﻿76 
  Dr. 
  A. 
  C. 
  Crehore 
  on 
  the 
  Formation 
  of 
  the 
  

  

  values 
  of 
  the 
  first 
  and 
  second 
  components 
  of 
  the 
  force 
  respec- 
  

   tively. 
  The 
  third 
  and 
  fourth 
  components 
  cancel 
  each 
  other 
  

   producing 
  a 
  resultant 
  of 
  zero. 
  If 
  we 
  do 
  not 
  care 
  to 
  con- 
  

   sider 
  terms 
  higher 
  than 
  the 
  inverse 
  second 
  power 
  of 
  r 
  equa- 
  

   tion 
  (18) 
  reduces 
  to 
  

  

  F.= 
  -jgr 
  ....... 
  (63) 
  

  

  which 
  is 
  simply 
  the 
  electrostatic 
  repulsion 
  between 
  the 
  

   electrons. 
  In 
  an 
  atom 
  this 
  is 
  exactly 
  balanced 
  or 
  neutralized 
  

   by 
  the 
  attraction 
  between 
  the 
  positive 
  spheres 
  and 
  the 
  

   electrons, 
  together 
  with 
  the 
  repulsion 
  between 
  the 
  positive 
  

   spheres 
  themselves, 
  thus 
  making 
  the 
  force 
  zero 
  as 
  far 
  as 
  the 
  

   first 
  component 
  is 
  concerned. 
  

  

  It 
  is 
  evident 
  that 
  the 
  only 
  terms 
  that 
  can 
  contribute 
  any- 
  

   thing 
  with 
  terms 
  in 
  1/r 
  2 
  in 
  (23), 
  the 
  second 
  component, 
  are 
  

  

  F 
  2 
  =— 
  ^ 
  [CO 
  cosa 
  + 
  SS'jr. 
  . 
  . 
  (61) 
  

  

  If 
  this 
  is 
  averaged 
  over 
  a 
  long 
  time 
  on 
  the 
  assumption 
  

   that 
  the 
  angular 
  velocities 
  of 
  the 
  two 
  electrons 
  are 
  incom- 
  

   mensurable, 
  the 
  result 
  is 
  zero 
  for 
  the 
  r~ 
  2 
  terms. 
  The 
  first 
  

   terms 
  that 
  do 
  not 
  vanish 
  with 
  this 
  hypothesis 
  are 
  those 
  in 
  r~ 
  4 
  . 
  

   But 
  if 
  the 
  assumption 
  is 
  made 
  that 
  the 
  angular 
  velocities 
  are 
  

   equal, 
  and 
  the 
  electrons 
  in 
  synchronism, 
  we 
  obtain 
  certain 
  

   terms 
  in 
  r~ 
  2 
  as 
  follows 
  — 
  

  

  ^tt 
  ixee'aa'at 
  2 
  ,., 
  . 
  . 
  , 
  nK 
  \ 
  

  

  F 
  2 
  = 
  £ 
  3 
  — 
  r(l 
  + 
  cos 
  a) 
  cos 
  7. 
  . 
  . 
  . 
  (65) 
  

  

  This 
  result 
  is 
  directly 
  obtained 
  from 
  the 
  expression 
  for 
  

   the 
  average 
  force 
  (25), 
  for 
  when 
  r 
  is 
  large 
  the 
  terms 
  con- 
  

   taining 
  A, 
  B, 
  C, 
  D, 
  and 
  E 
  are 
  negligible 
  compared 
  with 
  

   the 
  remaining 
  terms, 
  and 
  we 
  have 
  (65) 
  directly 
  from 
  this 
  

   equation. 
  The 
  total 
  attraction 
  between 
  the 
  two 
  atoms 
  of 
  

   which 
  these 
  two 
  electrons 
  are 
  constituents 
  is, 
  therefore, 
  found 
  

   by 
  taking 
  the 
  sum 
  of 
  the 
  forces 
  given 
  by 
  (65) 
  for 
  each 
  pair 
  

   of 
  electrons 
  in 
  the 
  two 
  atoms, 
  one 
  electron 
  from 
  each. 
  

  

  To 
  find 
  the 
  Radius 
  of 
  the 
  Outside 
  Ring 
  of 
  Electrons 
  

   in 
  an 
  Atom. 
  

  

  Consider 
  a 
  single 
  ring 
  of 
  n 
  x 
  electrons 
  distributed 
  at 
  equal 
  

   intervals 
  around 
  the 
  circumference 
  within 
  the 
  sphere 
  of 
  

   positive 
  electrification 
  of 
  the 
  atom, 
  revolving 
  with 
  a 
  constant 
  

   angular 
  velocity. 
  An 
  equation 
  of 
  equilibrium 
  may 
  be 
  derived 
  

   from 
  the 
  fundamental 
  equations 
  (1), 
  (2), 
  (3), 
  and 
  (4) 
  by 
  

  

  