﻿Molecules 
  of 
  the 
  Elements 
  and 
  their 
  Compounds. 
  55 
  

  

  This 
  is 
  from 
  18*6 
  to 
  4'9 
  times 
  shorter 
  than 
  the 
  calculated 
  

   wave 
  emitted 
  by 
  the 
  fundamental 
  period 
  of 
  the 
  electrons 
  in 
  

   the 
  atom, 
  and 
  the 
  difference 
  would 
  be 
  less 
  still 
  if 
  the 
  

   distance 
  between 
  the 
  two 
  atoms 
  of 
  the 
  molecule 
  is 
  less 
  than 
  

   10" 
  8 
  cm. 
  

  

  Linear 
  Velocity. 
  — 
  It 
  must 
  be 
  said 
  that 
  no 
  definite 
  result 
  

   lias 
  vet 
  been 
  reached 
  in 
  determining 
  the 
  linear 
  velocity 
  of 
  

   the 
  electron 
  in 
  the 
  atom, 
  except 
  that 
  it 
  seems 
  to 
  be 
  small 
  

   compared 
  with 
  that 
  of 
  light. 
  There 
  are 
  at 
  least 
  two 
  modes 
  

   of 
  inquiry; 
  first, 
  by 
  means 
  of 
  the 
  spectra. 
  If 
  the 
  atoms 
  

   described 
  represent 
  true 
  atoms 
  it 
  should 
  be 
  po>sible 
  to 
  

   account 
  for 
  the 
  various 
  spectra 
  of 
  the 
  elements 
  and 
  their 
  

   compounds. 
  Whittaker 
  * 
  has 
  iu 
  a 
  very 
  general 
  manner 
  

   derived 
  the 
  law 
  of 
  the 
  hydrogen 
  series, 
  and 
  has 
  shown 
  that 
  

   the 
  only 
  kind 
  of 
  terms 
  in 
  the 
  general 
  equations 
  that 
  can 
  

   account 
  for 
  such 
  a 
  law 
  are 
  those 
  that 
  arise 
  from 
  a 
  gyroscopic 
  

   connexion 
  between 
  the 
  atoms 
  of 
  a 
  molecule. 
  The 
  molecules 
  

   indicated 
  by 
  this 
  theory 
  are 
  simply 
  little 
  gyroscopes 
  con- 
  

   nected 
  in 
  a 
  semi-rigid 
  manner. 
  It 
  seems 
  as 
  though 
  it 
  

   might 
  be 
  possible 
  to 
  derive 
  the 
  law 
  of 
  the 
  hydrogen 
  series 
  

   in 
  this 
  manner, 
  and 
  the 
  subject 
  is 
  referred 
  to 
  here 
  in 
  the 
  

   hope 
  that 
  some 
  one 
  will 
  undertake 
  these 
  calculations. 
  

   If 
  successful, 
  not 
  only 
  will 
  the 
  spectra 
  be 
  derived, 
  but 
  

   the 
  linear 
  velocity, 
  and 
  the 
  relative 
  size 
  of 
  atom 
  and 
  

   distance 
  between 
  them 
  be 
  found. 
  It 
  will 
  also 
  be 
  possible 
  

   to 
  decide 
  whether 
  hydrogen 
  has 
  two 
  or 
  three 
  electrons 
  per 
  

   atom. 
  

  

  Second, 
  the 
  linear 
  velocity 
  might 
  be 
  derived 
  from 
  the 
  

   heats 
  of 
  combination 
  of 
  the 
  elements 
  and 
  compounds. 
  

   Attempts 
  have 
  been 
  made 
  to 
  do 
  this, 
  but 
  the 
  results 
  are 
  not 
  

   entirely 
  conclusive 
  for 
  the 
  following 
  reasons. 
  It 
  should 
  be 
  

   possible 
  to 
  calculate 
  the 
  energy 
  required 
  to 
  separate 
  the 
  

   atoms 
  of 
  a 
  molecule 
  on 
  this 
  theory 
  of 
  the 
  formation 
  of 
  

   molecules. 
  The 
  difficulty 
  is 
  that 
  the 
  energy 
  comes 
  out 
  a 
  

   different 
  quantity 
  according 
  to 
  the 
  path 
  along 
  which 
  the 
  

   atom 
  is 
  moved 
  from 
  any 
  fixed 
  position 
  to 
  infinity. 
  That 
  is 
  

   to 
  say, 
  the 
  energy 
  in 
  going 
  around 
  a 
  closed 
  path 
  is 
  not 
  zero 
  

   apparently. 
  No 
  doubt 
  this 
  is 
  due 
  to 
  some 
  difficulty 
  in 
  

   calculating 
  the 
  energy, 
  possibly 
  the 
  alteration 
  of 
  the 
  internal 
  

   phase 
  of 
  the 
  electrons 
  with 
  the 
  motion 
  from 
  point 
  to 
  point 
  

   which 
  has 
  been 
  neglected, 
  or 
  to 
  some 
  other 
  causes. 
  

  

  If 
  one 
  of 
  the 
  atoms 
  in 
  the 
  diatomic 
  molecule 
  (three 
  

   electrons) 
  is 
  separated 
  from 
  the 
  other 
  along 
  the 
  line 
  joining 
  

   their 
  centres 
  when 
  in 
  the 
  position 
  of 
  stable 
  equilibrium, 
  the 
  

  

  * 
  E. 
  T. 
  Whittaker, 
  Proc. 
  "Roy. 
  Soc. 
  ser. 
  A. 
  vol. 
  lxxxv. 
  no. 
  A 
  578, 
  

   June 
  9, 
  1911, 
  p. 
  262. 
  

  

  