 
  atoms 
  emitting 
  one 
  line 
  in 
  the 
  spec- 
  

   trum 
  arc 
  different 
  from 
  those 
  emitting 
  any 
  other 
  line. 
  Thus 
  an 
  atom, 
  

   when 
  it 
  emits 
  radiation, 
  emits 
  only 
  one 
  frequency 
  of 
  radiation 
  at 
  a 
  

   time. 
  

  

  