﻿and 
  from 
  fchii 
  

  

  of 
  Atoms 
  and 
  Molecules. 
  

   27r 
  2 
  me 
  i 
  /l 
  

  

  We 
  see 
  that 
  this 
  expression 
  accounts 
  for 
  the 
  law 
  connecting 
  

   the 
  lines 
  in 
  the 
  spectrum 
  of 
  hydrogen. 
  If 
  we 
  put 
  t 
  2 
  =2 
  and 
  

   let 
  Tj 
  vary, 
  we 
  get 
  the 
  ordinary 
  Buhner 
  series. 
  If 
  we 
  put 
  

   7- 
  2 
  =3 
  5 
  we 
  get 
  the 
  series 
  in 
  the 
  ultra-red 
  observed 
  by 
  Paschen* 
  

   and 
  previously 
  suspected 
  by 
  Bitz. 
  If 
  we 
  put 
  t 
  2 
  =1 
  and 
  

   r 
  2 
  = 
  4, 
  5, 
  . 
  ., 
  we 
  get 
  series 
  respectively 
  in 
  the 
  extreme 
  ultra- 
  

   violet 
  and 
  the 
  extreme 
  ultra-red, 
  which 
  are 
  not 
  observed, 
  but 
  

   the 
  existence 
  of 
  which 
  may 
  be 
  expected. 
  

  

  The 
  agreement 
  in 
  question 
  is 
  quantitative 
  as 
  well 
  as 
  

   qualitative. 
  Putting 
  

  

  ? 
  = 
  I'7.10- 
  10 
  , 
  -=5'31.10 
  17 
  , 
  and 
  7i=6*5. 
  10" 
  27 
  , 
  

  

  we 
  get 
  

  

  k 
  6 
  

  

  The 
  observed 
  value 
  for 
  the 
  factor 
  outside 
  the 
  bracket 
  in 
  the 
  

   formula 
  (4; 
  is 
  

  

  3-290 
  . 
  10 
  15 
  . 
  

  

  The 
  agreement 
  between 
  the 
  theoretical 
  and 
  observed 
  values 
  

   is 
  inside 
  the 
  uncertainty 
  due 
  to 
  experimental 
  errors 
  in 
  the 
  

   constants 
  entering 
  in 
  the 
  expression 
  for 
  the 
  theoretical 
  value. 
  

   We 
  shall 
  in 
  § 
  3 
  return 
  to 
  consider 
  the 
  possible 
  importance 
  

   of 
  the 
  agreement 
  in 
  question. 
  

  

  It 
  may 
  be 
  remarked 
  that 
  the 
  fact, 
  that 
  it 
  has 
  not 
  been 
  

   possible 
  to 
  observe 
  more 
  than 
  12 
  lines 
  of 
  the 
  Balmer 
  series 
  

   in 
  experiments 
  with 
  vacuum 
  tubes, 
  while 
  33 
  lines 
  are 
  ob- 
  

   served 
  in 
  the 
  spectra 
  of 
  some 
  celestial 
  bodies, 
  is 
  just 
  what 
  we 
  

   should 
  expect 
  from 
  the 
  above 
  theory. 
  According 
  to 
  the 
  

   equation 
  (3) 
  the 
  diameter 
  of 
  the 
  orbit 
  of 
  the 
  electron 
  in 
  

   the 
  different 
  stationary 
  states 
  is 
  proportional 
  to 
  t 
  2 
  . 
  For 
  

   t 
  = 
  12 
  the 
  diameter 
  is 
  equal 
  to 
  l*6.10~ 
  6 
  cm., 
  or 
  equal 
  to 
  

   the 
  mean 
  distance 
  between 
  the 
  molecule's 
  in 
  a 
  gas 
  at 
  a 
  

   pressure 
  of 
  about 
  7 
  mm. 
  mercury; 
  for 
  t 
  = 
  33 
  the 
  diameter 
  

   is 
  equal 
  to 
  1"2 
  . 
  10~ 
  6 
  cm., 
  corresponding 
  to 
  the 
  mean 
  distance 
  

   of 
  the 
  molecules 
  at 
  a 
  pressure 
  of 
  about 
  0*02 
  mm. 
  mercury. 
  

   According 
  to 
  the 
  theory 
  the 
  necessary 
  condition 
  for 
  the 
  

   appearance 
  of 
  a 
  great 
  number 
  of 
  lines 
  is 
  therefore 
  a 
  very 
  

   small 
  density 
  of 
  the 
  gas 
  ; 
  for 
  simultaneously 
  to 
  obtain 
  an 
  

  

  * 
  F. 
  Pascheri; 
  Ann. 
  d. 
  PJvjs. 
  xxvii. 
  p. 
  565 
  (1908). 
  

  

  