﻿56 
  Dr. 
  A. 
  C. 
  Crehore 
  on 
  the 
  Formation 
  of 
  the 
  

  

  e 
  2, 
  

   total 
  work 
  required 
  is 
  shown 
  to 
  be 
  E 
  = 
  "0716 
  -^/3 
  5 
  . 
  The 
  

  

  energy 
  of 
  dissociation 
  * 
  of 
  one 
  gram 
  of 
  hydrogen 
  at 
  constant 
  

   pressure 
  has 
  been 
  measured 
  to 
  be 
  136,000 
  calories, 
  that 
  is, 
  

   569 
  xlO 
  10 
  ergs. 
  From 
  this 
  the 
  energy 
  of 
  dissociation 
  of 
  

   one 
  molecule 
  of 
  hydrogen 
  is 
  found 
  to 
  be 
  25' 
  6 
  x 
  10 
  ~ 
  12 
  erg. 
  

   By 
  equating 
  the 
  calculated 
  and 
  the 
  measured 
  energy, 
  we 
  

   obtain 
  the 
  relation 
  

  

  3= 
  25^x10^ 
  ^ 
  = 
  . 
  0254xl0 
  _ 
  18 
  _ 
  

   •071b 
  e 
  2 
  co 
  2 
  

  

  In 
  using 
  r 
  = 
  10~ 
  8 
  as 
  the 
  dimensions 
  of 
  the 
  molecule 
  we 
  

   obtain 
  from 
  this 
  /3 
  = 
  '00281 
  ; 
  a 
  = 
  l'057 
  X 
  10" 
  11 
  cm. 
  ; 
  v 
  = 
  947, 
  

   and 
  ^ 
  = 
  8*43 
  X 
  10 
  7 
  cm. 
  per 
  sec. 
  If 
  however, 
  we 
  assume 
  that 
  

   the 
  longest 
  X-rays, 
  given 
  above, 
  have 
  substantially 
  the 
  same 
  

   period 
  as 
  the 
  electrons 
  in 
  their 
  orbits, 
  this 
  condition 
  is 
  

   obtained 
  by 
  assuming 
  that 
  the 
  distance 
  between 
  the 
  atoms 
  

   of 
  the 
  molecule 
  is 
  about 
  five 
  times 
  smaller, 
  namely, 
  

   r 
  = 
  2 
  x 
  10" 
  9 
  cm., 
  from 
  which 
  we 
  find 
  /3 
  = 
  '00096 
  ; 
  

   a 
  = 
  -72xl0- 
  12 
  cm. 
  ; 
  ^ 
  = 
  2770, 
  and 
  = 
  2*89 
  x 
  10 
  7 
  cm. 
  per 
  sec. 
  

  

  X=4-83xl0" 
  9 
  ; 
  ?i 
  = 
  -621 
  x 
  10 
  19 
  ; 
  o> 
  = 
  3-9xl0 
  19 
  . 
  

  

  It 
  seems 
  clear 
  that 
  we 
  do 
  not 
  need 
  to 
  assume 
  velocities 
  

   for 
  the 
  electrons 
  approaching 
  that 
  of 
  light 
  to 
  account 
  for 
  

   the 
  formation 
  of 
  molecules 
  by 
  this 
  theory. 
  Also, 
  the 
  

   dimensions 
  of 
  the 
  atoms 
  are 
  indicated 
  to 
  be 
  much 
  smaller 
  

   than 
  molecular 
  dimensions, 
  probably 
  nearer 
  to 
  the 
  size 
  of 
  an 
  

   electron 
  than 
  to 
  that 
  of 
  a 
  molecule. 
  The 
  radius 
  of 
  the 
  

   electron 
  has 
  been 
  calculated 
  to 
  be 
  about 
  1*8 
  X 
  10~ 
  13 
  cm., 
  and 
  

   the 
  smaller 
  value 
  of 
  the 
  radius 
  of 
  the 
  ring 
  of 
  electrons 
  

   in 
  the 
  three-ring 
  atom 
  above 
  is 
  less 
  than 
  ten 
  times 
  the 
  radius 
  

   of 
  the 
  electron. 
  

  

  Phase 
  Relations, 
  

  

  The 
  equations 
  (45) 
  and 
  (46) 
  which 
  determine 
  the 
  equi- 
  

   librium 
  positions 
  of 
  the 
  atoms 
  in 
  a 
  molecule 
  are 
  independent 
  

   of 
  the 
  phase 
  angle, 
  <y, 
  which 
  the 
  electrons 
  make 
  with 
  each 
  

   other. 
  This 
  is 
  merely 
  because 
  we 
  are 
  satisfied 
  with 
  this 
  

   degree 
  of 
  approximation. 
  If 
  the 
  terms 
  in 
  v~ 
  8 
  are 
  included, 
  

   some 
  of 
  these 
  terms 
  would 
  depend 
  upon 
  the 
  phase 
  angle. 
  

   The 
  forces 
  resolved 
  along 
  the 
  tangent 
  to 
  the 
  orbit 
  at 
  the 
  

   position 
  of 
  the 
  electron 
  are 
  given 
  by 
  (57) 
  to 
  (60). 
  By 
  these 
  

   equations 
  it 
  has 
  been 
  shown 
  that 
  in 
  the 
  case 
  of 
  two 
  atoms 
  

   with 
  three 
  electrons 
  each 
  the 
  phase 
  relation 
  of 
  the 
  electrons 
  

   for 
  equilibrium, 
  if 
  the 
  one 
  atom 
  were 
  on 
  the 
  axis 
  of 
  the 
  

  

  * 
  Langmuir, 
  Am. 
  Chem. 
  Soc. 
  Jour, 
  xxxiv. 
  pp. 
  860-877, 
  July 
  1912. 
  

  

  