﻿802 
  Mr. 
  H. 
  L. 
  P. 
  Jolly 
  on 
  the 
  

  

  integral 
  numbers. 
  Such 
  a 
  manifestation 
  would 
  demand 
  two 
  

   essential 
  conditions, 
  namely, 
  that 
  the 
  number 
  of 
  u 
  elementar- 
  

   quanta 
  " 
  emitted 
  by 
  each 
  of 
  the 
  centres 
  of 
  radiation 
  during 
  

   an 
  active 
  period 
  be 
  small, 
  and, 
  further, 
  that 
  an 
  increased 
  

   excitation 
  represents 
  an 
  increased 
  intrinsic 
  energy 
  of 
  the 
  

   individual 
  oscillators, 
  and 
  is 
  in 
  no 
  way 
  connected 
  with 
  an 
  

   increase 
  in 
  their 
  number. 
  

  

  Unfortunately, 
  it 
  appears 
  certain 
  that 
  the 
  latter 
  condition 
  

   is 
  radically 
  impossible 
  in 
  the 
  discharge 
  of 
  electricity 
  through 
  

   gases. 
  Indeed, 
  there 
  is 
  reason 
  to 
  believe, 
  as 
  will 
  be 
  shown 
  

   later, 
  that 
  the 
  number 
  of 
  centres 
  of 
  emission 
  is 
  actually 
  

   proportional 
  to 
  the 
  amount 
  of 
  current 
  passing. 
  Further, 
  it 
  

   should 
  be 
  realized 
  that, 
  even 
  if 
  a 
  simple 
  numerical 
  relation 
  

   between 
  the 
  changes 
  in 
  energy 
  of 
  spectrum 
  lines 
  existed, 
  

   the 
  accuracy 
  with 
  which 
  these 
  measurements 
  can 
  be 
  carried 
  

   out 
  is 
  quite 
  inadequate 
  to 
  establish 
  any 
  but 
  the 
  simplest 
  of 
  

   such 
  relations. 
  To 
  express 
  this 
  more 
  clearly 
  : 
  suppose 
  

   that 
  the 
  energy 
  of 
  two 
  lines 
  a 
  and 
  j3 
  were 
  represented 
  by 
  

   mh 
  a 
  and 
  nh^ 
  where 
  "m" 
  and 
  u 
  n 
  " 
  are 
  whole 
  numbers, 
  and 
  

   that 
  changes 
  in 
  these 
  values 
  could 
  only 
  give 
  rise 
  to 
  terms 
  

   (?n+l)7i 
  a 
  , 
  (m+2)A 
  a 
  ... 
  &c. 
  due 
  to 
  the 
  one 
  line, 
  and 
  (n+l)^, 
  

   (31 
  + 
  2)710... 
  &c. 
  due 
  to 
  the 
  other 
  line, 
  then 
  the 
  statement 
  in 
  

   the 
  previous 
  sentence 
  means 
  that 
  this 
  discontinuous 
  changing 
  

   of 
  the 
  energy 
  of 
  the 
  lines 
  could 
  only 
  be 
  established 
  in 
  the 
  

   cases 
  in 
  which 
  m 
  and 
  n 
  were 
  small 
  integers. 
  

  

  The 
  extreme 
  difficulty 
  of 
  the 
  measurements 
  arises 
  in 
  

   several 
  ways. 
  In 
  the 
  first 
  place, 
  the 
  total 
  amount 
  of 
  energy 
  

   emitted 
  as 
  radiation 
  from 
  gases 
  in 
  discharge-tubes 
  is 
  extra- 
  

   ordinarily 
  small, 
  and, 
  as 
  will 
  appear 
  in 
  the 
  sequel, 
  a 
  large 
  

   amount 
  of 
  time 
  and 
  experimenting 
  has 
  been 
  bestowed 
  upon 
  

   this 
  point 
  alone. 
  When 
  we 
  consider 
  the 
  low 
  pressure 
  of 
  the 
  

   gas 
  under 
  observation, 
  the 
  small 
  amount 
  of 
  energy 
  is 
  not 
  

   surprising. 
  A 
  column 
  of 
  air 
  at 
  1 
  mm. 
  pressure 
  enclosed 
  in 
  

   a 
  capillary 
  tube 
  of 
  1 
  mm. 
  diameter 
  (such 
  as 
  has 
  been 
  used 
  

   in 
  the 
  present 
  experiments) 
  would, 
  if 
  compressed 
  to 
  the 
  

   same 
  density 
  as 
  solid 
  platinum, 
  have 
  a 
  diameter 
  of 
  3 
  jjl. 
  

   A 
  platinum 
  wire 
  of 
  these 
  dimensions 
  would, 
  if 
  not 
  self- 
  

   luminous, 
  be 
  almost 
  invisible 
  to 
  the 
  naked 
  eye. 
  

  

  Apart 
  from 
  this 
  purely 
  quantitative 
  difficulty 
  there 
  is 
  

   another 
  — 
  the 
  apparent 
  capriciousness 
  of 
  all 
  discharge-tubes. 
  

  

  Those 
  who 
  have 
  studied 
  the 
  spectra 
  of 
  gases 
  qualitatively 
  

   have 
  complained 
  one 
  and 
  all 
  of 
  the 
  difficulty 
  of 
  reproducing 
  

   exactly 
  from 
  one 
  day 
  to 
  another 
  the 
  behaviour 
  of 
  a 
  gas 
  in 
  a 
  

   discharge-tube. 
  Changes 
  occur 
  for 
  which 
  none 
  but 
  tentative 
  

   explanations 
  can 
  be 
  given, 
  and 
  the 
  maintenance 
  of 
  a 
  constant 
  

   gaseous 
  source 
  for 
  spectroscopic 
  investigations, 
  let 
  us 
  say, 
  

  

  