﻿26 
  Dr. 
  A. 
  0. 
  Crehore 
  on 
  the 
  Formation 
  of 
  the 
  

  

  with 
  each 
  other 
  at 
  fixed 
  distances, 
  thus 
  forming 
  the 
  mole- 
  

   cules 
  of 
  compounds. 
  The 
  diatomic 
  molecules 
  consist 
  o£ 
  two 
  

   atoms 
  rigidly 
  held 
  at 
  fixed 
  distances 
  apart 
  resembling 
  the 
  

   well-known 
  dumb-bell 
  molecule 
  which 
  has 
  been 
  deduced 
  

   from 
  the 
  theory 
  of 
  heat. 
  The 
  reason 
  that 
  carbon 
  may 
  unite 
  

   with 
  more 
  hydrogen 
  atoms 
  than 
  nitrogen, 
  and 
  nitrogen 
  with 
  

   more 
  than 
  oxygen, 
  and 
  oxygen 
  with 
  more 
  than 
  fluorine, 
  

   becomes 
  apparent. 
  

  

  These 
  and 
  other 
  conclusions 
  are 
  deduced 
  from 
  the 
  me- 
  

   chanical 
  forces 
  between 
  moving 
  electrical 
  charges 
  that 
  have 
  

   been 
  derived 
  from 
  Maxwell's 
  electromagnetic 
  theory. 
  The 
  

   expression 
  for 
  this 
  mechanical 
  force 
  in 
  the 
  modern 
  theory 
  * 
  

   involves 
  the 
  transmission 
  of 
  all 
  of 
  the 
  effects 
  of 
  the 
  moving 
  

   charge 
  with 
  a 
  velocity 
  equal 
  to 
  that 
  of 
  light. 
  The 
  introduc- 
  

   tion 
  of 
  this 
  hypothesis 
  makes 
  the 
  formulae 
  difficult 
  to 
  use. 
  

   It 
  has 
  been 
  shown 
  f 
  that 
  if 
  the 
  velocity 
  of 
  transmission 
  is 
  

   allowed 
  to 
  increase 
  without 
  limit 
  these 
  more 
  recent 
  formulae 
  

   become 
  identical 
  with 
  those 
  derived 
  by 
  Thomson 
  in 
  1881. 
  

   These 
  latter 
  formulae 
  are 
  much 
  simpler 
  and 
  can 
  be 
  managed. 
  

   On 
  this 
  account, 
  and 
  for 
  other 
  reasons, 
  it 
  has 
  seemed 
  to 
  be 
  

   very 
  desirable 
  to 
  know 
  the 
  nature 
  of 
  the 
  results 
  that 
  can 
  be 
  

   obtained 
  by 
  the 
  use 
  of 
  these 
  simpler 
  formulae. 
  There 
  are 
  

   reasons 
  that 
  will 
  appear 
  which 
  make 
  it 
  not 
  unlikely 
  that 
  

   results 
  of 
  precisely 
  the 
  same 
  nature 
  as 
  to 
  the 
  formation 
  of 
  

   molecules 
  would 
  be 
  obtained 
  by 
  the 
  use 
  of 
  the 
  more 
  complex 
  

   equations 
  involving 
  the 
  velocity 
  of 
  light. 
  The 
  mathematical 
  

   deductions 
  in 
  this 
  paper 
  are, 
  therefore, 
  derived 
  from 
  these 
  

   Thomson 
  equations. 
  

  

  For 
  the 
  sake 
  of 
  clearness 
  the 
  derivation 
  of 
  the 
  formulae 
  

   are 
  given 
  in 
  the 
  hist 
  part 
  of 
  the 
  paper, 
  a 
  statement 
  and 
  dis- 
  

   cussion 
  of 
  the 
  conclusions 
  being 
  given 
  first, 
  and 
  reference 
  

   being 
  made 
  to 
  the 
  equations 
  as 
  required. 
  

  

  Before 
  any 
  theory 
  can 
  be 
  applied 
  to 
  find 
  how 
  two 
  atoms 
  

   will 
  act 
  upon 
  each 
  other, 
  it 
  is 
  necessary 
  to 
  have 
  some 
  hypo- 
  

   thesis 
  as 
  to 
  the 
  atom 
  itself. 
  The 
  distribution 
  of 
  the 
  electrons 
  

   within 
  the 
  atom 
  on 
  the 
  assumption 
  that 
  they 
  all 
  lie 
  in 
  one 
  

   plane 
  has 
  been 
  approximately 
  calculated 
  J. 
  Table 
  I. 
  show's 
  

   the 
  distribution 
  from 
  one 
  to 
  one 
  hundred 
  electrons. 
  These 
  

   calculations 
  were 
  based 
  upon 
  an 
  assumption 
  that 
  the 
  effect 
  

   of 
  the 
  electrons 
  in 
  all 
  the 
  inside 
  rings 
  upon 
  those 
  in 
  the 
  

   outside 
  ring 
  is 
  the 
  same 
  as 
  if 
  all 
  the 
  electrons 
  in 
  inside 
  rings 
  

   were 
  at 
  the 
  centre 
  of 
  the 
  sphere. 
  It 
  also 
  assumes 
  that 
  the 
  

   rings 
  are 
  true 
  circles. 
  From 
  experimental 
  evidence 
  it 
  seems 
  

  

  * 
  See 
  Abraham's 
  Elektrizitdt, 
  vol. 
  ii. 
  

  

  + 
  F. 
  R, 
  Sharpe, 
  Physical 
  Review, 
  vol. 
  xxv. 
  Sept. 
  1912, 
  p. 
  231. 
  

  

  \ 
  J. 
  J. 
  Thomson, 
  ' 
  the 
  Corpuscular 
  Theory 
  of 
  Matter/ 
  p. 
  109 
  (1907). 
  

  

  